Polymath Wiki - User contributions [en]

Main Page

2016-01-29T14:42:52Z

Gowers: /* Existing polymath projects */

{{RightTOC}}
This is the wiki for ''polymath'' projects - massively collaborative online mathematical projects. The idea of such projects originated in Tim Gowers' blog post [http://gowers.wordpress.com/2009/01/27/is-massively-collaborative-mathematics-possible/ Is massively collaborative mathematics possible?]

Many polymath projects will be proposed, planned, and run at [http://polymathprojects.org/ This Blog].

A Polymath [[logo]] is being trialled. If you have more suggestions, please add them to the [[logo]] page, or add to the discussion at [[Talk:logo]].

The wiki is currently locked down due to a major influx of spam (July 29, 2013). Please email mn@michaelnielsen.org if you'd like an account set up, and I'll do my best to reply quickly.

== Existing polymath projects ==

* [[Polymath1]]: New proofs and bounds for the density Hales-Jewett theorem. Initiated Feb 1, 2009; research results have now been published.
* [[Definable Banach Spaces|Polymath2]]: Must an “explicitly defined” Banach space contain <math>c_0</math> or <math>l_p</math>? Initiated Feb 17, 2009; attempts to relaunch via wiki, June 9 2010.
* [[imo 2009 q6|Mini-polymath1]]: Solving Problem 6 of the 2009 International Mathematical Olympiad. Initiated July 20, 2009; five proofs obtained so far.
* [[The polynomial Hirsch conjecture|Polymath3]]. The polynomial Hirsch conjecture. Proposed July 17, 2009; launched, September 30, 2010.
* [[finding primes|Polymath4]]: A deterministic way to find primes. Proposed July 27, 2009; launched Aug 9, 2009. Research results have now been published.
* [[The Erdős discrepancy problem|Polymath5]]: The Erdős discrepancy problem. Proposed Jan 10, 2010; launched Jan 19, 2010. Activity ceased by the end of 2012, but results from the project were used to solve the problem in 2015.
* [[imo 2010|Mini-polymath2]]: Solving Problem 5 the 2010 International Mathematical Olympiad. Proposed Jun 12, 2010; launched and solved, Jul 8 2010.
* [[Improving the bounds for Roth's theorem|Polymath6]]: Improving the bounds for Roth's theorem. Proposed Feb 5, 2011.
* [[imo 2011|Mini-polymath3]]: Solving a problem from the 2011 International Mathematical Olympiad. Proposed Jun 9, 2011; launched and solved, Jul 19, 2011.
* [[imo 2012|Mini-polymath4]]: Solving a problem from the 2012 International Mathematical Olympiad. Proposed, Jun 3, 2012; launched, July 12 2012.
* [[The hot spots conjecture|Polymath7]]: Establishing the Hot Spots conjecture for acute-angled triangles. Proposed, May 31st, 2012; launched, Jun 8, 2012.
* [[Bounded gaps between primes|Polymath8]]: Improving the bounds for small gaps between primes. Proposed, June 4, 2013; launched, June 4, 2013. Research results have now been published.
* [[Discretized Borel Determinacy and P=NP|Polymath9]]: exploring Borel determinacy-based methods for giving complexity bounds. Proposed, Oct 24, 2013; launched, Nov 3, 2013.
* [[The Erdos-Rado sunflower lemma|Polymath10]]: improving the bounds for the Erdos-Rado sunflower lemma. Launched, Nov 2, 2015.
* [[Frankl's union-closed conjecture|Polymath11]]: proving Frankl's union-closed conjecture. Proposed Jan 21, 2016; launched Jan 29, 2016.

== Polymath-like projects ==

* [http://portonmath.tiddlyspace.com/#%5B%5BTheory%20of%20singularities%20using%20generalized%20limits%5D%5D "Theory of singularities" research attempt] in the form of a TiddleSpace wiki
* [http://portonmath.tiddlyspace.com/#%5B%5BCartesian%20closedness%5D%5D Attempt to prove that certain categories are cartesian closed] in the form of a TiddleSpace wiki
* [http://theses.portonvictor.org/node/2 Mathematics research projects]
* Scott Aaronson's "philomath project": "[http://scottaaronson.com/blog/?p=453 Sensitivity vs. Block sensitivity]" (see also [http://mathoverflow.net/questions/31482/the-sensitivity-of-2-colorings-of-the-d-dimensional-integer-lattice this Math Overflow question]). Launched Jul 13, 2010.
* A wiki page clearinghouse for the [[Deolalikar P vs NP paper]]. Launched Aug 10, 2010.
* <del>[http://researchtrends.wikia.com/wiki/Main_Page Math Research Trends Wiki] "research in the middle"</del> This project is recommended to be discontinued in favor of [http://portonmath.wordpress.com/2013/03/23/collaborative-research/ collaborative research at PlanetMath].
* The page for the [[ABC conjecture]] contains links and information about Mochizuki's claimed proof of this conjecture.

== Proposed polymath projects ==

* [http://gilkalai.wordpress.com/2009/03/25/an-open-discussion-and-polls-around-roths-theorem/ The cap set problem]. Proposed March 25, 2009 (see also these [http://gilkalai.wordpress.com/2009/05/11/around-the-cap-set-problem-b/ two] [http://gilkalai.wordpress.com/2009/05/18/the-cap-set-problem-and-frankl-rodl-theorem-c/ followup] posts).
* [[Boshernitzan’s problem]]. Proposed July 27, 2009.
* [http://gowers.wordpress.com/2009/09/16/possible-future-polymath-projects/ Possible future polymath projects]. Discussion opened September 16, 2009.
* [http://rjlipton.wordpress.com/2011/05/12/a-possible-polymath-project/ A possible polymath project:] Proposal by Richard Lipton to attack a conjecture due to Erdos, about a class of Diophantine equations.

A (partial) list of proposed projects can be found [http://polymathprojects.org/category/polymath-proposals/ here].

If you have a tentative proposal for a polymath project, you can either make a post on it on your own blog, or place it [[other proposed projects|here]].

== Discussions about polymath ==

* [http://gowers.wordpress.com/2009/01/27/is-massively-collaborative-mathematics-possible/ Is massively collaborative mathematics possible?] Tim Gowers, January 27, 2009.
* [http://lucatrevisan.wordpress.com/2009/02/01/a-peoples-history-of-mathematics/ A people's history of mathematics] Luca Trevisan, February 1, 2009.
* [http://michaelnielsen.org/blog/?p=553 The polymath project] Michael Nielsen, February 3, 2009.
* [http://www.neverendingbooks.org/index.php/yet-another-math20-proposal.html Yet another math 2.0 proposal] Lieven le Bruyn, February 11, 2009.
* [http://gowers.wordpress.com/2009/03/10/polymath1-and-open-collaborative-mathematics/ Polymath1 and open collaborative mathematics] Tim Gowers, March 10, 2009.
* [http://maxwelldemon.com/2009/03/14/polymath/ Polymath] Edmund Harriss, March 14, 2009.
* [http://science.slashdot.org/article.pl?sid=09/03/18/194228 Massive open collaboration in mathematics declared a success] Slashdot, March 18, 2009.
* [http://michaelnielsen.org/blog/?p=581 How changing the technology of collaboration can change the nature of collaboration] Michael Nielsen, March 18, 2009.
* [http://michaelnielsen.org/blog/?p=584 The polymath project: scope of participation] Michael Nielsen, March 20, 2009.
* [http://gowers.wordpress.com/2009/03/24/can-polymath-be-scaled-up/ Can polymath be scaled up?] Tim Gowers, March 24, 2009.
* [http://whatisresearch.wordpress.com/2009/03/24/concluding-notes-on-the-polymath-project-and-a-challenge/ Concluding notes on the polymath project - and a challenge] Vilpulniak, March 24, 2009.
* [http://michaelnielsen.org/blog/on-scaling-up-the-polymath-project/ On scaling up the polymath project] Michael Nielsen, March 25, 2009.
* [http://numberwarrior.wordpress.com/2009/03/25/a-gentle-introduction-to-the-polymath-project/ A gentle introduction to the polymath project] Jason Dyer, March 25, 2009.
* [http://blogs.telegraph.co.uk/technology/iandouglas/9656357/tim_gowers_and_the_polymaths/ Tim Gowers and the polymaths] Ian Douglas (the Telegraph), April 29, 2009
* [http://terrytao.wordpress.com/2009/07/22/imo-2009-q6-mini-polymath-project-impressions-reflections-analysis/ IMO 2009 Q6 as mini-polymath project: impressions, reflections, analysis] Terence Tao, July 22, 2009.
* [http://polymathprojects.org/2009/07/27/selecting-the-next-polymath-project/ Selecting the next polymath project] Terence Tao, July 27, 2009.
* [http://blog.jonudell.net/2009/07/31/polymath-equals-user-innovatio/ Polymath equals user innovation] Jon Udell, July 31, 2009.
* [http://scienceblogs.com/christinaslisrant/2009/08/an_overview_of_the_polymath_pr.php An overview of the polymath project] Christina Pikas, August 1, 2009
* [http://whatisresearch.wordpress.com/2009/08/09/collaborative-mathematics-etc/ Collaborative mathematics etc.] Vipulniak, August 9, 2009
* [http://www.nature.com/nature/journal/v461/n7266/full/461879a.html Massively collaborative mathematics] Tim Gowers, Michael Nielsen, Nature, October 15, 2009
* [http://portonmath.wordpress.com/2009/10/25/collaborative-research-of-filters/ Collaborative math research – a real example] Victor Porton, October 24, 2009
* [http://whatisresearch.wordpress.com/2009/10/26/polymath-again/ Polymath again] Vipulniak, October 26, 2009
* [http://www.kennislink.nl/publicaties/wiskunde-met-zijn-allen Wiskunde met zijn allen] (Dutch), Alex van den Brandhof, Kennislink, November 12, 2009
* [http://www.sciencenews.org/view/generic/id/50532/title/Mathematics_by_collaboration Mathematics by collaboration], Julie Rehmeyer, ScienceNews, December 8, 2009
* [http://www.nytimes.com/projects/magazine/ideas/2009/#m Massively Collaborative Mathematics], Jordan Ellenberg, The Ninth Annual Year in Ideas, New York Times, 2009.
* [http://www.hypios.com/thinking/2010/01/13/massively-collaborative-mathematics-lessons-from-polymath1/ Massively Collaborative Mathematics: lessons from polymath1], Hypios, Jan 13 2010
* [http://ths1104.wordpress.com/2010/02/13/open-reflexions-sur-fond-de-polymaths/ Open réflexions sur fond de Polymaths] (French), ths1104, Feb 13 2010
* [http://www.javiertordable.com/blog/2010/02/25/collaborative-mathematics-future-of-science Collaborative Mathematics and The Future of Science] Javier Tordable, February 26 2010
* [http://www.scientificamerican.com/article.cfm?id=problem-solved-tic-tac-toe-blog Problem Solved, LOL: A Complex Tic-Tac-Toe Puzzle Falls Thanks to Blog Comments] Davide Castelvecchi, Scientific American, March 17 2010
* [http://www.thebigquestions.com/2010/04/08/blogging-tic-tac-toe-and-the-future-of-math/ Blogging, Tic Tac Toe, and the Future of Math] Steve Landsburg, The Big Questions, April 4 2010
* [http://www.siam.org/news/news.php?issue=0043.03 Massively Collaborative Mathematics] Julie Rehmeyer, SIAM News, Volume 43(3), April 2010 (to appear)
* [http://mbarany.com/publications.html#WikiSymPolymath `But this is blog maths and we're free to make up conventions as we go along': Polymath1 and the Modalities of `Massively Collaborative Mathematics.'] Michael Barany, Proceedings of the 6th International Symposium on Wikis and Open Collaboration, Gdansk, Poland, 2010.
* [http://www.cs.cmu.edu/~jcransh/papers/cranshaw_kittur.pdf J. Cranshaw and A. Kittur. The Polymath Project: Lessons from a successful online collaboration in mathematics]. In Proceedings of the Conference on Human Factors in Computing Systems, Vancouver, BC, Canada, May 2011.
* [http://www.newscientist.com/article/mg21028113.900-how-to-build-the-global-mathematics-brain.html How to build the global mathematics brain], Jacob Aron, New Scientist, 4 May 2011.
* [http://www.newscientist.com/article/mg21028112.900-mathematics-becomes-more-sociable.html Mathematics becomes more sociable], New Scientist, 5 May 2011.
* [http://polymathprojects.files.wordpress.com/2011/03/polymathias.jpg Mathematical Advances: Lone or Massively Collaborative Endeavors?] from IAS Institute Letter for fall 2010 based on a discussion organized by IAS fall 2010.
* [http://today.uconn.edu/blog/2010/10/will-crowdsourcing-revolutionize-scholarship Will ‘Crowdsourcing’ Revolutionize Scholarship?] An article in UConn Today by Jeremy Teitelbaum, Fall 2010.
* [http://online.wsj.com/article/SB10001424052970204644504576653573191370088.html The New Einsteins Will Be Scientists Who Share] The Wall street journal, October 2011.
* [http://www.nature.com/news/parallel-lines-1.14759?WT.ec_id=NATURE-20140227 Parallel lines], editorial, Nature 506, 407–408 (27 February 2014).
Additional links are very welcome.

== Other links ==

* [http://polymathprojects.org/ The polymath blog]
* [http://polymathprojects.org/general-polymath-rules/ General polymath rules]

== Note on anonymous editing ==

To help combat spam, anonymous editing has been disabled, and a captcha system added to hinder automated account creation. If this is causing problems, please email mn@michaelnielsen.org.

== Note on image uploads ==

Image uploads have been disabled, as they were causing problems with spam. If you'd like to upload an image, please email mn@michaelnielsen.org

Frankl's union-closed conjecture

2016-01-27T10:01:32Z

Gowers: Created page with "<h1>Polymath11 -- Frankl's union-closed conjecture</h1> A family <math>\mathcal{A}</math> of sets is called union closed if <math>A\cup B\in\mathcal{A}</math> whenev..."

<h1>Polymath11 -- Frankl's union-closed conjecture</h1>

A family <math>\mathcal{A}</math> of sets is called union closed if <math>A\cup B\in\mathcal{A}</math> whenever <math>A\in\mathcal{A}</math> and <math>B\in\mathcal{A}</math>. Frankl's conjecture is a disarmingly simple one: if <math>\mathcal{A}</math> is a union-closed family of n sets, then must there be an element that belongs to at least n/2 of the sets? The problem has been open for decades, despite the attention of several people.

Main Page

2016-01-27T09:37:42Z

Gowers: /* Existing polymath projects */ added Polymath11

{{RightTOC}}
This is the wiki for ''polymath'' projects - massively collaborative online mathematical projects. The idea of such projects originated in Tim Gowers' blog post [http://gowers.wordpress.com/2009/01/27/is-massively-collaborative-mathematics-possible/ Is massively collaborative mathematics possible?]

Many polymath projects will be proposed, planned, and run at [http://polymathprojects.org/ This Blog].

A Polymath [[logo]] is being trialled. If you have more suggestions, please add them to the [[logo]] page, or add to the discussion at [[Talk:logo]].

The wiki is currently locked down due to a major influx of spam (July 29, 2013). Please email mn@michaelnielsen.org if you'd like an account set up, and I'll do my best to reply quickly.

== Existing polymath projects ==

* [[Polymath1]]: New proofs and bounds for the density Hales-Jewett theorem. Initiated Feb 1, 2009; research results have now been published.
* [[Definable Banach Spaces|Polymath2]]: Must an “explicitly defined” Banach space contain <math>c_0</math> or <math>l_p</math>? Initiated Feb 17, 2009; attempts to relaunch via wiki, June 9 2010.
* [[imo 2009 q6|Mini-polymath1]]: Solving Problem 6 of the 2009 International Mathematical Olympiad. Initiated July 20, 2009; five proofs obtained so far.
* [[The polynomial Hirsch conjecture|Polymath3]]. The polynomial Hirsch conjecture. Proposed July 17, 2009; launched, September 30, 2010.
* [[finding primes|Polymath4]]: A deterministic way to find primes. Proposed July 27, 2009; launched Aug 9, 2009. Research results have now been published.
* [[The Erdős discrepancy problem|Polymath5]]: The Erdős discrepancy problem. Proposed Jan 10, 2010; launched Jan 19, 2010. Activity ceased by the end of 2012, but results from the project were used to solve the problem in 2015.
* [[imo 2010|Mini-polymath2]]: Solving Problem 5 the 2010 International Mathematical Olympiad. Proposed Jun 12, 2010; launched and solved, Jul 8 2010.
* [[Improving the bounds for Roth's theorem|Polymath6]]: Improving the bounds for Roth's theorem. Proposed Feb 5, 2011.
* [[imo 2011|Mini-polymath3]]: Solving a problem from the 2011 International Mathematical Olympiad. Proposed Jun 9, 2011; launched and solved, Jul 19, 2011.
* [[imo 2012|Mini-polymath4]]: Solving a problem from the 2012 International Mathematical Olympiad. Proposed, Jun 3, 2012; launched, July 12 2012.
* [[The hot spots conjecture|Polymath7]]: Establishing the Hot Spots conjecture for acute-angled triangles. Proposed, May 31st, 2012; launched, Jun 8, 2012.
* [[Bounded gaps between primes|Polymath8]]: Improving the bounds for small gaps between primes. Proposed, June 4, 2013; launched, June 4, 2013. Research results have now been published.
* [[Discretized Borel Determinacy and P=NP|Polymath9]]: exploring Borel determinacy-based methods for giving complexity bounds. Proposed, Oct 24, 2013; launched, Nov 3, 2013.
* [[The Erdos-Rado sunflower lemma|Polymath10]]: improving the bounds for the Erdos-Rado sunflower lemma. Launched, Nov 2, 2015.
* [[Frankl's union-closed conjecture|Polymath11]]: proving Frankl's union-closed conjecture. Proposed Jan 21, 2016.

== Polymath-like projects ==

* [http://portonmath.tiddlyspace.com/#%5B%5BTheory%20of%20singularities%20using%20generalized%20limits%5D%5D "Theory of singularities" research attempt] in the form of a TiddleSpace wiki
* [http://portonmath.tiddlyspace.com/#%5B%5BCartesian%20closedness%5D%5D Attempt to prove that certain categories are cartesian closed] in the form of a TiddleSpace wiki
* [http://theses.portonvictor.org/node/2 Mathematics research projects]
* Scott Aaronson's "philomath project": "[http://scottaaronson.com/blog/?p=453 Sensitivity vs. Block sensitivity]" (see also [http://mathoverflow.net/questions/31482/the-sensitivity-of-2-colorings-of-the-d-dimensional-integer-lattice this Math Overflow question]). Launched Jul 13, 2010.
* A wiki page clearinghouse for the [[Deolalikar P vs NP paper]]. Launched Aug 10, 2010.
* <del>[http://researchtrends.wikia.com/wiki/Main_Page Math Research Trends Wiki] "research in the middle"</del> This project is recommended to be discontinued in favor of [http://portonmath.wordpress.com/2013/03/23/collaborative-research/ collaborative research at PlanetMath].
* The page for the [[ABC conjecture]] contains links and information about Mochizuki's claimed proof of this conjecture.

== Proposed polymath projects ==

* [http://gilkalai.wordpress.com/2009/03/25/an-open-discussion-and-polls-around-roths-theorem/ The cap set problem]. Proposed March 25, 2009 (see also these [http://gilkalai.wordpress.com/2009/05/11/around-the-cap-set-problem-b/ two] [http://gilkalai.wordpress.com/2009/05/18/the-cap-set-problem-and-frankl-rodl-theorem-c/ followup] posts).
* [[Boshernitzan’s problem]]. Proposed July 27, 2009.
* [http://gowers.wordpress.com/2009/09/16/possible-future-polymath-projects/ Possible future polymath projects]. Discussion opened September 16, 2009.
* [http://rjlipton.wordpress.com/2011/05/12/a-possible-polymath-project/ A possible polymath project:] Proposal by Richard Lipton to attack a conjecture due to Erdos, about a class of Diophantine equations.

A (partial) list of proposed projects can be found [http://polymathprojects.org/category/polymath-proposals/ here].

If you have a tentative proposal for a polymath project, you can either make a post on it on your own blog, or place it [[other proposed projects|here]].

== Discussions about polymath ==

* [http://gowers.wordpress.com/2009/01/27/is-massively-collaborative-mathematics-possible/ Is massively collaborative mathematics possible?] Tim Gowers, January 27, 2009.
* [http://lucatrevisan.wordpress.com/2009/02/01/a-peoples-history-of-mathematics/ A people's history of mathematics] Luca Trevisan, February 1, 2009.
* [http://michaelnielsen.org/blog/?p=553 The polymath project] Michael Nielsen, February 3, 2009.
* [http://www.neverendingbooks.org/index.php/yet-another-math20-proposal.html Yet another math 2.0 proposal] Lieven le Bruyn, February 11, 2009.
* [http://gowers.wordpress.com/2009/03/10/polymath1-and-open-collaborative-mathematics/ Polymath1 and open collaborative mathematics] Tim Gowers, March 10, 2009.
* [http://maxwelldemon.com/2009/03/14/polymath/ Polymath] Edmund Harriss, March 14, 2009.
* [http://science.slashdot.org/article.pl?sid=09/03/18/194228 Massive open collaboration in mathematics declared a success] Slashdot, March 18, 2009.
* [http://michaelnielsen.org/blog/?p=581 How changing the technology of collaboration can change the nature of collaboration] Michael Nielsen, March 18, 2009.
* [http://michaelnielsen.org/blog/?p=584 The polymath project: scope of participation] Michael Nielsen, March 20, 2009.
* [http://gowers.wordpress.com/2009/03/24/can-polymath-be-scaled-up/ Can polymath be scaled up?] Tim Gowers, March 24, 2009.
* [http://whatisresearch.wordpress.com/2009/03/24/concluding-notes-on-the-polymath-project-and-a-challenge/ Concluding notes on the polymath project - and a challenge] Vilpulniak, March 24, 2009.
* [http://michaelnielsen.org/blog/on-scaling-up-the-polymath-project/ On scaling up the polymath project] Michael Nielsen, March 25, 2009.
* [http://numberwarrior.wordpress.com/2009/03/25/a-gentle-introduction-to-the-polymath-project/ A gentle introduction to the polymath project] Jason Dyer, March 25, 2009.
* [http://blogs.telegraph.co.uk/technology/iandouglas/9656357/tim_gowers_and_the_polymaths/ Tim Gowers and the polymaths] Ian Douglas (the Telegraph), April 29, 2009
* [http://terrytao.wordpress.com/2009/07/22/imo-2009-q6-mini-polymath-project-impressions-reflections-analysis/ IMO 2009 Q6 as mini-polymath project: impressions, reflections, analysis] Terence Tao, July 22, 2009.
* [http://polymathprojects.org/2009/07/27/selecting-the-next-polymath-project/ Selecting the next polymath project] Terence Tao, July 27, 2009.
* [http://blog.jonudell.net/2009/07/31/polymath-equals-user-innovatio/ Polymath equals user innovation] Jon Udell, July 31, 2009.
* [http://scienceblogs.com/christinaslisrant/2009/08/an_overview_of_the_polymath_pr.php An overview of the polymath project] Christina Pikas, August 1, 2009
* [http://whatisresearch.wordpress.com/2009/08/09/collaborative-mathematics-etc/ Collaborative mathematics etc.] Vipulniak, August 9, 2009
* [http://www.nature.com/nature/journal/v461/n7266/full/461879a.html Massively collaborative mathematics] Tim Gowers, Michael Nielsen, Nature, October 15, 2009
* [http://portonmath.wordpress.com/2009/10/25/collaborative-research-of-filters/ Collaborative math research – a real example] Victor Porton, October 24, 2009
* [http://whatisresearch.wordpress.com/2009/10/26/polymath-again/ Polymath again] Vipulniak, October 26, 2009
* [http://www.kennislink.nl/publicaties/wiskunde-met-zijn-allen Wiskunde met zijn allen] (Dutch), Alex van den Brandhof, Kennislink, November 12, 2009
* [http://www.sciencenews.org/view/generic/id/50532/title/Mathematics_by_collaboration Mathematics by collaboration], Julie Rehmeyer, ScienceNews, December 8, 2009
* [http://www.nytimes.com/projects/magazine/ideas/2009/#m Massively Collaborative Mathematics], Jordan Ellenberg, The Ninth Annual Year in Ideas, New York Times, 2009.
* [http://www.hypios.com/thinking/2010/01/13/massively-collaborative-mathematics-lessons-from-polymath1/ Massively Collaborative Mathematics: lessons from polymath1], Hypios, Jan 13 2010
* [http://ths1104.wordpress.com/2010/02/13/open-reflexions-sur-fond-de-polymaths/ Open réflexions sur fond de Polymaths] (French), ths1104, Feb 13 2010
* [http://www.javiertordable.com/blog/2010/02/25/collaborative-mathematics-future-of-science Collaborative Mathematics and The Future of Science] Javier Tordable, February 26 2010
* [http://www.scientificamerican.com/article.cfm?id=problem-solved-tic-tac-toe-blog Problem Solved, LOL: A Complex Tic-Tac-Toe Puzzle Falls Thanks to Blog Comments] Davide Castelvecchi, Scientific American, March 17 2010
* [http://www.thebigquestions.com/2010/04/08/blogging-tic-tac-toe-and-the-future-of-math/ Blogging, Tic Tac Toe, and the Future of Math] Steve Landsburg, The Big Questions, April 4 2010
* [http://www.siam.org/news/news.php?issue=0043.03 Massively Collaborative Mathematics] Julie Rehmeyer, SIAM News, Volume 43(3), April 2010 (to appear)
* [http://mbarany.com/publications.html#WikiSymPolymath `But this is blog maths and we're free to make up conventions as we go along': Polymath1 and the Modalities of `Massively Collaborative Mathematics.'] Michael Barany, Proceedings of the 6th International Symposium on Wikis and Open Collaboration, Gdansk, Poland, 2010.
* [http://www.cs.cmu.edu/~jcransh/papers/cranshaw_kittur.pdf J. Cranshaw and A. Kittur. The Polymath Project: Lessons from a successful online collaboration in mathematics]. In Proceedings of the Conference on Human Factors in Computing Systems, Vancouver, BC, Canada, May 2011.
* [http://www.newscientist.com/article/mg21028113.900-how-to-build-the-global-mathematics-brain.html How to build the global mathematics brain], Jacob Aron, New Scientist, 4 May 2011.
* [http://www.newscientist.com/article/mg21028112.900-mathematics-becomes-more-sociable.html Mathematics becomes more sociable], New Scientist, 5 May 2011.
* [http://polymathprojects.files.wordpress.com/2011/03/polymathias.jpg Mathematical Advances: Lone or Massively Collaborative Endeavors?] from IAS Institute Letter for fall 2010 based on a discussion organized by IAS fall 2010.
* [http://today.uconn.edu/blog/2010/10/will-crowdsourcing-revolutionize-scholarship Will ‘Crowdsourcing’ Revolutionize Scholarship?] An article in UConn Today by Jeremy Teitelbaum, Fall 2010.
* [http://online.wsj.com/article/SB10001424052970204644504576653573191370088.html The New Einsteins Will Be Scientists Who Share] The Wall street journal, October 2011.
* [http://www.nature.com/news/parallel-lines-1.14759?WT.ec_id=NATURE-20140227 Parallel lines], editorial, Nature 506, 407–408 (27 February 2014).
Additional links are very welcome.

== Other links ==

* [http://polymathprojects.org/ The polymath blog]
* [http://polymathprojects.org/general-polymath-rules/ General polymath rules]

== Note on anonymous editing ==

To help combat spam, anonymous editing has been disabled, and a captcha system added to hinder automated account creation. If this is causing problems, please email mn@michaelnielsen.org.

== Note on image uploads ==

Image uploads have been disabled, as they were causing problems with spam. If you'd like to upload an image, please email mn@michaelnielsen.org

The Erdos-Rado sunflower lemma

2015-11-06T15:52:14Z

Gowers: /* The problem */

== The problem ==

A sunflower (a.k.a. Delta-system) of size <math>r</math> is a family of sets <math>A_1, A_2, \dots, A_r</math> such that every element that belongs to more than one of the sets belongs to all of them. A basic and simple result of Erdos and Rado asserts that

:Erdos-Rado Delta-system theorem: There is a function <math>f(k,r)</math> so that every family <math>\cal F</math> of <math>k</math>-sets with more than <math>f(k,r)</math> members contains a sunflower of size <math>r</math>.

(We denote by <math>f(k,r)</math> the smallest integer that suffices for the assertion of the theorem to be true.) The simple proof giving <math>f(k,r)\le k! (r-1)^k</math> can be found [https://gilkalai.wordpress.com/2008/09/28/extremal-combinatorics-iii-some-basic-theorems/ here].

The best known general upper bound on <math>f(k,r)</math> (in the regime where <math>r</math> is bounded and <math>k</math> is large) is

:<math>\displaystyle f(k,r) \leq D(r,\alpha) k! \left( \frac{(\log\log\log k)^2}{\alpha \log\log k} \right)^k</math>

for any <math>\alpha < 1</math>, and some <math>D(r,\alpha)</math> depending on <math>r,\alpha</math>, proven by Kostkocha from 1996. The objective of this project is to improve this bound, ideally to obtain the Erdos-Rado conjecture

:<math>\displaystyle f(k,r) \leq C^k </math>

for some <math>C=C(r)</math> depending on <math>r</math> only. This is known for <math>r=1,2</math> but remains open for larger r.

== Threads ==

* [https://gilkalai.wordpress.com/2015/11/03/polymath10-the-erdos-rado-delta-system-conjecture Polymath10: The Erdos Rado Delta System Conjecture], Gil Kalai, Nov 2, 2015. Active

== External links ==

* [https://en.wikipedia.org/wiki/Sunflower_(mathematics) Sunflower (mathematics)] (Wikipedia article)
* [http://mathoverflow.net/questions/163689/what-is-the-best-lower-bound-for-3-sunflowers What is the best lower bound for 3-sunflowers?] (Mathoverflow)

== Bibliography ==

Edits to improve the bibliography (by adding more links, Mathscinet numbers, bibliographic info, etc.) are welcome!

* Intersection theorems for systems of sets, H. L. Abbott, D. Hanson, and N. Sauer, J. Comb. Th. Ser. A 12 (1972), 381–389
* [https://www.math.uni-bielefeld.de/ahlswede/homepage/public/114.pdf The Complete Nontrivial-Intersection Theorem for Systems of Finite Sets], R. Ahlswede, L. Khachatrian, Journal of Combinatorial Theory, Series A 76, 121-138 (1996).
* [http://renyi.hu/~p_erdos/1960-04.pdf Intersection theorems for systems of sets], P. Erdős, R. Rado, Journal of the London Mathematical Society, Second Series 35 (1960), 85–90.
* [http://arxiv.org/abs/1205.6847 On the Maximum Number of Edges in a Hypergraph with Given Matching Number], P. Frankl
* An intersection theorem for systems of sets, A. V. Kostochka, Random Structures and Algorithms, 9(1996), 213-221.
* [http://www.math.uiuc.edu/~kostochk/docs/2000/survey3.pdf Extremal problems on <math>\Delta</math>-systems], A. V. Kostochka
* [http://arxiv.org/abs/1202.4196 On Erdos' extremal problem on matchings in hypergraphs], T. Luczak, K. Mieczkowska
* Intersection theorems for systems of sets, J. H. Spencer, Canad. Math. Bull. 20 (1977), 249-254.

Journal publishing reform

2012-03-08T10:48:36Z

Gowers: /* Other blog posts, letters, and opinion pieces */

Journal publishing reform

2012-03-07T23:29:37Z

Gowers: /* Other blog posts, letters, and opinion pieces */

Journal publishing reform

2012-02-28T15:10:10Z

Gowers: /* Other blog posts, letters, and opinion pieces */

[[Image:elsevier_poster.jpg|right|300px|Credit: Michael Eisen]]

This is a collection of links to information, opinion, activism, and other issues concerning the practices of research journal publishers (particularly in the mathematical sciences). Further contributions are welcome.

== The cost of knowledge ==

[http://thecostofknowledge.com/ The cost of knowledge] is a web page at which one may register a protest against the practices of Elsevier by pledging not to submit a paper to an Elsevier journal, not to referee for an Elsevier journal, not to join an editorial board of an Elsevier journal, or some combination of the three. This site was inspired by the following blog post:

* [http://gowers.wordpress.com/2012/01/21/elsevier-my-part-in-its-downfall/ Elsevier - my part in its downfall], Timothy Gowers, January 21, 2012.

A more detailed statement of purpose of the boycott, can be [http://gowers.files.wordpress.com/2012/02/elsevierstatementfinal.pdf found here]. It is written and signed by [http://en.wikipedia.org/wiki/Scott_Aaronson Scott Aaronson], [http://en.wikipedia.org/wiki/Douglas_N._Arnold Douglas N. Arnold], [http://en.wikipedia.org/wiki/Artur_Ávila Artur Ávila], [http://en.wikipedia.org/wiki/John_C._Baez John Baez], [http://www-m3.ma.tum.de/Allgemeines/FolkmarBornemann Folkmar Bornemann], [http://en.wikipedia.org/wiki/Danny_Calegari Danny Calegari], [http://research.microsoft.com/en-us/um/people/cohn/ Henry Cohn], [http://en.wikipedia.org/wiki/Ingrid_Daubechies Ingrid Daubechies], [http://en.wikipedia.org/wiki/Jordan_Ellenberg Jordan Ellenberg], [http://www.math.uchicago.edu/~emerton/ Matthew Emerton], [http://wavelets.ens.fr/EQUIPE/marie.htm Marie Farge], [http://en.wikipedia.org/wiki/David_Gabai David Gabai], [http://en.wikipedia.org/wiki/Timothy_Gowers Timothy Gowers], [http://en.wikipedia.org/wiki/Ben_J._Green Ben Green], [http://de.wikipedia.org/wiki/Martin_Grötschel Martin Grötschel], [http://en.wikipedia.org/wiki/Michael_Harris_%28mathematician%29 Michael Harris], [http://en.wikipedia.org/wiki/Fr%C3%A9d%C3%A9ric_H%C3%A9lein Frédéric Hélein], [http://en.wikipedia.org/wiki/Robion_Kirby Rob Kirby], [http://en.wikipedia.org/wiki/Vincent_Lafforgue Vincent Lafforgue], [http://en.wikipedia.org/wiki/Greg_Lawler Gregory F. Lawler], [http://en.wikipedia.org/wiki/Randall_J._LeVeque Randall J. LeVeque], [http://en.wikipedia.org/wiki/Laszlo_lovasz Laszlo Lovasz], [http://www.math.umn.edu/~olver/ Peter J. Olver], [http://www.maths.qmul.ac.uk/~olof/ Olof Sisask], [http://en.wikipedia.org/wiki/Terence_tao Terence Tao], [http://en.wikipedia.org/wiki/Richard_Taylor_%28mathematician%29 Richard Taylor], [http://en.wikipedia.org/wiki/Bernard_Teissier Bernard Teissier], [http://en.wikipedia.org/wiki/Burt_Totaro Burt Totaro], [http://en.wikipedia.org/wiki/Lloyd_Trefethen Lloyd N. Trefethen], [http://kyokan.ms.u-tokyo.ac.jp/~tsuboi/ Takashi Tsuboi], [http://en.wikipedia.org/wiki/Marie-France_Vign%C3%A9ras Marie-France Vigneras], [http://en.wikipedia.org/wiki/Wendelin_Werner Wendelin Werner], [http://math.uchicago.edu/~wilkinso/ Amie Wilkinson], and [http://page.mi.fu-berlin.de/gmziegler/ Gunter M. Ziegler].

See also [http://blog.thecostofknowledge.com/ the blog associated to the cost of knowledge site]. A poster for the protest may be [http://math.ucr.edu/home/baez/elsevier_boycott_poster.pdf found here].

There have since been many reactions to this protest:

=== Reactions from blogs ===

* [http://gowers.wordpress.com/2012/01/23/httpthecostofknowledge-com/ The cost of knowledge], Timothy Gowers, January 23, 2012.
* [http://johncarlosbaez.wordpress.com/2012/01/26/ban-elsevier/ Ban Elsevier], John Baez, January 26, 2012.
* [http://www.scottaaronson.com/blog/?p=891 Boycott Elsevier!], Scott Aaronson, January 26, 2012.
* [http://terrytao.wordpress.com/2012/01/26/the-cost-of-knowledge/ The cost of knowledge], Terence Tao, January 26, 2012.
* [http://dabacon.org/pontiff/?p=5982 Why boycott Elsevier?], Adam Harrow, January 27, 2012.
* [http://cameroncounts.wordpress.com/2012/01/29/publishers-wars/ Publisher's wars], Peter Cameron, January 29, 2012.
* [http://gowers.wordpress.com/2012/01/29/whats-wrong-with-electronic-journals/ What's wrong with electronic journals], Tim Gowers, January 29, 2012.
* [http://sbseminar.wordpress.com/2012/01/30/thinking-about-elsevier-replacements/ Thinking about Elsevier replacements], David Speyer, January 30, 2012.
* [http://blogs.lse.ac.uk/impactofsocialsciences/2012/02/01/stand-down-journal-referee/ Comfort is the death knell of academia: why I’m standing down as a journal referee], Matthew Todd, LSE Impact Blog, February 1, 2012.
* [http://www.scilogs.de/wblogs/blog/detritus/sonstiges/2012-02-01/boykottiert-elsevier-unterst-tzt-open-access Boykottiert Elsevier! Unterstützt Open Access!], Martin Ballaschk, February 1, 2012. (German)
* [http://scholarlykitchen.sspnet.org/2012/02/02/mysteries-of-the-elsevier-boycott Mysteries of the Elsevier Boycott], Rick Anderson, February 2, 2012.
** [http://breakingculture.tumblr.com/post/17112742228/unraveling-boycott-mysteries Unraveling (some of) the mysteries of the Elsevier Boycott], Sean Johnson Andrews, February 6, 2012.
** [http://www.against-the-grain.com/2012/02/multigrain-discussion-another-response-to-the-elsevier-boycott/ Multigrain Discussion: Another Response to the Elsevier Boycott], Chuck Hamaker, February 14, 2012.
* [http://scholarlykitchen.sspnet.org/2012/02/02/the-elsevier-boycott-does-it-make-sense The Elsevier Boycott — Does It Make Sense?], Kent Anderson, February 2, 2012.
* [http://www.michaeleisen.org/blog/?p=890 You are Elsevier: time to overcome our fears and kill subscription journals], Michael Eisen, February 3, 2012.
** [http://scienceblogs.com/denialism/2012/02/eisen_calls_for_elsevier_boyco.php Eisen calls for Elsevier Boycott - but can we all go OA?], Mark Hoofnagle, February 6, 2012.
* [http://stochastictrend.blogspot.com/2012/02/in-defence-of-elsevier.html In Defence of Elsevier], David Stern, February 4, 2012.
* [http://blog.mathunion.org/journals/?no_cache=1&tx_t3blog_pi1%5BblogList%5D%5BshowUid%5D=30&tx_t3blog_pi1%5BblogList%5D%5Byear%5D=2012&tx_t3blog_pi1%5BblogList%5D%5Bmonth%5D=02&tx_t3blog_pi1%5BblogList%5D%5Bday%5D=05&cHash=a2d6424f899302a7ea3b75b9bb591802 More reasons to support the Elsevier boycott], Doug Arnold, IMU blog on mathematical journals, February 5, 2012.
* [http://gowers.wordpress.com/2012/02/08/a-more-formal-statement-about-mathematical-publishing/ A more formal statement about mathematical publishing], Timothy Gowers, February 8, 2012.
* [http://scientopia.org/blogs/drugmonkey/2012/02/08/explaining-resistance-to-the-elsevier-boycott-practicalities/ Explaining resistance to the Elsevier boycott: Practicalities.], DrugMonkey, February 8, 2012.
* [http://neurodojo.blogspot.com/2012/02/whens-scientists-and-published.html When scientists’ and publishers’ motivations align], Zen Faulkes, February 9, 2012.
* [https://etechlib.wordpress.com/2012/02/11/about-the-elsevier-controversy-and-essential-science/ About the Elsevier Controversy and Essential Science], PF Anderson, February 11, 2012.
* [http://www.science3point0.com/palphy/2012/02/12/journal-mega-bundles-thecostofknowledge/ Journal mega-bundles & TheCostOfKnowledge], Ross Mounce, February 12, 2012.
* [http://mathbabe.org/2012/02/13/mathematics-has-an-occupy-moment/ Mathematics has an Occupy moment], Cathy O'Neil, February 13, 2012.
* [http://svpow.wordpress.com/2012/02/13/a-window-of-opportunity-for-elsevier/ A window of opportunity for Elsevier], Mike Taylor, February 13, 2012.
* [http://mhpbooks.com/49648/5000-profs-join-boycott-of-elsevier-publications-in-international-academic-spring/ 5,000 profs join boycott of Elsevier publications in international “academic spring”], Dennis Johnson, February 14, 2012.
* [http://blogs.lse.ac.uk/impactofsocialsciences/2012/02/15/after-elsevier-boycott-green-open-access What comes after the Elsevier boycott? The answer might be found by following the ‘Green’ road to open access], Neil Stewart, LSE Impact Blog, February 15, 2012.
* [http://mhpbooks.com/50115/whats-next-in-the-elsevier-boycott/ What’s next in the Elsevier boycott?], Dennis Johnson, Melville House, February 16, 2012.
* [http://lj.libraryjournal.com/2012/02/opinion/barbara-fister/joining-the-movement-a-call-to-action-peer-to-peer-review/ Joining the Movement: A Call to Action | Peer to Peer Review] Barbara Fister, Library Journal, February 16, 2012
* [http://www.scilogs.de/wblogs/blog/mathematik-im-alltag/allgemein/2012-02-19/boykottiert-elsevier-ich-boykottiere-elsevier Boykottiert Elsevier! Ich boykottiere Elsevier!], Gunter Ziegler, February 19, 2012. (German)
* [http://burttotaro.wordpress.com/2012/02/19/i-am-not-a-radical-but-i-am-boycotting-elsevier/ I am not a radical, but I am boycotting Elsevier], Burt Totaro, February 19, 2012.
* [http://audsandens.blogspot.com/2012/02/taking-control-more-reasons-for.html Taking Control: More Reasons for the Elsevier Boycott], Aaron Barlow, February 20, 2012.
* [http://www.weeklyweinersmith.com/?p=211 The Elsevier Boycott], Zach and Kelly Wienersmith, February 21, 2012. (Podcast)
* [http://scienceblogs.com/webeasties/2012/02/the_future_of_science_pub.php The Future of Science Publishing], Kevin Bonham, February 21, 2012.
* [http://scienceblogs.com/confessions/2012/02/elsevier_boycott_time_for_libr.php Elsevier boycott: Time for librarians to rise up!], John Dupuis, February 21, 2012.
* [http://blogs.lse.ac.uk/impactofsocialsciences/2012/02/22/elsevier-price-boycotters-untruth/ Elsevier have a right to price their journals as they see fit, but they must be honest in their reasoning and not attack boycotters with untruths], Tim Leunig, LSE Impact blog, February 22, 2012.
* [http://thethesiswhisperer.wordpress.com/2012/02/22/the-academic-writers-strike/ The academic writer’s strike], Inger Mewburn, February 22, 2012.
* [http://gigaom.com/2012/02/22/why-do-we-need-academic-journals-in-the-first-place/ Why do we need academic journals in the first place?], Mathew Ingram, GigaOM, February 22, 2012.
* [http://ittakes30.wordpress.com/2012/02/23/why-boycott-elsevier/ Why boycott Elsevier?], Becky Ward, February 23, 2012.
* [http://breakingculture.tumblr.com/post/18380845829/elseviers-strategy-and-the-long-war Elsevier's strategy and the long war], Sean Johnson Andrews, February 27, 2012.
* [http://gavialib.com/2012/02/elsevier-blinks-once/ Elsevier blinks, once], Library Loon, February 27, 2012.
* [http://www.scienceguide.nl/201202/%E2%80%9Cthe-rwa-is-dead%E2%80%9D.aspx "The RWA is dead"], Cameron Neylon, ScienceGuide, February 27, 2012.
* [http://svpow.wordpress.com/2012/02/27/holy-poop-they-did-it-elsevier-withdraws-support-for-the-research-works-act/ Holy poop! They did it! Elsevier withdraws support for the Research Works Act], Michael Taylor, February 27, 2012.
* [http://www.michaeleisen.org/blog/?p=988 We won the Battle of the Research Works Act. Now let’s win the War for Open Access.], Michael Eisen, February 27, 2012.
* [http://poeticeconomics.blogspot.com/2012/02/elsevier-numbers-illustrate-once-again.html Elsevier numbers illustrate - once again - just how much more sense open access makes!], Heather Morrison, February 27, 2012.
* [http://svpow.wordpress.com/2012/02/28/can-elsevier-save-itself/ Can Elsevier save itself?], Michael Taylor, February 28, 2012.
* [http://johncarlosbaez.wordpress.com/2012/02/28/research-work-act-dead-what-next/ Research Work Act Dead — What Next?], John Baez, February 28, 2012.

=== News aggregators ===

* [http://news.ycombinator.com/item?id=3494340 Fields medalist Tim Gowers: Elsevier — my part in its downfall], Hacker News, January 21, 2012
* [http://www.reddit.com/r/math/comments/oqirf/one_mathematicians_stance_against_elsevier/ One mathematician's stance against Elsevier], Reddit, January 22, 2012.
* [http://news.ycombinator.com/item?id=3501561 The Cost of Knowledge: Researchers taking a stand against Elsevier], Hacker News, January 23, 2012.
* [http://science.slashdot.org/story/12/01/27/1322234/scientists-organize-elsevier-boycott Scientists organize Elsevier boycott], Slashdot, January 27, 2012.
* [http://www.metafilter.com/112178/Scientists-boycott-Elsevier Scientists boycott Elsevier], Metafilter, January 29, 2012.
* [http://news.ycombinator.com/item?id=3534298 Elsevier Publishing Boycott Gathers Steam Among Academics], Hacker News, January 31, 2012.
* [http://www.reddit.com/r/PhilosophyofScience/comments/p2e36/the_cost_of_knowledge_is_an_online_campaign/ The Cost of Knowledge is an online campaign encouraging scientists to boycott Elsevier journals and their high subscription prices. Should knowledge be free?], Reddit, January 30, 2012.
* [http://www.reddit.com/r/math/comments/pepuo/thanks_to_angry_mathematicians_elseviers/ Thanks to angry mathematicians, Elsevier's publishing model might be about to go up in smoke], Reddit, February 7, 2012.
* [http://www.reddit.com/r/science/comments/pv7tn/the_high_price_of_knowledge_should_journals/ The high price of knowledge - should journals charge authors high fees to publish? Is there any other way? Academic publisher Elsevier hit with growing boycott], Reddit, February 18, 2012.
* [http://news.slashdot.org/story/12/02/27/2339215/publisher-pulls-supports-research-works-act-killed Publisher Pulls Supports; 'Research Works Act' Killed], Slashdot, February 27, 2012.

=== Coverage by the media ===

* [http://www.theregister.co.uk/2012/01/28/scientists_boycott_elsevier/ Blog blast births boffin boycott of publisher Elsevier], Iain Thomson, the Register, January 28, 2012.
* [http://www.forbes.com/sites/timworstall/2012/01/28/elseviers-publishing-model-might-be-about-to-go-up-in-smoke/ Elsevier's Publishing Model Might be About to Go Up in Smoke], Tim Worstall, Forbes, January 28, 2012.
* [http://www.wired.com/wiredscience/2012/01/testify-the-open-science-movement-catches-fire/ Testify: The Open-Science Movement Catches Fire] David Dobbs, Wired, January 30, 2012.
* [http://chronicle.com/blogs/wiredcampus/elsevier-publishing-boycott-gathers-steam-among-academics/35216 Elsevier Publishing Boycott Gathers Steam Among Academics], Josh Fischman, The Chronicle of Higher Education, January 30, 2012.
* [http://www.techdirt.com/articles/20120130/13030217589/will-academics-boycott-elsevier-be-tipping-point-open-access-another-embarrassing-flop.shtml Will Academics' Boycott Of Elsevier Be The Tipping Point For Open Access -- Or Another Embarrassing Flop?], Glyn Moody, Techdirt, January 31, 2012.
* [http://boingboing.net/2012/01/31/scientists-boycott-elsevier-ov.html Scientists and scholars boycott Elsevier over bad business practices and copyright maximalism], Cory Doctorow, Boingboing, January 31, 2012.
* [http://lj.libraryjournal.com/2012/01/publishing/petition-targeting-elseviers-business-practices-begins-to-snowball/ Petition Targeting Elsevier’s Business Practices Begins to Snowball], Michael Kelley, Library Journal, January 31, 2012.
* [http://www.thebookseller.com/news/academics-call-boycott-elsevier.html Academics call for boycott of Elsevier], Charlotte Williams, The Bookseller, January 31, 2012.
* [http://chronicle.com/article/As-Journal-Boycott-Grows/130600/ As Journal Boycott Grows, Elsevier Defends Its Practices], Josh Fischman, The Chronicle of Higher Education, January 31, 2012.
* [http://arstechnica.com/science/news/2012/01/researchers-boycott-publisher-will-they-embrace-instant-publishing.ars Researchers boycott publisher; will they embrace instant publishing?], John Timmer, Ars Technica, January 31, 2012.
* [http://www.elmundo.es/elmundosalud/2012/01/30/noticias/1327952591.html Boicot científico a Elsevier], Cristina de Martos, El Mundo, January 31, 2012. (Spanish)
* [http://nos.nl/op3/artikel/335992-elsevier-in-de-clinch-met-wetenschappers.html Elsevier in de clinch met wetenschappers], NOS News, January 31, 2012. (Dutch)
* [http://news.sciencemag.org/scienceinsider/2012/02/thousands-of-scientists-vow-to-b.html Thousands of Scientists Vow to Boycott Elsevier to Protest Journal Prices], Jop de Vrieze, Science Insider, February 1, 2012.
* [http://www.mmm-online.com/elsevier-begins-outreach-as-push-back-on-publisher-threatens-to-widen/article/225855/ Elsevier begins outreach as push-back on publisher threatens to widen], Deborah Weinstein, Medical Marketing & Media, February 1, 2012.
* [http://www.care2.com/causes/scientists-fight-for-open-access-for-their-research.html Scientists Fight For Open Access For Research], Kristina Chew, Care2, February 1, 2012.
* [http://www.bloomberg.com/news/2012-02-01/samsung-csr-nfl-elsevier-motorola-intellectual-property.html Samsung, CSR, NFL, Elsevier, Motorola: Intellectual Property], Victoria Slind-Flor, Bloomberg, February 1, 2012. (Brief mention only.)
* [http://mediadecoder.blogs.nytimes.com/2012/02/01/the-breakfast-meeting-a-week-of-negative-ads-and-new-chief-at-sony/ The Breakfast Meeting: A Week of Negative Ads, and New Chief at Sony], Noam Cohen, New York Times, February 1, 2012. (Brief mention only.)
* [http://www.guardian.co.uk/science/2012/feb/02/academics-boycott-publisher-elsevier Scientists sign petition to boycott academic publisher Elsevier], Alison Flood, the Guardian, February 2, 2012.
* [http://blogues.cyberpresse.ca/sciences/2012/02/02/fronde-contre-les-revues-savantes-delsevier/ Étonnante fronde de chercheurs contre les revues savantes d’Elsevier], Jean-François Cliche, le Soleil, February 2, 2012. (French)
* [http://www.wired.com/wiredscience/2012/02/is-the-open-science-revolution-for-real/ Is the Open Science Revolution For Real?], David Dobbs, Wired, February 3, 2012.
* [http://www.economist.com/node/21545974 The price of information], the Economist, February 4, 2012.
* [http://archiv.twoday.net/stories/64967798/ Zum Elsevier-Boykott], Klaus Graf, Archivalia, February 5, 2012. (German)
* [http://paidcontent.org/article/419-academics-revolt-against-elseviers-journal-pricing/ Academics Revolt Against Elsevier’s Journal Pricing], Robert Andrews, PaidContent, February 6, 2012.
* [http://theconversation.edu.au/spread-the-word-scientists-are-tearing-down-publishers-walls-5098 Spread the word: scientists are tearing down publishers' walls], Alex Holcombe, the Conversation, February 7, 2012.
* [http://www2.ljworld.com/news/2012/feb/07/heard-hill-university-senate-considering-boycottin/ Heard on the Hill: University Senate considering boycotting publisher Elsevier; newspaper readership program popular at other places, too; KUMC researcher mentioned in LA Times story on Alzheimer’s], Andy Hyland, LJWorld, February 7, 2012.
* [http://hon.jp/news/modules/rsnavi/showarticle.php?id=3082 欧米圏で“学術の春”運動始まる、電子ジャーナル出版大手Elsevierに対し学者たちのボイコット運動が急拡大], editorial, hon.jp Daywatch, Feb 7, 2012. (Japanese)
* [http://the-scientist.com/2012/02/07/occupy-elsevier/ Occupy Elsevier?], Bob Grant, the Scientist, February 7, 2012.
* [http://www.theaustralian.com.au/higher-education/academics-boycott-publisher-elsevier/story-e6frgcjx-1226265110496?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+TheAustralianHigherEducationNews+%28The+Australian+%7C+Higher+Education%29&utm_content=Google+Reader Academics boycott publisher Elsevier], Bernard Lane, the Australian, February 8, 2012.
* [http://latimesblogs.latimes.com/jacketcopy/2012/02/wed-book-news-bezos-the-elsevier-boycott-and-more.html Wednesday book news: Bezos, the Elsevier boycott and more], Carolyn Kellogg, Los Angeles Times, February 8, 2012. (Brief mention only.)
* [http://www.guardian.co.uk/higher-education-network/blog/2012/feb/08/open-access-journals-elsvier-boycott Open access journals: are we asking the right questions?], Martin Paul Eve, the Guardian, February 8, 2012.
* [http://www.varsity.co.uk/news/4370 The Academic Spring], Patrick O'Grady, Varsity, February 8, 2012.
* [http://www.timeshighereducation.co.uk/story.asp?sectioncode=26&storycode=418952 Elsevier defends stance on anti-open-access bill], John Gill, Times Higher Education, February 9, 2012.
* [http://www.nature.com/news/elsevier-boycott-gathers-pace-1.10010 Elsevier boycott gathers pace], John Whitfield, Nature, February 9, 2012.
* [http://www.wired.com/wiredscience/2012/02/open-science-revolt-occupies-congress/ Open Science Revolt Occupies Congress], David Dobbs, Wired, February 9, 2012.
* [http://blogs.independent.co.uk/2012/02/09/the-future-of-academic-publishing/ The future of academic publishing], Mike Taylor, the Independent, February 9, 2012.
* [http://www.tcs.cam.ac.uk/issue/news/cambridge-professor-leads-boycott-of-elsevier-publications/ Cambridge Professor leads boycott of Elsevier Publications], Emily Loud, the Cambridge Student Online, February 9, 2012.
* [http://www.utimes.pitt.edu/?p=19679 Protest launched against journal publisher], Kimberly Barlow, University Times, February 9, 2012.
* [http://jeps.efpsa.org/blog/2012/02/10/a-revolution-in-scientific-publishing/ A revolution in scientific publishing?], Sina Scherer, JEPS Bulletin, February 10, 2012.
* [http://libraries.mit.edu/sites/news/elsevier-boycott-grows/7785/ Elsevier Boycott Grows: MIT Faculty Speak About Participation], Ellen Duranceau, MIT Libraries News, February 10, 2012.
* [http://www1.folha.uol.com.br/ciencia/1046769-cientistas-boicotam-a-maior-editora-de-periodicos-do-mundo.shtml Cientistas boicotam a maior editora de periódicos do mundo], Sabine Righetti, Folha, February 10, 2012. (Portugese)
* [http://www.bostonglobe.com/opinion/2012/02/12/why-scientists-are-boycotting-publisher/9sCpDEP7BkkX1INfakn3NL/story.html Why scientists are boycotting a publisher], Gareth Cook, the Boston Globe, February 12, 2012.
** [http://bostonglobe.com/opinion/letters/2012/02/16/elsevier-committed-universal-access-content-sustainable-publishing-model/70QfCpSOvy0IUibSK6eCTL/story.html Elsevier committed to universal access to content, sustainable publishing model], Lynne Herndon (former CEO of Cell press), letter to the editor, the Boston Globe, February 16, 2012.
*** [http://quomodocumque.wordpress.com/2012/02/16/elseviers-sorry-defense-of-the-research-works-act/ Elsevier’s sorry defense of the Research Works Act], Jordan Ellenberg, February 16, 2012.
* [http://newsbreaks.infotoday.com/NewsBreaks/The-Cost-of-Knowledge-Versus-Elsevier--Signatures-and-Growing-80575.asp The Cost of Knowledge Versus Elsevier: 5,600 Signatures and Growing], Robin Peek, Information Today, February 13, 2012.
* [http://www.pourlascience.fr/ewb_pages/a/actualite-la-fronde-des-chercheurs-contre-i-elsevier-i-29118.php La fronde des chercheurs contre Elsevier], Maurice Mashaal, Pour la Science, February 13, 2012.
* [http://www.newscientist.com/article/dn21467-web-freedoms-fuel-academic-spring-journal-protest.html Web freedoms fuel 'academic spring' journal protest], Jacob Aron, New Scientist, February 13, 2012.
* [http://www.nytimes.com/2012/02/14/science/researchers-boycott-elsevier-journal-publisher.html Mathematicians Organize Boycott of a Publisher], Thomas Lin, New York Times, February 13, 2012.
* [http://motherjones.com/blue-marble/2012/02/science-uprising Science Uprising], Julia Whitty, Mother Jones, February 13, 2012.
* [http://www.kansan.com/news/2012/feb/13/professors-boycott/ Professors boycott prominent publishing company], Kelsey Cipolla, The University Daily Kansan, February 13, 2012.
* [http://www.purdueexponent.org/opinion/editorials/article_a6e96c79-5c95-54b8-bf85-eca8de6bb3db.html Monopoly on research publishing is unethical], Editorial, The Exponent, February 14, 2012.
* [http://today.duke.edu/2012/02/elsevierboycott Duke Scholars Join Boycott Against Elsevier], Ashley Yeager, Duke Today, February 14, 2012.
* [https://theconversation.edu.au/academics-line-up-to-boycott-worlds-biggest-journal-publisher-5384 Academics line up to boycott world’s biggest journal publisher], Justin Norrie, the Conversation, February 15, 2012.
* [http://www.ft.com/cms/s/0/2494fbc4-5873-11e1-9f28-00144feabdc0.html Reed chief hits back at critics of division], Salamander Davoudi, February 16, 2012.
* [http://www.timeshighereducation.co.uk/story.asp?storycode=419018 Occupy publishing], Timothy Gowers, Times Higher Education, February 16, 2012.
* [http://www.abc.net.au/science/articles/2012/02/17/3433568.htm Academics boycott journal publisher], Eleanor Bell, ABC news, February 17, 2012.
* [http://www.onthemedia.org/2012/feb/17/trouble-elsevier-leading-academic-publisher/ Trouble for Elsevier, the leading academic publisher], Rick Karr, On the media, NPR, February 17, 2012. (Audio)
** [http://crookedtimber.org/2012/02/21/some-questions-for-elsevier/ Some questions for Elsevier], Harry Brighouse, Crooked Timber, February 21, 2012.
* [http://blogs.theaustralian.news.com.au/thecommonroom/index.php/theaustralian/comments/journal_publishers_in_strife_and_in_denial/ Journal publishers: in strife and in denial], The common room blog, The Australian, February 20, 2012.
* [http://www.smh.com.au/national/education/academics-join-world-fight-against-publisher-20120220-1tjk6.html Academics join world fight against publisher], Nicky Phillips, Sydney Morning Herald, February 21, 2012.
* [http://blogs.discovermagazine.com/crux/2012/02/21/its-not-academic-how-publishers-are-squelching-science-communication/ It’s Not Academic: How Publishers Are Squelching Science Communication], Michael Taylor, Discover Magazine, February 21, 2012.
* [http://www.theaustralian.com.au/higher-education/nhmrc-ceo-supports-elsevier-boycott-says-all-research-must-be-made-open-access/story-e6frgcjx-1226278163029 NHMRC CEO supports Elsevier boycott; says all research must be made open access], Julie Hare, The Australian, February 22, 2012.
* [http://www.wired.com/wiredscience/2012/02/elsevier-boycott-not-a-petition-but-a-declaration-of-independence/ Elsevier Boycott Not a Petition, But “A Declaration of Independence”], David Dobbs, Wired Magazine, February 22, 2012.
* [http://www.insidehighered.com/blogs/library-babel-fish/why-are-we-boycotting-elsevier Why Are We Boycotting Elsevier?], Barbara Fister, Inside Higher Ed, February 24, 2012.
* [http://www.cbc.ca/news/technology/story/2012/02/27/science-elsevier-boycott.html Amid boycott, Elsevier backtracks on research bill], CBC news, February 27, 2012.
* [http://chronicle.com/article/Legislation-to-Bar/130949/ Legislation to Bar Public-Access Requirement on Federal Research Is Dead], Jennifer Howard, Chronicle of Higher Education, February 27, 2012.
* [http://www.newsday.com/opinion/positive-news-for-access-to-tax-funded-science-1.3562266 Positive news for access to tax-funded science], Editorial, Newsday, February 27, 2012.

=== Open letters to Elsevier ===

* [http://math.berkeley.edu/~kirby/elsevier.html Letter to Elsevier], Rob Kirby, December 30, 1997.
* [http://www.library.yale.edu/~llicense/ListArchives/0310/msg00048.html Call for Boycott of Cell Press Journals], Peter Walter and Keith Yamomoto, October 19, 2003.
** [http://genomebiology.com/2003/4/10/spotlight-20031024-02 Researchers boycott Cell Press], Alison McCook, Genome Biology, October 24, 2003.
* [http://www.cs.colorado.edu/~hal/jalg.html Journal of Algorithms editorial board resignation], December 13, 2003.
* [http://math.ucr.edu/home/baez/topology-letter.pdf Topology editorial board resignation letter], August 10, 2006.
* [http://idiolect.org.uk/elsevier/docs/academics_openletter.pdf Arms fairs and academics], 138 signatories, February 28, 2007.
* [http://idiolect.org.uk/notes/?p=643 An open letter to Elsevier and all those involved in the IEHG], Keith Halfacree, April 10, 2007.
* [http://www.coar-repositories.org/news/coar-writes-open-letter-as-reaction-to-elseviers-practices/ Open Letter to Elsevier], Norbert Lossau, Chair of the Executive Board, Confederation of Open Access Repositories, February 6, 2012.
* [https://plus.google.com/105282922684661032446/posts/WCZqgPVehmx Letter to Elsevier], Cynthia Parr, February 10, 2012.
* [http://darwin.eeb.uconn.edu/uncommon-ground/2012/02/declining-elsevier.html Declining elsevier], Kent Holsinger, February 10, 2012.
* [http://occamstypewriter.org/scurry/2012/02/12/an-open-letter-to-elsevier/ An Open Letter to Elsevier], Stephen Curry, February 12, 2012.
* [http://svpow.wordpress.com/2012/02/15/a-response-to-one-elsevier-employee-and-an-open-letter-to-the-rest/ A response to one Elsevier employee, and an open letter to the rest], Matt Wedel, February 15, 2012.
* [http://fakeelsevier.wordpress.com/2012/02/19/dear-elsevier-employees-with-love-from-fakeelsevier/ Dear Elsevier employees, with love, from @FakeElsevier], FakeElsevier, February 19, 2012.
* [http://proteinsandwavefunctions.blogspot.com/2012/02/dear-elsevier.html Dear Elsevier], Jan Jensen, February 27, 2012.

=== Responses by Elsevier ===

* [http://gowers.wordpress.com/2012/01/21/elsevier-my-part-in-its-downfall/#comment-14679 A response by David Clark at Elsevier], January 23, 2012.
* [http://www.elsevier.com/wps/find/intro.cws_home/elsevieropenletter An open letter to the research community: journal prices, discounts, and access], Elsevier, initially published Feb 6, 2012, then edited slightly on February 27, 2012.
** [http://bjoern.brembs.net/news.php?item.833.11 Against Own Assertion, Elsevier Doubled Price For Access], Bjorn Brembs, February 11, 2012.
** [http://gowers.wordpress.com/2012/02/26/elseviers-open-letter-point-by-point-and-some-further-arguments/ Elsevier’s open letter point by point, and some further arguments], Timothy Gowers, February 26, 2012.
* [http://www.epjournal.net/blog/2012/02/elsevier-and-evolution-human-behavior/ Elsevier and Evolution & Human Behavior], Robert Kurzban (co-editor-in-chief of the Elsevier journal Evolution & Human Behavior), February 6, 2012.
* [http://poynder.blogspot.com/2012/02/elseviers-alicia-wise-on-rwa-west-wing.html Elsevier’s Alicia Wise on the RWA, the West Wing, and Universal Access], Richard Poynder, February 9, 2012.
* [http://www.elsevier.com/wps/find/intro.cws_home/newmessagerwa Elsevier withdraws support for the Research Works Act], Elsevier, February 27, 2012.
** [http://bjoern.brembs.net/news.php?item.840.11 Even Now The RWA Was Worth It For Elsevier], Bjorn Brembs, February 27, 2012.
* [http://www.elsevier.com/wps/find/P11.cws_home/lettertothecommunity A letter to the mathematics community], Elsevier, February 27, 2012.
* [http://listserv.crl.edu/wa.exe?A2=LIBLICENSE-L;2ec80b73.1202 Elsevier withdraws support for the Research Works Act], Chrysanne Lowe, Vice President, Marketing Communications, Elsevier, February 27, 2012.

=== Other coverage ===

* [http://www.arl.org/sparc/media/prime-time-for-public-access.shtml Prime Time for Public Access], Heather Joseph, Executive Director, SPARC, February 9, 2012.
* [http://www.openaire.eu/en/news-a-events/news/343-elseviers-practices-opposing-open-access Elsevier’s practices opposing open access], Open Access Infrastructure for Research in Europe, February 16, 2012.
* [http://www.insidehighered.com/views/2012/02/23/essay-open-access-scholarship Values and Scholarship], Joint letter by eleven research provosts, Inside Higher Ed, February 23, 2012.
* [http://en.wikipedia.org/wiki/The_Cost_of_Knowledge The wikipedia page] for this protest.

See also [http://scienceblogs.com/confessions/2012/02/around_the_web_research_works.php this list of links], which is focused more around the Research Works Act, but also contains many links regarding the boycott, as well as [http://www.math.ntnu.no/~stacey/Mathforge/Math2.0 Math 2.0], a discussion forum for all topics related to the future of mathematical publishing.

== Other pledges, boycotts, and petitions ==

* [http://www.researchwithoutwalls.org/ Research Without Walls]
* [http://www.openaccesspledge.com/ Open Access Pledge]
* [http://www-fourier.ujf-grenoble.fr/petitions/index.php?petition=3 Appel pour des négociations équilibrées avec les éditeurs de revues scientifiques] - a petition concerning the bundling and pricing practices of Springer
* [http://www.thepetitionsite.com/207/support-the-open-access-movement-stop-the-research-works-act/?cid=FB_TAF A petition to stop the Research Works Act]
* [http://www.taxpayeraccess.org/action/FRPAA2012.shtml Call to action: Tell Congress you support the Bipartisan Federal Research Public Access Act (H.R. 4004 and S. 2096)], Alliance for taxpayer access, February 9, 2012.

* See these tag libraries from the [http://oad.simmons.edu/oadwiki/OA_tracking_project Open Access Tracking Project] (more comprehensive after April 2009 than before):
** [http://www.connotea.org/tag/oa.boycotts oa.boycotts]
** [http://www.connotea.org/tag/oa.declarations oa.declarations]
** [http://www.connotea.org/tag/oa.petitions oa.petitions]
** [http://www.connotea.org/tag/oa.pledges oa.pledges]

== Other blog posts, letters, and opinion pieces ==
* [http://math.berkeley.edu/~kirby/journals.html Comparative price of math journals], Rob Kirby, May 27, 1997.
** [http://math.berkeley.edu/~kirby/elsevier.html Open letter to Elsevier], Rob Kirby, December 30, 1997.
** [http://math.berkeley.edu/~kirby/jp00.html 2000 data update]
* [http://www.ams.org/notices/199804/branin.pdf Reforming Scholarly Publishing in the Sciences: A Librarian Perspective], Joseph J. Branin and Mary Case, Notices of the American Mathematical Society, 475-486, April 1998.
* [http://www.ams.org/notices/200007/forum-birman.pdf Scientific Publishing: A Mathematician’s Viewpoint], Joan Birman, Notices of the American Mathematical Society, 770-774, July 2000.
* [http://homepages.cwi.nl/~apt/ps/cacm01.pdf One More Revolution to Make: Free Scientific Publishing], Krzysztof R. Apt, Communications of ACM, 44(5), pp. 25-28, 2001.
* [http://www.nieuwarchief.nl/serie5/deel02/sep2001/pdf/apt.pdf Towards free access to scientific literature], Krzysztof R. Apt, Nieuw Archief voor Wiskunde, 5/2 nr. 3, September 2001, pp. 251-255.
* [http://stromme.uib.no/kuperberg.pdf Scholarly Mathematical Communication at a Crossroads], Greg Kuperberg, Nieuw Arch. Wisk., (5) 3 no.3, September 2002.
* [http://people.ccmr.cornell.edu/~ginsparg/blurb/pg02pr.html Can Peer Review be better Focused?], Paul Ginsparg, March 2003.
* [http://www.ams.org/notices/200402/commentary.pdf Fleeced?], Rob Kirby, Notices of the American Mathematical Society, 161-162, February 2004.
* [http://www.ams.org/notices/200405/commentary.pdf We can make a change], Gerard van der Geer, Notices of the American Mathematical Society, May 2004.
* [http://www.math.columbia.edu/~neumann/journal.html What we can do about journal pricing], Walter Neumann, September 2005.
** The discussions mentioned in that email led to the [http://web.archive.org/web/20110525195311/http://members.cox.net/banffprotocol/ Banff protocol] (web site now only available through web archive).
* [http://www.scottaaronson.com/writings/journal.html Review of The Access Principle by John Willinsky], Scott Aaronson, 2006
* [http://digitalstrategies.blogspot.com/2008/06/scientific-publication-in-internet-era.html Scientific Publishing in the Internet Era] Efthymios Constantinides June 17, 2008
* [http://arstechnica.com/science/news/2008/11/elsevier-beyond-the-pale-of-scientific-respectability.ars Publishing economics harm science's credibility], Chris Lee, Ars Technica, November 2008.
* [http://www.ima.umn.edu/~arnold/siam-columns/integrity-under-attack.pdf Integrity under attack: The State of Scholarly Publishing], Douglas Arnold, SIAM news, December 2009.
* [http://scholarlykitchen.sspnet.org/2010/01/04/why-hasnt-scientific-publishing-been-disrupted-already/ Why Hasn’t Scientific Publishing Been Disrupted Already?], Michael Clarke, January 4, 2010.
* [http://math.ucr.edu/home/baez/journals.html What We Can Do About Science Journals], John Baez, January 24, 2011.
* [http://blog.mathunion.org/journals/?no_cache=1&tx_t3blog_pi1%5BblogList%5D%5BshowUid%5D=17&tx_t3blog_pi1%5BblogList%5D%5Byear%5D=2011&tx_t3blog_pi1%5BblogList%5D%5Bmonth%5D=12&tx_t3blog_pi1%5BblogList%5D%5Bday%5D=07&cHash=bb9177d8192db5b5756aca088ea79677 What might be done about high prices of journals?], IMU blog on mathematical journals, July 12, 2011.
* [http://www.monbiot.com/2011/08/29/the-lairds-of-learning/ The lairds of learning] George Monbiot, August 29, 2011.
** [http://sedgemore.com/2011/09/serials-crisis-and-corn-laws/ Serials crisis and corn laws], Francis Sedgemore, September 7, 2011.
* [http://www.guardian.co.uk/commentisfree/2011/aug/29/academic-publishers-murdoch-socialist Academic publishers make Murdoch look like a socialist], George Monbiot, the Guardian, August 29, 2011.
* [http://www.timeshighereducation.co.uk/story.asp?storycode=417576 Peers, review your actions], Michael Taylor, Times Higher Education, September 29, 2011.
* [http://gowers.wordpress.com/2011/10/31/how-might-we-get-to-a-new-model-of-mathematical-publishing/ How might we get to a new model of mathematical publishing?], Timothy Gowers, October 31, 2011.
** [http://gowers.wordpress.com/2011/11/03/a-more-modest-proposal/ A more modest proposal], Timothy Gowers, November 3, 2011.
** [http://boolesrings.org/krautzberger/2011/11/26/the-recent-publishing-debate-a-timeline/ A timeline of the debate initiated by this post], Peter Krautzberger, November 26, 2011.
* [http://www.nytimes.com/2012/01/11/opinion/research-bought-then-paid-for.html Research Bought, Then Paid For], Michael B. Eisen, New York Times opinion piece, January 10, 2012
** [http://www.nytimes.com/2012/01/23/opinion/should-research-be-more-freely-available.html?_r=1 Should Research Be More Freely Available?], Jeffrey M. Drazen (Editor in Chief of The New England Journal of Medicine), Gene D. Sprouse (treasurer of [http://www.aps.org APS]), and Joseph W. Serene (publisher at [http://www.aps.org APS]), letters to the New York Times, January 23, 2012.
* [http://www.guardian.co.uk/science/2012/jan/16/academic-publishers-enemies-science?CMP=twt_fd Academic publishers have become the enemies of science], Mike Taylor, the Guardian, January 16, 2011.
** [http://www.guardian.co.uk/science/2012/jan/27/academic-publishers-enemies-science-wrong Branding academic publishers 'enemies of science' is offensive and wrong], Graham Taylor, January 27, 2011.
** [http://nelh.blogspot.com/2012/02/elsevier-double-dipping-and-nhs.html Elsevier, double-dipping, and the NHS], Ben Toth, February 11, 2012.
* [http://www.michaeleisen.org/blog/?p=873 Nature’s shiny sounding copout on open access], Michael Eisen, January 26, 2012.
* [http://svpow.wordpress.com/2012/01/27/publishers-invent-a-whole-new-form-of-evil-suing-their-customers/ Publishers invent a whole new form of evil: suing their customers], Mike Taylor, SV-POW, January 27, 2012.
* [http://occamstypewriter.org/scurry/2012/01/28/why-i-chose-to-decline-an-invitation-to-review-by-elsevier/ Why I chose to decline an invitation to review by Elsevier], Stephen Curry, January 28, 2012.
* [http://sbseminar.wordpress.com/2012/02/01/journals-and-the-arxiv/ Journals and the arXiv], Scott Morrison, February 1, 2012.
* [http://occupypublishing.blogspot.com.au/2012/02/scientific-journals-in-e-publishing-age.html scientific journals in the e-publishing age], Phillip Thrift, February 1, 2012.
* [http://gowers.wordpress.com/2012/02/02/abstract-thoughts-about-online-review-systems Abstract thoughts about online review systems], Tim Gowers, February 2, 2012.
* [http://cameronneylon.net/blog/the-research-works-act-and-the-breakdown-of-mutual-incomprehension/ The Research Works Act and the breakdown of mutual incomprehension], Cameron Neylon, February 3, 2012.
* [http://sbseminar.wordpress.com/2012/02/09/a-forum-on-mathematical-publishing/ A forum on mathematical publishing], Scott Morrison, February 9, 2012.
* [http://vort.org/2012/02/09/moral-imperative-open-science/ The moral imperative for Open Science], Russell Neches, February 9, 2012.
* [http://johncarlosbaez.wordpress.com/2012/02/10/the-federal-research-public-access-act/ The Federal Research Public Access Act], John Baez, February 10, 2012.
* [http://www.guardian.co.uk/science/blog/2012/feb/10/parable-farmers-teleporting-duplicator The parable of the farmers and the Teleporting Duplicator], Michael Taylor, the Guardian, February 10, 2012.
* [http://svpow.wordpress.com/2012/02/11/why-isnt-anyone-publishing-open-access-articles-in-elsevier-journals/ Why isn’t anyone publishing open-access articles in Elsevier journals?], Mike Taylor, February 11, 2012.
* [http://michaelnielsen.org/blog/how-you-can-help-the-federal-research-public-access-act-frpaa-become-law/ How you can help the Federal Research Public Access Act (FRPAA) become law], Michael Nielsen (interviewing Heather Joseph), February 14, 2012.
* [http://lisnews.org/elsevier_filters_recommendation_engine_to_show_elsevier_titles_only Elsevier Filters Recommendation Engine to Show Elsevier Titles Only], LISNews, February 14, 2012.
* [http://techcrunch.com/2012/02/15/the-dangerous-research-works-act/ The Dangerous “Research Works Act”], Richard Price, TechCrunch, February 15, 2012.
* [http://www.ethlife.ethz.ch/archive_articles/120217_bibliothek_neubauer/index_EN A thorn in the side for science publishers], Wolfram Neubauer, February 17, 2012.
** [http://johncarlosbaez.wordpress.com/2012/02/20/elsevier-and-springer-sue-university-library/ Elsevier and Springer Sue University Library], John Baez, February 20, 2012.
* [http://www.newsday.com/opinion/make-tax-funded-scientific-research-public-1.3555902 Make tax-funded scientific research public], Editorial, Newsday, February 26, 2012.
* [http://ilaba.wordpress.com/2012/02/26/women-in-math-and-the-overhaul-of-the-publishing-system/ Women in math, and the overhaul of the publishing system], Izabella Laba, February 26, 2012.

== Media ==

* [http://www.nature.com/nature/journal/v445/n7126/full/445347a.html PR's 'pit bull' takes on open access], Jim Giles, Nature, January 25, 2007. Summary: A coalition of scientific publishers (including Elsevier, Wiley, and the American Chemical Society) organises to oppose open access.
* [http://www.guardian.co.uk/business/2008/may/30/armstrade.weaponstechnology Reed Elsevier makes its final farewell to arms], Katie Allen, the Guardian, 30 May 2008. Summary: Reed Elsevier was until 2009 organizing arms trade fairs.
** [http://www.acme-journal.org/vol8/Stafford09.pdf Lessons from the Campaign against Elsevier "We won, but how did we win?"], Tom Stafford, ACME: An International E-Journal for Critical Geographies 2009, 8 (3), 494-504.
** [http://www.caat.org.uk/issues/armsfairs/reedelsevier.php Campaign success: Reed Elsevier sells international arms fairs], Campaign against arms trade, March 9, 2009.
* [http://classic.the-scientist.com/blog/display/55679/ Elsevier Published 6 Fake Journals], Bob Grant, The Scientist, May 7, 2009. Summary: Elsevier was paid by unnamed pharmaceutical companies to publish six journals that looked like independent peer-reviewed medical journals, but which were not.
** [http://en.wikipedia.org/wiki/Australasian_Journal_of_Bone_%26_Joint_Medicine The wikipedia page on these six journals].
** The Elsevier fake-journal tally eventually rose to [http://www.earlham.edu/~peters/fos/2009/06/elsevier-fake-journal-tally-now-9.html nine].
** [http://www.guardian.co.uk/commentisfree/2009/may/09/bad-science-medical-journals-companies The danger of drugs... and data], Ben Goldacre, the Guardian, May 8, 2009.
** [http://www.elsevier.com/wps/find/authored_newsitem.cws_home/companynews05_01203 Elsevier press release on this incident], May 7, 2009.
* [http://www.insidehighered.com/news/2009/06/23/elsevier Elsevier Won't Pay for Praise], Scott Jashik, Inside Higher Ed, June 23, 2009. Summary: Elsevier suspends its practice of offering Amazon gift cards to anyone who would give their textbooks a five-star rating.

== Other Information ==

* '''On Elsevier'''
** [http://www.reed-elsevier.com/mediacentre/pressreleases/Documents/2010/Reed%20Elsevier%202009%20Results%20Announcement%2017%20February%202010%20FINAL.pdf Reed Elsevier's 2009 report] Elsevier reported a profit of 1.1 billion dollars on revenue of 3.2 billion dollars.
** [http://en.wikipedia.org/wiki/Elsevier#Criticism_and_controversies Criticism and controversies of Elsevier] (Wikipedia)
** [http://gizmodo.com/5870241 Elsevier support for the Stop Online Piracy Act (SOPA)] (Gizmodo)
*** [http://en.wikipedia.org/wiki/List_of_organizations_that_support_the_Stop_Online_Piracy_Act List of organizations with official stances on the Stop Online Piracy Act] (Wikipedia)
** [http://www.michaeleisen.org/blog/?p=846 Elsevier support for the Research Works Act (RWA)] (Michael Nielsen)
*** [http://poynder.blogspot.com/2012/01/elsevier-needs-to-get-out-more.html Elsevier needs to get out more] (Richard Poynder)
*** [http://freethoughtblogs.com/pharyngula/2012/01/16/elsevier-evil/ Elsevier = evil] (Phyrangula)
*** [http://www.michaeleisen.org/blog/?p=807 Elsevier-funded NY Congresswoman Carolyn Maloney Wants to Deny Americans Access to Taxpayer Funded Research] (Michael Eisen)
**** [http://www.michaeleisen.org/blog/?p=807#comment-52048 A response by Tom Reller] (Vice President and Head of Global Corporate Relations at Elsevier)
*** Note however that the editorial board of [http://www.thelancet.com/ the Lancet], a very prestigious medical journal published by Elsevier, has [http://www.thelancet.com/journals/lancet/article/PIIS0140-6736(12)60125-1/fulltext come out strongly against the Research Works Act]. Also, rival publisher Wiley [http://poynder.blogspot.com/2012/02/john-wiley-sons-have-no-plans-to.html has no plans to support the act].
*** [http://www.elsevier.com/wps/find/intro.cws_home/elsevierstatement A message to the research community: Elsevier, access, and the Research Works Act], Elsevier, February 3, 2012.
*** [http://www.elsevier.com/wps/find/P11.cws_home/lettertothecommunity Elsevier withdrew its support for the Research Works Act] on February 27, 2012. Several hours later, [https://plus.google.com/107980702132412632948/posts/a4DzVk9n7fG the act was withdrawn by its Congressional sponsors].
** [http://www.whitehouse.gov/sites/default/files/microsites/ostp/scholarly-pubs-%28%23168%29%20Elsevier%20submission.pdf Elsevier submission to the Office of Science and Technology Policy on open access], January 2012.
*** [http://openaccess.kb.se/?p=637 Elsevier tries to block institutional OA mandates], Jan Hagerlid, January 31, 2012.
** [http://www.researchinformation.info/riaut03elsevier.html Why commercial publishers are good for research], Arie Jongejan, CEO Science & Technology, Elsevier, Autumn 2003.
** [http://www.elsevier.com/wps/find/authorsview.authors/preprints Elsevier's policy on authors making their papers available on preprint servers] (Short version: Elsevier allows draft versions of papers to be placed on public servers such as the arXiv, and revised versions of papers to be placed on personal or institutional pages, but final versions of papers are only permitted at the journal site itself.)

* '''Stock analyses and financial data of Elsevier and other publishers'''
** [http://www.econ.ucsb.edu/~tedb/Journals/morganstanley.pdf Scientific Publishing: Knowledge is Power], Morgan Stanley, September 20, 2002.
** [http://dl.dropbox.com/u/4398178/Reciprocal%20Space%20Files/001-BR-EndoftheBigDeal-2011.pdf Reed Elsevier: The inevitable crunch point – downgrading to under perform because of growing concerns on Elsevier], Bernstein Research, March 10, 2011.
** [http://dl.dropbox.com/u/4398178/Reciprocal%20Space%20Files/002-BR-ElsevierNegotiations-2011.pdf Reed Elsevier, Bringing down the house – Why Elsevier is vulnerable in its upcoming Big Deal negotiations], Bernstein Research, March 29, 2011.
** [http://dl.dropbox.com/u/4398178/Reciprocal%20Space%20Files/003-BR-ReedCostofKnowledge-2012.pdf Occupy Elsevier], Bernstein Research, February 6, 2012.
** [https://plus.google.com/117663015413546257905/posts/1xRiEyWnipc Noise around boycott against Elsevier offers short term trading opportunity], Exane Paribas, February 7, 2012.
*** [http://cameronneylon.net/blog/a-tale-of-two-analysts/ A tale of two analysts], Cameron Neylon, February 15, 2012.
** [http://www.sec.gov/Archives/edgar/data/929869/000095012311023614/u10507e20vf.htm Reed Elsevier's 2012 annual report (form 20-F) filing with the SEC]

* '''On open access'''
** [http://en.wikipedia.org/wiki/Open_access Open Access]
** [http://oad.simmons.edu Open Access Directory]
** [http://www.earlham.edu/~peters/fos/overview.htm Open Access Overview] (Peter Suber)

* '''On scholarly journals'''
** [http://www.unc.edu/scholcomdig/whitepapers/panitch-michalak.html The serials crisis] Judith Panitch and Sarah Michalak, A White Paper for the UNC-Chapel Hill Scholarly Communications Convocation, January, 2005.
** [http://www.ams.org/membership/mem-journal-survey AMS Journal Price Survey]
*** [http://www.mathematik.uni-bielefeld.de/~rehmann/BIB/AMS/Publisher.html Math Journal Price Survey], from 2008 data.
** [http://en.wikipedia.org/wiki/Serials_crisis Journal subscription prices have increased far more rapidly than either inflation or spending on research]
** [http://www.mcafee.cc/Journal/Summary.pdf A summary of journal price averages in various disciplines including mathematics as of 2010] (see also [http://www.mcafee.cc/Journal/ the parent site, which contains more detailed information]).
** [http://www.econ.ucsb.edu/~tedb/Journals/BundleContracts.html Big Deal Contract Project] - an analysis of journal bundling contracts, and the attempts by publishers such as Elsevier to prevent them from becoming public.
** [http://oad.simmons.edu/oadwiki/OA_journal_business_models Open access journal business models] (from the Open Access Directory)
** [http://www.mathunion.org/fileadmin/CEIC/bestpractice/bpfinal.pdf Best Current Practices for Journals], endorsed by the International Mathematical Union general assembly, August 16, 2010.
** [http://www.msri.org/attachments/workshops/587/MSRIfinalreport.pdf Mathematics journals: what is valued and what may change], Report of the workshop held at MSRI, Berkeley, California on February 14 – 16 2011.
** [http://www.ams.org/notices/201203/rtx120300436p.pdf Do Mathematicians Get the Author Rights They Want?], Kristine K. Fowler, Notices of the American Mathematical Society, March 2012.

* '''Miscellaneous links'''
** [http://www.math.umd.edu/research/crisis.html The Crisis in Scientific Publishing] - a collection of links hosted by the University of Maryland.
** [http://www.azimuthproject.org/azimuth/show/Academic+publishing Academic publishing] - a wiki collection of links at the Azimuth project.

== Elsevier mathematics journals ==

This list is taken from [http://www.elsevier.com/wps/find/P11.cws_home/mathjournals here]

* [http://www.elsevier.com/wps/find/journaldescription.cws_home/708310/ Acta Mathematica Scientia]
* [http://www.elsevier.com/locate/yaama Advances in Applied Mathematics]
* [http://www.elsevier.com/locate/advengsoft Advances in Engineering Software]
* [http://www.journals.elsevier.com/advances-in-mathematics/ Advances in Mathematics] (*)
* [http://www.elsevier.com/locate/anihpc Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire]
* [http://www.elsevier.com/locate/apal Annals of Pure & Applied Logic] (*)
* [http://www.elsevier.com/wps/find/journaldescription.cws_home/600714 Annales Scientifiques de l'École Normale Supérieure] (Until 2008)
** This journal is [http://www.math.ens.fr/edition/annales/ now published by the Société mathématique de France].
* [http://www.elsevier.com/locate/arcontrol Annual Reviews in Control]
* [http://www.journals.elsevier.com/applied-and-computational-harmonic-analysis/ Applied & Computional Harmonic Analysis]
** Ingrid Daubechies resigned her position as editor-in-chief in 2012, according to her statement on [http://thecostofknowledge.com the Elsevier boycott site].
* [http://www.elsevier.com/locate/apm Applied Mathematical Modelling]
* [http://www.elsevier.com/locate/amc Applied Mathematics & Computation]
* [http://www.journals.elsevier.com/applied-mathematics-letters/ Applied Mathematics Letters]
** [http://retractionwatch.wordpress.com/2011/06/13/applied-mathematics-letters-posts-apology-for-retracting-intelligent-design-friendly-paper/ Applied Mathematics Letters posts apology for retracting Intelligent Design-friendly paper], Retraction Watch, 13 June 2011.
** [http://www.timeshighereducation.co.uk/story.asp?sectioncode=26&storycode=416514&c=1 Second thoughts result in payout], Paul Jump, Times Higher Education, 16 June 2011.
* [http://www.elsevier.com/locate/apnum Applied Numerical Mathematics]
* [http://www.elsevier.com/locate/artint Artificial Intelligence]
* [http://www.elsevier.com/locate/automatica Automatica]
* [http://www.elsevier.com/locate/btt Biometric Technology Today]
* [http://www.elsevier.com/locate/biosystems Biosystems]
* [http://www.elsevier.com/locate/bulsci Bulletin des Sciences Mathématiques]
* [http://www.journals.elsevier.com/chaos-solitons-and-fractals/ Chaos, Solitons & Fractals]
** There was a significant amount of controversy regarding the quality control at this journal during the tenure of a past editor-in-chief, who stepped down in 2009. Unfortunately, most of the primary reporting on this has been taken down due to ongoing litigation.
** [http://en.wikipedia.org/wiki/Elsevier#Chaos.2C_Solitons_.26_Fractals The Wikipedia section on this issue]
** [http://sbseminar.wordpress.com/2008/11/30/laffaire-el-naschie/ L’affaire El Naschie], Secret Blogging Seminar, November 30, 2008.
** [http://www.ima.umn.edu/~arnold/siam-columns/integrity-under-attack.pdf Integrity under attack: The State of Scholarly Publishing], Douglas Arnold, SIAM news, December 2009.
** [http://www.bbc.co.uk/news/science-environment-15697636 Nature journal libel case begins], Pallab Ghosh, BBC News, November 11, 2011.
* [http://www.elsevier.com/locate/cnsns Communications in Nonlinear Science and Numerical Simulation]
* [http://www.elsevier.com/wps/find/journaldescription.cws_home/600301/description#description Comptes Rendus Mathematique]
* [http://www.elsevier.com/locate/comgeo Computational Geometry]
* [http://www.elsevier.com/locate/csda Computational Statistics & Data Analysis]
* [http://www.elsevier.com/locate/cma Computer Methods in Applied Mechanics and Engineering]
* [http://www.journals.elsevier.com/computers-and-mathematics-with-applications Computers & Mathematics with Applications]
** [http://www.sciencedirect.com/science/article/pii/S0898122109005070 A computer application in mathematics], M. Sivasubramanian, S. Kalimuthu, in Computers and Mathematics with Applications, vol. 59 (2010) pp. 296-297. (This article is discussed in [http://blog.mathunion.org/journals/?no_cache=1&tx_t3blog_pi1%5BblogList%5D%5BshowUid%5D=30&tx_t3blog_pi1%5BblogList%5D%5Byear%5D=2012&tx_t3blog_pi1%5BblogList%5D%5Bmonth%5D=02&tx_t3blog_pi1%5BblogList%5D%5Bday%5D=05&cHash=a2d6424f899302a7ea3b75b9bb591802 this blog post] on the IMU mathematics journal blog, and is also available [http://www.math.hkbu.edu.hk/~ttang/newspaper/funnyarticle11.pdf here].)
** The editorial board [http://about.elsevier.com/pdf/LetterFromEditor.pdf was replaced in 2012].
* [http://www.elsevier.com/locate/conengprac Control Engineering Practice]
* [http://www.elsevier.com/locate/difgeo Differential Geometry and its Applications] (*)
* [http://www.elsevier.com/locate/dam Discrete Applied Mathematics]
* [http://www.elsevier.com/locate/disc Discrete Mathematics]
* [http://www.elsevier.com/locate/disopt Discrete Optimization]
* [http://www.elsevier.com/locate/endm Electronic Notes in Discrete Mathematics]
* [http://www.elsevier.com/locate/entcs Electronic Notes in Theoretical Computer Science]
* [http://www.elsevier.com/locate/enganabound Engineering Analysis with Boundary Elements]
* [http://www.elsevier.com/locate/engappai Engineering Applications of Artificial Intelligence]
* [http://www.elsevier.com/locate/ejc European Journal of Combinatorics] (*)
** Gunther Ziegler [http://www.scilogs.de/wblogs/blog/mathematik-im-alltag/allgemein/2012-02-19/boykottiert-elsevier-ich-boykottiere-elsevier resigned his position] as an editor of this journal in 2012.
* [http://www.elsevier.com/locate/ejor European Journal of Operational Research]
* [http://www.elsevier.com/locate/expomath Expositiones Mathematicae]
* [http://www.elsevier.com/locate/ffa Finite Fields and their Applications] (*)
* [http://www.elsevier.com/locate/fss Fuzzy Sets and Systems]
* [http://www.elsevier.com/locate/hm Historia Mathematica]
* [http://www.elsevier.com/locate/indag Indagationes Mathematicae]
* [http://www.elsevier.com/locate/ins Information Sciences]
* [http://www.elsevier.com/locate/ijforecast International Journal of Forecasting]
* [http://www.elsevier.com/locate/nlm International Journal of Non-Linear Mechanics]
* [http://www.elsevier.com/locate/matpur Journal de Mathématiques Pures et Appliquées]
* [http://www.elsevier.com/locate/yjabr Journal of Algebra] (*)
* [http://www.sciencedirect.com/science/journal/01966774 Journal of Algorithms]
** [http://www.cs.colorado.edu/~hal/jalg.html Editorial board resignation], December 13, 2003.
** [http://www.cs.colorado.edu/~hal/chronicle.txt Editorial Board of Scientific Journal Quits, Accusing Elsevier of Price-Gouging], Brock Read, the Chronicle of Higher Education, February 9, 2004.
* [http://www.elsevier.com/locate/jal Journal of Applied Logic]
* [http://www.elsevier.com/locate/jat Journal of Approximation Theory]
* [http://www.elsevier.com/locate/yjcta Journal of Combinatorial Theory, series A] (*)
** Gunther Ziegler [http://www.scilogs.de/wblogs/blog/mathematik-im-alltag/allgemein/2012-02-19/boykottiert-elsevier-ich-boykottiere-elsevier resigned his position] as an editor of this journal in 2012.
* [http://www.elsevier.com/locate/yjctb Journal of Combinatorial Theory, series B] (*)
* [http://www.elsevier.com/locate/jco Journal of Complexity]
* [http://www.elsevier.com/locate/cam Journal of Computational & Applied Mathematics]
* [http://www.elsevier.com/locate/jcss Journal of Computer and System Sciences]
* [http://www.elsevier.com/locate/yjdeq Journal of Differential Equations]
* [http://www.elsevier.com/locate/jda Journal of Discrete Algorithms]
* [http://www.elsevier.com/locate/jeconom Journal of Econometrics]
* [http://www.elsevier.com/locate/yjfan Journal of Functional Analysis] (*)
* [http://www.elsevier.com/locate/geomphys Journal of Geometry and Physics]
* [http://www.elsevier.com/locate/jmaa Journal of Mathematical Analysis & Applications]
* [http://www.elsevier.com/locate/jmateco Journal of Mathematical Economics]
* [http://www.elsevier.com/locate/yjmva Journal of Multivariate Analysis]
* [http://www.elsevier.com/locate/jnt Journal of Number Theory] (*)
** Marie-France Vigneras resigned her position as an editor in 2012, according to her statement on the Elsevier boycott site.
* [http://www.elsevier.com/locate/jprocont Journal of Process Control]
* [http://www.journals.elsevier.com/journal-of-pure-and-applied-algebra/ Journal of Pure & Applied Algebra] (*)
* [http://www.elsevier.com/locate/jspi Journal of Statistical Planning & Inference]
* [http://www.elsevier.com/locate/fi Journal of the Franklin Institute]
* [http://www.elsevier.com/locate/jkss Journal of the Korean Statistical Society]
* [http://www.elsevier.com/locate/laa Linear Algebra and its Applications] (*)
* [http://www.elsevier.com/locate/mcm Mathematical and Computer Modelling]
* [http://www.elsevier.com/locate/mbs Mathematical Biosciences]
* [http://www.elsevier.com/locate/mss Mathematical Social Science]
* [http://www.elsevier.com/locate/matcom Mathematics and Computers in Simulation]
* [http://www.elsevier.com/locate/neunet Neural Networks]
* [http://www.elsevier.com/locate/na Nonlinear Analysis]
** [http://www.sciencedirect.com/science/article/pii/S0362546X04000409 On the second part of Hilbert's 16th problem], E. Oxenhielm, Nonlinear Analysis 57 (1), April 2004.
*** [http://news.bbc.co.uk/2/hi/science/nature/3243736.stm Historic maths problem 'cracked'] David Whitehouse, BBC, November 27, 2003.
*** [http://tesugen.com/archives/03/12/elin-oxenhielm-update Elin Oxenhielm update], Peter Lindberg, December 3, 2003.
*** [http://www.nature.com/news/2003/031209/full/news031208-4.html Mathematicians dispute proof of century-old problem], John Whitfield, Nature, December 9, 2003.
*** [http://plus.maths.org/content/struggling-sixteen Struggling for sixteen], Rachel Thomas, Plus magazine, December 16, 2003.
*** The paper was eventually [http://www.sciencedirect.com/science/article/pii/S0362546X04000409 withdrawn from the journal by the editors].
** [http://www.sciencedirect.com/science/article/pii/S0362546X0500235X On some contradictory computations in multi-dimensional mathematics], L. Carvalho, Nonlinear Analysis 63 (5-7), November 2005, 725--734. (Claims that the change of variables formula is incorrect.)
*** [http://math.ucr.edu/home/baez/corfield/2006/03/new-bogdanoff-affair_114355412211228579.html A New Bogdanoff Affair?], David Corfield, March 28, 2006.
*** [http://www.sciencedirect.com/science/article/pii/S0362546X06004597 A comment on: ''On some contradictory computations in multi-dimensional mathematics''], E. Capelas de Oliveira, W. Rodrigues, Nonlinear Anal. 67 (7), October 2007, 2316–2320.
*** As of 2012, the original paper of Carvalho has not been retracted from the journal. (However, it is no longer listed as a publication on [http://www.icmc.usp.br/~andcarva/publicac.html Carvalho's web page].)
** [http://blog.mikael.johanssons.org/archive/2006/03/this-is-me-losing-all-faith-in-non-linear-analysis/ This is me losing all faith in Nonlinear Analysis], Mikael Johansson, March 28, 2006.
* [http://www.elsevier.com/locate/nahs Nonlinear Analysis: Hybrid Systems]
* [http://www.elsevier.com/locate/nonrwa Nonlinear Analysis: Real world applications]
* [http://www.elsevier.com/locate/orl Operations Research Letters]
* [http://www.elsevier.com/locate/pr Pattern Recognition]
* [http://www.elsevier.com/locate/physa Physica A: Statistical Mechanics and its Applications]
* [http://www.elsevier.com/locate/physd Physica D: Nonlinear Phenomena]
* [http://www.elsevier.com/locate/simpat Simulation Modelling Practice & Theory]
* [http://www.elsevier.com/locate/stamet Statistical Methodology]
* [http://www.elsevier.com/locate/stapro Statistics and Probability Letters]
* [http://www.elsevier.com/locate/spa Stochastic Processes and their Applications] (*)
* [http://www.elsevier.com/locate/sysconle Systems & Control Letters]
* [http://www.sciencedirect.com/science/journal/00409383 Topology]
** [http://math.ucr.edu/home/baez/topology-letter.pdf Editorial board resignation letter, 10 August 2006]
** [http://www.nysun.com/arts/rebellion-erupts-over-journals-of-academia/42317/ A Rebellion Erupts Over Journals Of Academia], Gary Shapiro, New York Sun, 26 October, 2006.
** [http://www.ams.org/notices/200705/comm-toped-web.pdf Jumping Ship: Topology editorial board resigns], Allyn Jackson, Notices of the American Mathematical Society, May 2007.
** [http://en.wikipedia.org/wiki/Topology_(journal) Wikipedia page on the journal]
** This journal was [http://www.info.sciverse.com/techsupport/journals/jnldiscontinued.htm discontinued in 2012].
* [http://www.journals.elsevier.com/topology-and-its-applications/ Topology & its Applications] (*)
** In 2001, a group of editors of this journal [http://www.uflib.ufl.edu/oa/2009/posters/constitutional-declarationsdeniselgposter2-1.pdf resigned] to form [http://www.msp.warwick.ac.uk/agt/2012/12-01/ Algebraic & Geometric Topology].

(*) On February 27, 2012, [http://www.elsevier.com/wps/find/P11.cws_home/lettertothecommunity Elsevier announced] that the archives of these 14 journals, from 1995 to four years before the current date, would be made open access.

== Open Access journals ==

* These lists are taken from the [http://www.doaj.org/ Directory of Open Access Journals] (limited to peer-reviewed journals).
** Perhaps someone could spell out or cut/paste the DOAJ lists below, like the Elsevier list above.

* In [http://www.doaj.org/doaj?func=subject&cpid=58&uiLanguage=en mathematics]

* In [http://www.doaj.org/doaj?func=subject&cpid=59&uiLanguage=en statistics]

* In [http://www.doaj.org/doaj?func=subject&cpid=114&uiLanguage=en computer science], e.g.
** [http://www.jair.org/ Journal of Artificial Intelligence Research]
** [http://www.lmcs-online.org Logical Methods in Computer Science]
** [http://jmlr.csail.mit.edu/ Journal of Machine Learning Research]
** [http://theoryofcomputing.org/ Theory of Computing]
** [http://www.jucs.org/ Journal of Universal Computer Science]
** [http://cjtcs.cs.uchicago.edu/ Chicago Journal of Theoretical Computer Science]

* In [http://www.doaj.org/doaj?func=subject&cpid=49&uiLanguage=en physics], e.g.
** [http://prx.aps.org/ Physical Review X]
** [http://iopscience.iop.org/1367-2630/ The New Journal of Physics]

== Mathematics journal price tables ==

The following tables list the ten most expensive mathematics journals by volume list price (as of 2008), and (for comparison) the ten mathematics journals with the highest impact factor (as of 2000). One should caution that due to complicated (and, in some cases, [http://www.econ.ucsb.edu/~tedb/Journals/BundleContracts.html deliberately obscured]) bundling agreements, the actual price of subscriptions to many journals (including Elsevier journals) may differ somewhat from the official list price. Nevertheless, these tables should convey the rough order of magnitude, at least, of journal costs from publisher to publisher.

Data is drawn from [http://www.mathematik.uni-bielefeld.de/~rehmann/BIB/AMS/Price_per_Volume.html this set of 2007 journal price data] and [http://in-cites.com/research/2001/oct_15_2001-2.html this list of 2000 ISI impact factors]. All prices in US dollars.

=== Top ten mathematics journals by volume list price ===

{|
|Title
|Publisher
|Price/volume
|Price/page
|-
|J. Math. Sci. (New York)
|Springer
|9998
|1.38
|-
|Theoret. Comput. Sci.
|Elsevier
|6551
|1.02
|-
|J. Math. Anal. Appl.
|Academic Press/Elsevier
|6362
|0.36
|-
|J. Algebra
|Academic Press/Elsevier
|5736
|0.51
|-
|Nonlinear Anal.
|Elsevier
|5426
|0.84
|-
|Discrete Math.
|Elsevier
|5269
|1.63
|-
|Appl. Math. Comput.
|Elsevier
|5250
|0.38
|-
|Math. Methods Appl. Sci.
|Wiley/Teubner
|4995
|2.09
|-
|Linear Algebra Appl.
|Elsevier
|4885
|0.94
|-
|Math. Nachr.
|Wiley/VCH Verlag
|4795
|2.58
|}

=== Top ten mathematics journals by impact factor ===

{|
|Title
|Publisher
|Price/volume
|Price/page
|-
|Bull. Amer. Math. Soc.
|American Mathematical Society
|418
|0.64
|-
|Acta Mathematica
|Institut Mittag-Leffler
|392
|0.65
|-
|J. Amer. Math. Soc.
|American Mathematical Society
|287
|0.24
|-
|Comm. Pure Appl. Math.
|Wiley
|3205
|1.74
|-
|Inventiones Mathemat.
|Springer-Verlag
|3232
|1.21
|-
|Annals of Mathematics
|Princeton University Press
|260
|0.13
|-
|Advances in Mathematics
|Elsevier/Academic Press
|3221
|0.41
|-
|Mem. Amer. Math. Soc.
|American Mathematical Society
|N/A
|N/A
|-
|Commun. Contemp. Math.
|World Scientific
|483
|0.51
|-
|Geom. Func. Anal.
|Springer/Birkhauser
|1185
|0.88
|}

== Data from libraries ==

Pricing data from libraries is often hard to come by (for instance, many bundling contracts come with confidentiality agreements). More links in this section would be greatly appreciated.

* [http://www.bibliothek.kit.edu/cms/english/most-expensive-journals%20.php Here is a list of the 10 most expensive journals subscribed to by the Karlsruhe Institute of Technology] as of 2010/2011. 8 of the 10 are published by Elsevier.
* [http://libraries.mit.edu/sites/scholarly/mit-open-access/open-access-at-mit/mit-open-access-policy/publishers-and-the-mit-faculty-open-access-policy/elsevier-fact-sheet/ Elsevier Fact Sheet], MIT libraries. MIT avoids bundling in order to obtain flexibility in its subscriptions, but pays Elsevier almost $2 million/year for its journals.
* [http://www.purdueexponent.org/campus/article_19f1031d-0396-5b21-870a-c7f9f6ca91bc.html According to this news article], Purdue pays Elsevier $2.3 million/year for digital access to its journals, with price increases of approximately 5 percent per year.
* The [http://www.econ.ucsb.edu/~tedb/Journals/BundleContracts.html Bundle Contract Project] seeks to collect bundling contracts from commercial publishers.

Journal publishing reform

2012-02-27T16:17:28Z

Gowers: /* Responses by Elsevier */

[[Image:elsevier_poster.jpg|right|300px|Credit: Michael Eisen]]

This is a collection of links to information, opinion, activism, and other issues concerning the practices of research journal publishers (particularly in the mathematical sciences). Further contributions are welcome.

== The cost of knowledge ==

[http://thecostofknowledge.com/ The cost of knowledge] is a web page at which one may register a protest against the practices of Elsevier by pledging not to submit a paper to an Elsevier journal, not to referee for an Elsevier journal, not to join an editorial board of an Elsevier journal, or some combination of the three. This site was inspired by the following blog post:

* [http://gowers.wordpress.com/2012/01/21/elsevier-my-part-in-its-downfall/ Elsevier - my part in its downfall], Timothy Gowers, January 21, 2012.

A more detailed statement of purpose of the boycott, can be [http://gowers.files.wordpress.com/2012/02/elsevierstatementfinal.pdf found here]. It is written and signed by [http://en.wikipedia.org/wiki/Scott_Aaronson Scott Aaronson], [http://en.wikipedia.org/wiki/Douglas_N._Arnold Douglas N. Arnold], [http://en.wikipedia.org/wiki/Artur_Ávila Artur Ávila], [http://en.wikipedia.org/wiki/John_C._Baez John Baez], [http://www-m3.ma.tum.de/Allgemeines/FolkmarBornemann Folkmar Bornemann], [http://en.wikipedia.org/wiki/Danny_Calegari Danny Calegari], [http://research.microsoft.com/en-us/um/people/cohn/ Henry Cohn], [http://en.wikipedia.org/wiki/Ingrid_Daubechies Ingrid Daubechies], [http://en.wikipedia.org/wiki/Jordan_Ellenberg Jordan Ellenberg], [http://www.math.uchicago.edu/~emerton/ Matthew Emerton], [http://wavelets.ens.fr/EQUIPE/marie.htm Marie Farge], [http://en.wikipedia.org/wiki/David_Gabai David Gabai], [http://en.wikipedia.org/wiki/Timothy_Gowers Timothy Gowers], [http://en.wikipedia.org/wiki/Ben_J._Green Ben Green], [http://de.wikipedia.org/wiki/Martin_Grötschel Martin Grötschel], [http://en.wikipedia.org/wiki/Michael_Harris_%28mathematician%29 Michael Harris], [http://en.wikipedia.org/wiki/Fr%C3%A9d%C3%A9ric_H%C3%A9lein Frédéric Hélein], [http://en.wikipedia.org/wiki/Robion_Kirby Rob Kirby], [http://en.wikipedia.org/wiki/Vincent_Lafforgue Vincent Lafforgue], [http://en.wikipedia.org/wiki/Greg_Lawler Gregory F. Lawler], [http://en.wikipedia.org/wiki/Randall_J._LeVeque Randall J. LeVeque], [http://en.wikipedia.org/wiki/Laszlo_lovasz Laszlo Lovasz], [http://www.math.umn.edu/~olver/ Peter J. Olver], [http://www.maths.qmul.ac.uk/~olof/ Olof Sisask], [http://en.wikipedia.org/wiki/Terence_tao Terence Tao], [http://en.wikipedia.org/wiki/Richard_Taylor_%28mathematician%29 Richard Taylor], [http://en.wikipedia.org/wiki/Bernard_Teissier Bernard Teissier], [http://en.wikipedia.org/wiki/Burt_Totaro Burt Totaro], [http://en.wikipedia.org/wiki/Lloyd_Trefethen Lloyd N. Trefethen], [http://kyokan.ms.u-tokyo.ac.jp/~tsuboi/ Takashi Tsuboi], [http://en.wikipedia.org/wiki/Marie-France_Vign%C3%A9ras Marie-France Vigneras], [http://en.wikipedia.org/wiki/Wendelin_Werner Wendelin Werner], [http://math.uchicago.edu/~wilkinso/ Amie Wilkinson], and [http://page.mi.fu-berlin.de/gmziegler/ Gunter M. Ziegler].

See also [http://blog.thecostofknowledge.com/ the blog associated to the cost of knowledge site]. A poster for the protest may be [http://math.ucr.edu/home/baez/elsevier_boycott_poster.pdf found here].

There have since been many reactions to this protest:

=== Reactions from blogs ===

* [http://gowers.wordpress.com/2012/01/23/httpthecostofknowledge-com/ The cost of knowledge], Timothy Gowers, January 23, 2012.
* [http://johncarlosbaez.wordpress.com/2012/01/26/ban-elsevier/ Ban Elsevier], John Baez, January 26, 2012.
* [http://www.scottaaronson.com/blog/?p=891 Boycott Elsevier!], Scott Aaronson, January 26, 2012.
* [http://terrytao.wordpress.com/2012/01/26/the-cost-of-knowledge/ The cost of knowledge], Terence Tao, January 26, 2012.
* [http://dabacon.org/pontiff/?p=5982 Why boycott Elsevier?], Adam Harrow, January 27, 2012.
* [http://cameroncounts.wordpress.com/2012/01/29/publishers-wars/ Publisher's wars], Peter Cameron, January 29, 2012.
* [http://gowers.wordpress.com/2012/01/29/whats-wrong-with-electronic-journals/ What's wrong with electronic journals], Tim Gowers, January 29, 2012.
* [http://sbseminar.wordpress.com/2012/01/30/thinking-about-elsevier-replacements/ Thinking about Elsevier replacements], David Speyer, January 30, 2012.
* [http://blogs.lse.ac.uk/impactofsocialsciences/2012/02/01/stand-down-journal-referee/ Comfort is the death knell of academia: why I’m standing down as a journal referee], Matthew Todd, LSE Impact Blog, February 1, 2012.
* [http://www.scilogs.de/wblogs/blog/detritus/sonstiges/2012-02-01/boykottiert-elsevier-unterst-tzt-open-access Boykottiert Elsevier! Unterstützt Open Access!], Martin Ballaschk, February 1, 2012. (German)
* [http://scholarlykitchen.sspnet.org/2012/02/02/mysteries-of-the-elsevier-boycott Mysteries of the Elsevier Boycott], Rick Anderson, February 2, 2012.
** [http://breakingculture.tumblr.com/post/17112742228/unraveling-boycott-mysteries Unraveling (some of) the mysteries of the Elsevier Boycott], Sean Johnson Andrews, February 6, 2012.
** [http://www.against-the-grain.com/2012/02/multigrain-discussion-another-response-to-the-elsevier-boycott/ Multigrain Discussion: Another Response to the Elsevier Boycott], Chuck Hamaker, February 14, 2012.
* [http://scholarlykitchen.sspnet.org/2012/02/02/the-elsevier-boycott-does-it-make-sense The Elsevier Boycott — Does It Make Sense?], Kent Anderson, February 2, 2012.
* [http://www.michaeleisen.org/blog/?p=890 You are Elsevier: time to overcome our fears and kill subscription journals], Michael Eisen, February 3, 2012.
** [http://scienceblogs.com/denialism/2012/02/eisen_calls_for_elsevier_boyco.php Eisen calls for Elsevier Boycott - but can we all go OA?], Mark Hoofnagle, February 6, 2012.
* [http://stochastictrend.blogspot.com/2012/02/in-defence-of-elsevier.html In Defence of Elsevier], David Stern, February 4, 2012.
* [http://blog.mathunion.org/journals/?no_cache=1&tx_t3blog_pi1%5BblogList%5D%5BshowUid%5D=30&tx_t3blog_pi1%5BblogList%5D%5Byear%5D=2012&tx_t3blog_pi1%5BblogList%5D%5Bmonth%5D=02&tx_t3blog_pi1%5BblogList%5D%5Bday%5D=05&cHash=a2d6424f899302a7ea3b75b9bb591802 More reasons to support the Elsevier boycott], Doug Arnold, IMU blog on mathematical journals, February 5, 2012.
* [http://gowers.wordpress.com/2012/02/08/a-more-formal-statement-about-mathematical-publishing/ A more formal statement about mathematical publishing], Timothy Gowers, February 8, 2012.
* [http://scientopia.org/blogs/drugmonkey/2012/02/08/explaining-resistance-to-the-elsevier-boycott-practicalities/ Explaining resistance to the Elsevier boycott: Practicalities.], DrugMonkey, February 8, 2012.
* [http://neurodojo.blogspot.com/2012/02/whens-scientists-and-published.html When scientists’ and publishers’ motivations align], Zen Faulkes, February 9, 2012.
* [https://etechlib.wordpress.com/2012/02/11/about-the-elsevier-controversy-and-essential-science/ About the Elsevier Controversy and Essential Science], PF Anderson, February 11, 2012.
* [http://www.science3point0.com/palphy/2012/02/12/journal-mega-bundles-thecostofknowledge/ Journal mega-bundles & TheCostOfKnowledge], Ross Mounce, February 12, 2012.
* [http://mathbabe.org/2012/02/13/mathematics-has-an-occupy-moment/ Mathematics has an Occupy moment], Cathy O'Neil, February 13, 2012.
* [http://svpow.wordpress.com/2012/02/13/a-window-of-opportunity-for-elsevier/ A window of opportunity for Elsevier], Mike Taylor, February 13, 2012.
* [http://mhpbooks.com/49648/5000-profs-join-boycott-of-elsevier-publications-in-international-academic-spring/ 5,000 profs join boycott of Elsevier publications in international “academic spring”], Dennis Johnson, February 14, 2012.
* [http://blogs.lse.ac.uk/impactofsocialsciences/2012/02/15/after-elsevier-boycott-green-open-access What comes after the Elsevier boycott? The answer might be found by following the ‘Green’ road to open access], Neil Stewart, LSE Impact Blog, February 15, 2012.
* [http://mhpbooks.com/50115/whats-next-in-the-elsevier-boycott/ What’s next in the Elsevier boycott?], Dennis Johnson, Melville House, February 16, 2012.
* [http://lj.libraryjournal.com/2012/02/opinion/barbara-fister/joining-the-movement-a-call-to-action-peer-to-peer-review/ Joining the Movement: A Call to Action | Peer to Peer Review] Barbara Fister, Library Journal, February 16, 2012
* [http://www.scilogs.de/wblogs/blog/mathematik-im-alltag/allgemein/2012-02-19/boykottiert-elsevier-ich-boykottiere-elsevier Boykottiert Elsevier! Ich boykottiere Elsevier!], Gunter Ziegler, February 19, 2012. (German)
* [http://burttotaro.wordpress.com/2012/02/19/i-am-not-a-radical-but-i-am-boycotting-elsevier/ I am not a radical, but I am boycotting Elsevier], Burt Totaro, February 19, 2012.
* [http://audsandens.blogspot.com/2012/02/taking-control-more-reasons-for.html Taking Control: More Reasons for the Elsevier Boycott], Aaron Barlow, February 20, 2012.
* [http://www.weeklyweinersmith.com/?p=211 The Elsevier Boycott], Zach and Kelly Wienersmith, February 21, 2012. (Podcast)
* [http://scienceblogs.com/webeasties/2012/02/the_future_of_science_pub.php The Future of Science Publishing], Kevin Bonham, February 21, 2012.
* [http://scienceblogs.com/confessions/2012/02/elsevier_boycott_time_for_libr.php Elsevier boycott: Time for librarians to rise up!], John Dupuis, February 21, 2012.
* [http://blogs.lse.ac.uk/impactofsocialsciences/2012/02/22/elsevier-price-boycotters-untruth/ Elsevier have a right to price their journals as they see fit, but they must be honest in their reasoning and not attack boycotters with untruths], Tim Leunig, LSE Impact blog, February 22, 2012.
* [http://thethesiswhisperer.wordpress.com/2012/02/22/the-academic-writers-strike/ The academic writer’s strike], Inger Mewburn, February 22, 2012.
* [http://gigaom.com/2012/02/22/why-do-we-need-academic-journals-in-the-first-place/ Why do we need academic journals in the first place?], Mathew Ingram, GigaOM, February 22, 2012.
* [http://ittakes30.wordpress.com/2012/02/23/why-boycott-elsevier/ Why boycott Elsevier?], Becky Ward, February 23, 2012.

=== News aggregators ===

* [http://news.ycombinator.com/item?id=3494340 Fields medalist Tim Gowers: Elsevier — my part in its downfall], Hacker News, January 21, 2012
* [http://www.reddit.com/r/math/comments/oqirf/one_mathematicians_stance_against_elsevier/ One mathematician's stance against Elsevier], Reddit, January 22, 2012.
* [http://news.ycombinator.com/item?id=3501561 The Cost of Knowledge: Researchers taking a stand against Elsevier], Hacker News, January 23, 2012.
* [http://science.slashdot.org/story/12/01/27/1322234/scientists-organize-elsevier-boycott Scientists organize Elsevier boycott], Slashdot, January 27, 2012.
* [http://www.metafilter.com/112178/Scientists-boycott-Elsevier Scientists boycott Elsevier], Metafilter, January 29, 2012.
* [http://www.reddit.com/r/math/comments/pepuo/thanks_to_angry_mathematicians_elseviers/ Thanks to angry mathematicians, Elsevier's publishing model might be about to go up in smoke], Reddit, February 7, 2012.

=== Coverage by the media ===

* [http://www.theregister.co.uk/2012/01/28/scientists_boycott_elsevier/ Blog blast births boffin boycott of publisher Elsevier], Iain Thomson, the Register, January 28, 2012.
* [http://www.forbes.com/sites/timworstall/2012/01/28/elseviers-publishing-model-might-be-about-to-go-up-in-smoke/ Elsevier's Publishing Model Might be About to Go Up in Smoke], Tim Worstall, Forbes, January 28, 2012.
* [http://www.wired.com/wiredscience/2012/01/testify-the-open-science-movement-catches-fire/ Testify: The Open-Science Movement Catches Fire] David Dobbs, Wired, January 30, 2012.
* [http://chronicle.com/blogs/wiredcampus/elsevier-publishing-boycott-gathers-steam-among-academics/35216 Elsevier Publishing Boycott Gathers Steam Among Academics], Josh Fischman, The Chronicle of Higher Education, January 30, 2012.
* [http://www.techdirt.com/articles/20120130/13030217589/will-academics-boycott-elsevier-be-tipping-point-open-access-another-embarrassing-flop.shtml Will Academics' Boycott Of Elsevier Be The Tipping Point For Open Access -- Or Another Embarrassing Flop?], Glyn Moody, Techdirt, January 31, 2012.
* [http://boingboing.net/2012/01/31/scientists-boycott-elsevier-ov.html Scientists and scholars boycott Elsevier over bad business practices and copyright maximalism], Cory Doctorow, Boingboing, January 31, 2012.
* [http://lj.libraryjournal.com/2012/01/publishing/petition-targeting-elseviers-business-practices-begins-to-snowball/ Petition Targeting Elsevier’s Business Practices Begins to Snowball], Michael Kelley, Library Journal, January 31, 2012.
* [http://www.thebookseller.com/news/academics-call-boycott-elsevier.html Academics call for boycott of Elsevier], Charlotte Williams, The Bookseller, January 31, 2012.
* [http://chronicle.com/article/As-Journal-Boycott-Grows/130600/ As Journal Boycott Grows, Elsevier Defends Its Practices], Josh Fischman, The Chronicle of Higher Education, January 31, 2012.
* [http://arstechnica.com/science/news/2012/01/researchers-boycott-publisher-will-they-embrace-instant-publishing.ars Researchers boycott publisher; will they embrace instant publishing?], John Timmer, Ars Technica, January 31, 2012.
* [http://www.elmundo.es/elmundosalud/2012/01/30/noticias/1327952591.html Boicot científico a Elsevier], Cristina de Martos, El Mundo, January 31, 2012. (Spanish)
* [http://nos.nl/op3/artikel/335992-elsevier-in-de-clinch-met-wetenschappers.html Elsevier in de clinch met wetenschappers], NOS News, January 31, 2012. (Dutch)
* [http://news.sciencemag.org/scienceinsider/2012/02/thousands-of-scientists-vow-to-b.html Thousands of Scientists Vow to Boycott Elsevier to Protest Journal Prices], Jop de Vrieze, Science Insider, February 1, 2012.
* [http://www.mmm-online.com/elsevier-begins-outreach-as-push-back-on-publisher-threatens-to-widen/article/225855/ Elsevier begins outreach as push-back on publisher threatens to widen], Deborah Weinstein, Medical Marketing & Media, February 1, 2012.
* [http://www.care2.com/causes/scientists-fight-for-open-access-for-their-research.html Scientists Fight For Open Access For Research], Kristina Chew, Care2, February 1, 2012.
* [http://www.bloomberg.com/news/2012-02-01/samsung-csr-nfl-elsevier-motorola-intellectual-property.html Samsung, CSR, NFL, Elsevier, Motorola: Intellectual Property], Victoria Slind-Flor, Bloomberg, February 1, 2012. (Brief mention only.)
* [http://mediadecoder.blogs.nytimes.com/2012/02/01/the-breakfast-meeting-a-week-of-negative-ads-and-new-chief-at-sony/ The Breakfast Meeting: A Week of Negative Ads, and New Chief at Sony], Noam Cohen, New York Times, February 1, 2012. (Brief mention only.)
* [http://www.guardian.co.uk/science/2012/feb/02/academics-boycott-publisher-elsevier Scientists sign petition to boycott academic publisher Elsevier], Alison Flood, the Guardian, February 2, 2012.
* [http://blogues.cyberpresse.ca/sciences/2012/02/02/fronde-contre-les-revues-savantes-delsevier/ Étonnante fronde de chercheurs contre les revues savantes d’Elsevier], Jean-François Cliche, le Soleil, February 2, 2012. (French)
* [http://www.wired.com/wiredscience/2012/02/is-the-open-science-revolution-for-real/ Is the Open Science Revolution For Real?], David Dobbs, Wired, February 3, 2012.
* [http://www.economist.com/node/21545974 The price of information], the Economist, February 4, 2012.
* [http://archiv.twoday.net/stories/64967798/ Zum Elsevier-Boykott], Klaus Graf, Archivalia, February 5, 2012. (German)
* [http://paidcontent.org/article/419-academics-revolt-against-elseviers-journal-pricing/ Academics Revolt Against Elsevier’s Journal Pricing], Robert Andrews, PaidContent, February 6, 2012.
* [http://theconversation.edu.au/spread-the-word-scientists-are-tearing-down-publishers-walls-5098 Spread the word: scientists are tearing down publishers' walls], Alex Holcombe, the Conversation, February 7, 2012.
* [http://www2.ljworld.com/news/2012/feb/07/heard-hill-university-senate-considering-boycottin/ Heard on the Hill: University Senate considering boycotting publisher Elsevier; newspaper readership program popular at other places, too; KUMC researcher mentioned in LA Times story on Alzheimer’s], Andy Hyland, LJWorld, February 7, 2012.
* [http://hon.jp/news/modules/rsnavi/showarticle.php?id=3082 欧米圏で“学術の春”運動始まる、電子ジャーナル出版大手Elsevierに対し学者たちのボイコット運動が急拡大], editorial, hon.jp Daywatch, Feb 7, 2012. (Japanese)
* [http://the-scientist.com/2012/02/07/occupy-elsevier/ Occupy Elsevier?], Bob Grant, the Scientist, February 7, 2012.
* [http://www.theaustralian.com.au/higher-education/academics-boycott-publisher-elsevier/story-e6frgcjx-1226265110496?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+TheAustralianHigherEducationNews+%28The+Australian+%7C+Higher+Education%29&utm_content=Google+Reader Academics boycott publisher Elsevier], Bernard Lane, the Australian, February 8, 2012.
* [http://latimesblogs.latimes.com/jacketcopy/2012/02/wed-book-news-bezos-the-elsevier-boycott-and-more.html Wednesday book news: Bezos, the Elsevier boycott and more], Carolyn Kellogg, Los Angeles Times, February 8, 2012. (Brief mention only.)
* [http://www.guardian.co.uk/higher-education-network/blog/2012/feb/08/open-access-journals-elsvier-boycott Open access journals: are we asking the right questions?], Martin Paul Eve, the Guardian, February 8, 2012.
* [http://www.varsity.co.uk/news/4370 The Academic Spring], Patrick O'Grady, Varsity, February 8, 2012.
* [http://www.timeshighereducation.co.uk/story.asp?sectioncode=26&storycode=418952 Elsevier defends stance on anti-open-access bill], John Gill, Times Higher Education, February 9, 2012.
* [http://www.nature.com/news/elsevier-boycott-gathers-pace-1.10010 Elsevier boycott gathers pace], John Whitfield, Nature, February 9, 2012.
* [http://www.wired.com/wiredscience/2012/02/open-science-revolt-occupies-congress/ Open Science Revolt Occupies Congress], David Dobbs, Wired, February 9, 2012.
* [http://blogs.independent.co.uk/2012/02/09/the-future-of-academic-publishing/ The future of academic publishing], Mike Taylor, the Independent, February 9, 2012.
* [http://www.tcs.cam.ac.uk/issue/news/cambridge-professor-leads-boycott-of-elsevier-publications/ Cambridge Professor leads boycott of Elsevier Publications], Emily Loud, the Cambridge Student Online, February 9, 2012.
* [http://www.utimes.pitt.edu/?p=19679 Protest launched against journal publisher], Kimberly Barlow, University Times, February 9, 2012.
* [http://jeps.efpsa.org/blog/2012/02/10/a-revolution-in-scientific-publishing/ A revolution in scientific publishing?], Sina Scherer, JEPS Bulletin, February 10, 2012.
* [http://libraries.mit.edu/sites/news/elsevier-boycott-grows/7785/ Elsevier Boycott Grows: MIT Faculty Speak About Participation], Ellen Duranceau, MIT Libraries News, February 10, 2012.
* [http://www1.folha.uol.com.br/ciencia/1046769-cientistas-boicotam-a-maior-editora-de-periodicos-do-mundo.shtml Cientistas boicotam a maior editora de periódicos do mundo], Sabine Righetti, Folha, February 10, 2012. (Portugese)
* [http://www.bostonglobe.com/opinion/2012/02/12/why-scientists-are-boycotting-publisher/9sCpDEP7BkkX1INfakn3NL/story.html Why scientists are boycotting a publisher], Gareth Cook, the Boston Globe, February 12, 2012.
** [http://bostonglobe.com/opinion/letters/2012/02/16/elsevier-committed-universal-access-content-sustainable-publishing-model/70QfCpSOvy0IUibSK6eCTL/story.html Elsevier committed to universal access to content, sustainable publishing model], Lynne Herndon (former CEO of Cell press), letter to the editor, the Boston Globe, February 16, 2012.
*** [http://quomodocumque.wordpress.com/2012/02/16/elseviers-sorry-defense-of-the-research-works-act/ Elsevier’s sorry defense of the Research Works Act], Jordan Ellenberg, February 16, 2012.
* [http://newsbreaks.infotoday.com/NewsBreaks/The-Cost-of-Knowledge-Versus-Elsevier--Signatures-and-Growing-80575.asp The Cost of Knowledge Versus Elsevier: 5,600 Signatures and Growing], Robin Peek, Information Today, February 13, 2012.
* [http://www.pourlascience.fr/ewb_pages/a/actualite-la-fronde-des-chercheurs-contre-i-elsevier-i-29118.php La fronde des chercheurs contre Elsevier], Maurice Mashaal, Pour la Science, February 13, 2012.
* [http://www.newscientist.com/article/dn21467-web-freedoms-fuel-academic-spring-journal-protest.html Web freedoms fuel 'academic spring' journal protest], Jacob Aron, New Scientist, February 13, 2012.
* [http://www.nytimes.com/2012/02/14/science/researchers-boycott-elsevier-journal-publisher.html Mathematicians Organize Boycott of a Publisher], Thomas Lin, New York Times, February 13, 2012.
* [http://motherjones.com/blue-marble/2012/02/science-uprising Science Uprising], Julia Whitty, Mother Jones, February 13, 2012.
* [http://www.kansan.com/news/2012/feb/13/professors-boycott/ Professors boycott prominent publishing company], Kelsey Cipolla, The University Daily Kansan, February 13, 2012.
* [http://www.purdueexponent.org/opinion/editorials/article_a6e96c79-5c95-54b8-bf85-eca8de6bb3db.html Monopoly on research publishing is unethical], Editorial, The Exponent, February 14, 2012.
* [http://today.duke.edu/2012/02/elsevierboycott Duke Scholars Join Boycott Against Elsevier], Ashley Yeager, Duke Today, February 14, 2012.
* [https://theconversation.edu.au/academics-line-up-to-boycott-worlds-biggest-journal-publisher-5384 Academics line up to boycott world’s biggest journal publisher], Justin Norrie, the Conversation, February 15, 2012.
* [http://www.ft.com/cms/s/0/2494fbc4-5873-11e1-9f28-00144feabdc0.html Reed chief hits back at critics of division], Salamander Davoudi, February 16, 2012.
* [http://www.timeshighereducation.co.uk/story.asp?storycode=419018 Occupy publishing], Timothy Gowers, Times Higher Education, February 16, 2012.
* [http://www.abc.net.au/science/articles/2012/02/17/3433568.htm Academics boycott journal publisher], Eleanor Bell, ABC news, February 17, 2012.
* [http://www.onthemedia.org/2012/feb/17/trouble-elsevier-leading-academic-publisher/ Trouble for Elsevier, the leading academic publisher], Rick Karr, On the media, NPR, February 17, 2012. (Audio)
** [http://crookedtimber.org/2012/02/21/some-questions-for-elsevier/ Some questions for Elsevier], Harry Brighouse, Crooked Timber, February 21, 2012.
* [http://blogs.theaustralian.news.com.au/thecommonroom/index.php/theaustralian/comments/journal_publishers_in_strife_and_in_denial/ Journal publishers: in strife and in denial], The common room blog, The Australian, February 20, 2012.
* [http://www.smh.com.au/national/education/academics-join-world-fight-against-publisher-20120220-1tjk6.html Academics join world fight against publisher], Nicky Phillips, Sydney Morning Herald, February 21, 2012.
* [http://blogs.discovermagazine.com/crux/2012/02/21/its-not-academic-how-publishers-are-squelching-science-communication/ It’s Not Academic: How Publishers Are Squelching Science Communication], Michael Taylor, Discover Magazine, February 21, 2012.
* [http://www.theaustralian.com.au/higher-education/nhmrc-ceo-supports-elsevier-boycott-says-all-research-must-be-made-open-access/story-e6frgcjx-1226278163029 NHMRC CEO supports Elsevier boycott; says all research must be made open access], Julie Hare, The Australian, February 22, 2012.
* [http://www.wired.com/wiredscience/2012/02/elsevier-boycott-not-a-petition-but-a-declaration-of-independence/ Elsevier Boycott Not a Petition, But “A Declaration of Independence”], David Dobbs, Wired Magazine, February 22, 2012.
* [http://www.insidehighered.com/blogs/library-babel-fish/why-are-we-boycotting-elsevier Why Are We Boycotting Elsevier?], Barbara Fister, Inside Higher Ed, February 24, 2012.

=== Open letters to Elsevier ===

* [http://math.berkeley.edu/~kirby/elsevier.html Letter to Elsevier], Rob Kirby, December 30, 1997.
* [http://www.library.yale.edu/~llicense/ListArchives/0310/msg00048.html Call for Boycott of Cell Press Journals], Peter Walter and Keith Yamomoto, October 19, 2003.
** [http://genomebiology.com/2003/4/10/spotlight-20031024-02 Researchers boycott Cell Press], Alison McCook, Genome Biology, October 24, 2003.
* [http://www.cs.colorado.edu/~hal/jalg.html Journal of Algorithms editorial board resignation], December 13, 2003.
* [http://math.ucr.edu/home/baez/topology-letter.pdf Topology editorial board resignation letter], August 10, 2006.
* [http://idiolect.org.uk/elsevier/docs/academics_openletter.pdf Arms fairs and academics], 138 signatories, February 28, 2007.
* [http://idiolect.org.uk/notes/?p=643 An open letter to Elsevier and all those involved in the IEHG], Keith Halfacree, April 10, 2007.
* [http://www.coar-repositories.org/news/coar-writes-open-letter-as-reaction-to-elseviers-practices/ Open Letter to Elsevier], Norbert Lossau, Chair of the Executive Board, Confederation of Open Access Repositories, February 6, 2012.
* [https://plus.google.com/105282922684661032446/posts/WCZqgPVehmx Letter to Elsevier], Cynthia Parr, February 10, 2012.
* [http://darwin.eeb.uconn.edu/uncommon-ground/2012/02/declining-elsevier.html Declining elsevier], Kent Holsinger, February 10, 2012.
* [http://occamstypewriter.org/scurry/2012/02/12/an-open-letter-to-elsevier/ An Open Letter to Elsevier], Stephen Curry, February 12, 2012.
* [http://svpow.wordpress.com/2012/02/15/a-response-to-one-elsevier-employee-and-an-open-letter-to-the-rest/ A response to one Elsevier employee, and an open letter to the rest], Matt Wedel, February 15, 2012.
* [http://fakeelsevier.wordpress.com/2012/02/19/dear-elsevier-employees-with-love-from-fakeelsevier/ Dear Elsevier employees, with love, from @FakeElsevier], FakeElsevier, February 19, 2012.

=== Responses by Elsevier ===

* [http://gowers.wordpress.com/2012/01/21/elsevier-my-part-in-its-downfall/#comment-14679 A response by David Clark at Elsevier], January 23, 2012.
* [http://www.elsevier.com/wps/find/intro.cws_home/elsevieropenletter An open letter to the research community: journal prices, discounts, and access], Elsevier, undated as of Feb 6, 2012.
** [http://bjoern.brembs.net/news.php?item.833.11 Against Own Assertion, Elsevier Doubled Price For Access], Bjorn Brembs, February 11, 2012.
** [http://gowers.wordpress.com/2012/02/26/elseviers-open-letter-point-by-point-and-some-further-arguments/ Elsevier’s open letter point by point, and some further arguments], Timothy Gowers, February 26, 2012.
* [http://www.epjournal.net/blog/2012/02/elsevier-and-evolution-human-behavior/ Elsevier and Evolution & Human Behavior], Robert Kurzban (co-editor-in-chief of the Elsevier journal Evolution & Human Behavior), February 6, 2012.
* [http://poynder.blogspot.com/2012/02/elseviers-alicia-wise-on-rwa-west-wing.html Elsevier’s Alicia Wise on the RWA, the West Wing, and Universal Access], Richard Poynder, February 9, 2012.
* [http://www.elsevier.com/wps/find/intro.cws_home/newmessagerwa Elsevier withdraws support for the Research Works Act], Elsevier, Feb 27, 2012.
*[http://www.elsevier.com/wps/find/P11.cws_home/lettertothecommunity A letter to the mathematics community], Elsevier, Feb 27, 2012.

=== Other coverage ===

* [http://www.arl.org/sparc/media/prime-time-for-public-access.shtml Prime Time for Public Access], Heather Joseph, Executive Director, SPARC, February 9, 2012.
* [http://www.openaire.eu/en/news-a-events/news/343-elseviers-practices-opposing-open-access Elsevier’s practices opposing open access], Open Access Infrastructure for Research in Europe, February 16, 2012.
* [http://www.insidehighered.com/views/2012/02/23/essay-open-access-scholarship Values and Scholarship], Joint letter by eleven research provosts, Inside Higher Ed, February 23, 2012.
* [http://en.wikipedia.org/wiki/The_Cost_of_Knowledge The wikipedia page] for this protest.

See also [http://scienceblogs.com/confessions/2012/02/around_the_web_research_works.php this list of links], which is focused more around the Research Works Act, but also contains many links regarding the boycott, as well as [http://www.math.ntnu.no/~stacey/Mathforge/Math2.0 Math 2.0], a discussion forum for all topics related to the future of mathematical publishing.

== Other pledges, boycotts, and petitions ==

* [http://www.researchwithoutwalls.org/ Research Without Walls]
* [http://www.openaccesspledge.com/ Open Access Pledge]
* [http://www-fourier.ujf-grenoble.fr/petitions/index.php?petition=3 Appel pour des négociations équilibrées avec les éditeurs de revues scientifiques] - a petition concerning the bundling and pricing practices of Springer
* [http://www.thepetitionsite.com/207/support-the-open-access-movement-stop-the-research-works-act/?cid=FB_TAF A petition to stop the Research Works Act]
* [http://www.taxpayeraccess.org/action/FRPAA2012.shtml Call to action: Tell Congress you support the Bipartisan Federal Research Public Access Act (H.R. 4004 and S. 2096)], Alliance for taxpayer access, February 9, 2012.

* See these tag libraries from the [http://oad.simmons.edu/oadwiki/OA_tracking_project Open Access Tracking Project] (more comprehensive after April 2009 than before):
** [http://www.connotea.org/tag/oa.boycotts oa.boycotts]
** [http://www.connotea.org/tag/oa.declarations oa.declarations]
** [http://www.connotea.org/tag/oa.petitions oa.petitions]
** [http://www.connotea.org/tag/oa.pledges oa.pledges]

== Other blog posts, letters, and opinion pieces ==
* [http://math.berkeley.edu/~kirby/journals.html Comparative price of math journals], Rob Kirby, May 27, 1997.
** [http://math.berkeley.edu/~kirby/elsevier.html Open letter to Elsevier], Rob Kirby, December 30, 1997.
** [http://math.berkeley.edu/~kirby/jp00.html 2000 data update]
* [http://www.ams.org/notices/200007/forum-birman.pdf Scientific Publishing: A Mathematician’s Viewpoint], Joan Birman, Notices of the American Mathematical Society, 770-774, July 2000.
* [http://homepages.cwi.nl/~apt/ps/cacm01.pdf One More Revolution to Make: Free Scientific Publishing], Krzysztof R. Apt, Communications of ACM, 44(5), pp. 25-28, 2001.
* [http://www.nieuwarchief.nl/serie5/deel02/sep2001/pdf/apt.pdf Towards free access to scientific literature], Krzysztof R. Apt, Nieuw Archief voor Wiskunde, 5/2 nr. 3, September 2001, pp. 251-255.
* [http://stromme.uib.no/kuperberg.pdf Scholarly Mathematical Communication at a Crossroads], Greg Kuperberg, Nieuw Arch. Wisk., (5) 3 no.3, September 2002.
* [http://people.ccmr.cornell.edu/~ginsparg/blurb/pg02pr.html Can Peer Review be better Focused?], Paul Ginsparg, March 2003.
* [http://www.ams.org/notices/200402/commentary.pdf Fleeced?], Rob Kirby, Notices of the American Mathematical Society, 161-162, February 2004.
* [http://www.ams.org/notices/200405/commentary.pdf We can make a change], Gerard van der Geer, Notices of the American Mathematical Society, May 2004.
* [http://www.math.columbia.edu/~neumann/journal.html What we can do about journal pricing], Walter Neumann, September 2005.
** The discussions mentioned in that email led to the [http://web.archive.org/web/20110525195311/http://members.cox.net/banffprotocol/ Banff protocol] (web site now only available through web archive).
* [http://www.scottaaronson.com/writings/journal.html Review of The Access Principle by John Willinsky], Scott Aaronson, 2006
* [http://digitalstrategies.blogspot.com/2008/06/scientific-publication-in-internet-era.html Scientific Publishing in the Internet Era] Efthymios Constantinides June 17, 2008
* [http://arstechnica.com/science/news/2008/11/elsevier-beyond-the-pale-of-scientific-respectability.ars Publishing economics harm science's credibility], Chris Lee, Ars Technica, November 2008.
* [http://www.ima.umn.edu/~arnold/siam-columns/integrity-under-attack.pdf Integrity under attack: The State of Scholarly Publishing], Douglas Arnold, SIAM news, December 2009.
* [http://scholarlykitchen.sspnet.org/2010/01/04/why-hasnt-scientific-publishing-been-disrupted-already/ Why Hasn’t Scientific Publishing Been Disrupted Already?], Michael Clarke, January 4, 2010.
* [http://math.ucr.edu/home/baez/journals.html What We Can Do About Science Journals], John Baez, January 24, 2011.
* [http://blog.mathunion.org/journals/?no_cache=1&tx_t3blog_pi1%5BblogList%5D%5BshowUid%5D=17&tx_t3blog_pi1%5BblogList%5D%5Byear%5D=2011&tx_t3blog_pi1%5BblogList%5D%5Bmonth%5D=12&tx_t3blog_pi1%5BblogList%5D%5Bday%5D=07&cHash=bb9177d8192db5b5756aca088ea79677 What might be done about high prices of journals?], IMU blog on mathematical journals, July 12, 2011.
* [http://www.monbiot.com/2011/08/29/the-lairds-of-learning/ The lairds of learning] George Monbiot, August 29, 2011.
** [http://sedgemore.com/2011/09/serials-crisis-and-corn-laws/ Serials crisis and corn laws], Francis Sedgemore, September 7, 2011.
* [http://www.guardian.co.uk/commentisfree/2011/aug/29/academic-publishers-murdoch-socialist Academic publishers make Murdoch look like a socialist], George Monbiot, the Guardian, August 29, 2011.
* [http://www.timeshighereducation.co.uk/story.asp?storycode=417576 Peers, review your actions], Michael Taylor, Times Higher Education, September 29, 2011.
* [http://gowers.wordpress.com/2011/10/31/how-might-we-get-to-a-new-model-of-mathematical-publishing/ How might we get to a new model of mathematical publishing?], Timothy Gowers, October 31, 2011.
** [http://gowers.wordpress.com/2011/11/03/a-more-modest-proposal/ A more modest proposal], Timothy Gowers, November 3, 2011.
** [http://boolesrings.org/krautzberger/2011/11/26/the-recent-publishing-debate-a-timeline/ A timeline of the debate initiated by this post], Peter Krautzberger, November 26, 2011.
* [http://www.nytimes.com/2012/01/11/opinion/research-bought-then-paid-for.html Research Bought, Then Paid For], Michael B. Eisen, New York Times opinion piece, January 10, 2012
** [http://www.nytimes.com/2012/01/23/opinion/should-research-be-more-freely-available.html?_r=1 Should Research Be More Freely Available?], Jeffrey M. Drazen (Editor in Chief of The New England Journal of Medicine), Gene D. Sprouse (treasurer of [http://www.aps.org APS]), and Joseph W. Serene (publisher at [http://www.aps.org APS]), letters to the New York Times, January 23, 2012.
* [http://www.guardian.co.uk/science/2012/jan/16/academic-publishers-enemies-science?CMP=twt_fd Academic publishers have become the enemies of science], Mike Taylor, the Guardian, January 16, 2011.
** [http://www.guardian.co.uk/science/2012/jan/27/academic-publishers-enemies-science-wrong Branding academic publishers 'enemies of science' is offensive and wrong], Graham Taylor, January 27, 2011.
** [http://nelh.blogspot.com/2012/02/elsevier-double-dipping-and-nhs.html Elsevier, double-dipping, and the NHS], Ben Toth, February 11, 2012.
* [http://www.michaeleisen.org/blog/?p=873 Nature’s shiny sounding copout on open access], Michael Eisen, January 26, 2012.
* [http://svpow.wordpress.com/2012/01/27/publishers-invent-a-whole-new-form-of-evil-suing-their-customers/ Publishers invent a whole new form of evil: suing their customers], Mike Taylor, SV-POW, January 27, 2012.
* [http://occamstypewriter.org/scurry/2012/01/28/why-i-chose-to-decline-an-invitation-to-review-by-elsevier/ Why I chose to decline an invitation to review by Elsevier], Stephen Curry, January 28, 2012.
* [http://sbseminar.wordpress.com/2012/02/01/journals-and-the-arxiv/ Journals and the arXiv], Scott Morrison, February 1, 2012.
* [http://occupypublishing.blogspot.com.au/2012/02/scientific-journals-in-e-publishing-age.html scientific journals in the e-publishing age], Phillip Thrift, February 1, 2012.
* [http://gowers.wordpress.com/2012/02/02/abstract-thoughts-about-online-review-systems Abstract thoughts about online review systems], Tim Gowers, February 2, 2012.
* [http://cameronneylon.net/blog/the-research-works-act-and-the-breakdown-of-mutual-incomprehension/ The Research Works Act and the breakdown of mutual incomprehension], Cameron Neylon, February 3, 2012.
* [http://sbseminar.wordpress.com/2012/02/09/a-forum-on-mathematical-publishing/ A forum on mathematical publishing], Scott Morrison, February 9, 2012.
* [http://vort.org/2012/02/09/moral-imperative-open-science/ The moral imperative for Open Science], Russell Neches, February 9, 2012.
* [http://johncarlosbaez.wordpress.com/2012/02/10/the-federal-research-public-access-act/ The Federal Research Public Access Act], John Baez, February 10, 2012.
* [http://www.guardian.co.uk/science/blog/2012/feb/10/parable-farmers-teleporting-duplicator The parable of the farmers and the Teleporting Duplicator], Michael Taylor, the Guardian, February 10, 2012.
* [http://svpow.wordpress.com/2012/02/11/why-isnt-anyone-publishing-open-access-articles-in-elsevier-journals/ Why isn’t anyone publishing open-access articles in Elsevier journals?], Mike Taylor, February 11, 2012.
* [http://michaelnielsen.org/blog/how-you-can-help-the-federal-research-public-access-act-frpaa-become-law/ How you can help the Federal Research Public Access Act (FRPAA) become law], Michael Nielsen (interviewing Heather Joseph), February 14, 2012.
* [http://lisnews.org/elsevier_filters_recommendation_engine_to_show_elsevier_titles_only Elsevier Filters Recommendation Engine to Show Elsevier Titles Only], LISNews, February 14, 2012.
* [http://techcrunch.com/2012/02/15/the-dangerous-research-works-act/ The Dangerous “Research Works Act”], Richard Price, TechCrunch, February 15, 2012.
* [http://www.ethlife.ethz.ch/archive_articles/120217_bibliothek_neubauer/index_EN A thorn in the side for science publishers], Wolfram Neubauer, February 17, 2012.
** [http://johncarlosbaez.wordpress.com/2012/02/20/elsevier-and-springer-sue-university-library/ Elsevier and Springer Sue University Library], John Baez, February 20, 2012.
* [http://www.newsday.com/opinion/make-tax-funded-scientific-research-public-1.3555902 Make tax-funded scientific research public], Editorial, Newsday, February 26, 2012.
* [http://ilaba.wordpress.com/2012/02/26/women-in-math-and-the-overhaul-of-the-publishing-system/ Women in math, and the overhaul of the publishing system], Izabella Laba, February 26, 2012.

== Media ==

* [http://www.nature.com/nature/journal/v445/n7126/full/445347a.html PR's 'pit bull' takes on open access], Jim Giles, Nature, January 25, 2007. Summary: A coalition of scientific publishers (including Elsevier, Wiley, and the American Chemical Society) organises to oppose open access.
* [http://www.guardian.co.uk/business/2008/may/30/armstrade.weaponstechnology Reed Elsevier makes its final farewell to arms], Katie Allen, the Guardian, 30 May 2008. Summary: Reed Elsevier was until 2009 organizing arms trade fairs.
** [http://www.acme-journal.org/vol8/Stafford09.pdf Lessons from the Campaign against Elsevier "We won, but how did we win?"], Tom Stafford, ACME: An International E-Journal for Critical Geographies 2009, 8 (3), 494-504.
** [http://www.caat.org.uk/issues/armsfairs/reedelsevier.php Campaign success: Reed Elsevier sells international arms fairs], Campaign against arms trade, March 9, 2009.
* [http://classic.the-scientist.com/blog/display/55679/ Elsevier Published 6 Fake Journals], Bob Grant, The Scientist, May 7, 2009. Summary: Elsevier was paid by unnamed pharmaceutical companies to publish six journals that looked like independent peer-reviewed medical journals, but which were not.
** [http://en.wikipedia.org/wiki/Australasian_Journal_of_Bone_%26_Joint_Medicine The wikipedia page on these six journals].
** The Elsevier fake-journal tally eventually rose to [http://www.earlham.edu/~peters/fos/2009/06/elsevier-fake-journal-tally-now-9.html nine].
** [http://www.guardian.co.uk/commentisfree/2009/may/09/bad-science-medical-journals-companies The danger of drugs... and data], Ben Goldacre, the Guardian, May 8, 2009.
** [http://www.elsevier.com/wps/find/authored_newsitem.cws_home/companynews05_01203 Elsevier press release on this incident], May 7, 2009.
* [http://www.insidehighered.com/news/2009/06/23/elsevier Elsevier Won't Pay for Praise], Scott Jashik, Inside Higher Ed, June 23, 2009. Summary: Elsevier suspends its practice of offering Amazon gift cards to anyone who would give their textbooks a five-star rating.

== Other Information ==

* '''On Elsevier'''
** [http://www.reed-elsevier.com/mediacentre/pressreleases/Documents/2010/Reed%20Elsevier%202009%20Results%20Announcement%2017%20February%202010%20FINAL.pdf Reed Elsevier's 2009 report] Elsevier reported a profit of 1.1 billion dollars on revenue of 3.2 billion dollars.
** [http://en.wikipedia.org/wiki/Elsevier#Criticism_and_controversies Criticism and controversies of Elsevier] (Wikipedia)
** [http://gizmodo.com/5870241 Elsevier support for the Stop Online Piracy Act (SOPA)] (Gizmodo)
*** [http://en.wikipedia.org/wiki/List_of_organizations_that_support_the_Stop_Online_Piracy_Act List of organizations with official stances on the Stop Online Piracy Act] (Wikipedia)
** [http://www.michaeleisen.org/blog/?p=846 Elsevier support for the Research Works Act (RWA)] (Michael Nielsen)
*** [http://poynder.blogspot.com/2012/01/elsevier-needs-to-get-out-more.html Elsevier needs to get out more] (Richard Poynder)
*** [http://freethoughtblogs.com/pharyngula/2012/01/16/elsevier-evil/ Elsevier = evil] (Phyrangula)
*** [http://www.michaeleisen.org/blog/?p=807 Elsevier-funded NY Congresswoman Carolyn Maloney Wants to Deny Americans Access to Taxpayer Funded Research] (Michael Eisen)
**** [http://www.michaeleisen.org/blog/?p=807#comment-52048 A response by Tom Reller] (Vice President and Head of Global Corporate Relations at Elsevier)
*** Note however that the editorial board of [http://www.thelancet.com/ the Lancet], a very prestigious medical journal published by Elsevier, has [http://www.thelancet.com/journals/lancet/article/PIIS0140-6736(12)60125-1/fulltext come out strongly against the Research Works Act].
*** [http://www.elsevier.com/wps/find/intro.cws_home/elsevierstatement A message to the research community: Elsevier, access, and the Research Works Act], Elsevier, undated as of Feb 6 2012.
** [http://www.whitehouse.gov/sites/default/files/microsites/ostp/scholarly-pubs-%28%23168%29%20Elsevier%20submission.pdf Elsevier submission to the Office of Science and Technology Policy on open access], January 2012.
*** [http://openaccess.kb.se/?p=637 Elsevier tries to block institutional OA mandates], Jan Hagerlid, January 31, 2012.
** [http://www.researchinformation.info/riaut03elsevier.html Why commercial publishers are good for research], Arie Jongejan, CEO Science & Technology, Elsevier, Autumn 2003.
** [http://www.elsevier.com/wps/find/authorsview.authors/preprints Elsevier's policy on authors making their papers available on preprint servers] (Short version: Elsevier allows draft versions of papers to be placed on public servers such as the arXiv, and revised versions of papers to be placed on personal or institutional pages, but final versions of papers are only permitted at the journal site itself.)

* '''Stock analyses and financial data of Elsevier and other publishers'''
** [http://www.econ.ucsb.edu/~tedb/Journals/morganstanley.pdf Scientific Publishing: Knowledge is Power], Morgan Stanley, September 20, 2002.
** [http://dl.dropbox.com/u/4398178/Reciprocal%20Space%20Files/001-BR-EndoftheBigDeal-2011.pdf Reed Elsevier: The inevitable crunch point – downgrading to under perform because of growing concerns on Elsevier], Bernstein Research, March 10, 2011.
** [http://dl.dropbox.com/u/4398178/Reciprocal%20Space%20Files/002-BR-ElsevierNegotiations-2011.pdf Reed Elsevier, Bringing down the house – Why Elsevier is vulnerable in its upcoming Big Deal negotiations], Bernstein Research, March 29, 2011.
** [http://dl.dropbox.com/u/4398178/Reciprocal%20Space%20Files/003-BR-ReedCostofKnowledge-2012.pdf Occupy Elsevier], Bernstein Research, February 6, 2012.
** [https://plus.google.com/117663015413546257905/posts/1xRiEyWnipc Noise around boycott against Elsevier offers short term trading opportunity], Exane Paribas, February 7, 2012.
*** [http://cameronneylon.net/blog/a-tale-of-two-analysts/ A tale of two analysts], Cameron Neylon, February 15, 2012.
* [http://www.sec.gov/Archives/edgar/data/929869/000095012311023614/u10507e20vf.htm Reed Elsevier's 2012 annual report (form 20-F) filing with the SEC]

* '''On open access'''
** [http://en.wikipedia.org/wiki/Open_access Open Access]
** [http://oad.simmons.edu Open Access Directory]
** [http://www.earlham.edu/~peters/fos/overview.htm Open Access Overview] (Peter Suber)

* '''On scholarly journals'''
** [http://www.unc.edu/scholcomdig/whitepapers/panitch-michalak.html The serials crisis] Judith Panitch and Sarah Michalak, A White Paper for the UNC-Chapel Hill Scholarly Communications Convocation, January, 2005.
** [http://www.ams.org/membership/mem-journal-survey AMS Journal Price Survey]
*** [http://www.mathematik.uni-bielefeld.de/~rehmann/BIB/AMS/Publisher.html Math Journal Price Survey], from 2008 data.
** [http://en.wikipedia.org/wiki/Serials_crisis Journal subscription prices have increased far more rapidly than either inflation or spending on research]
** [http://www.mcafee.cc/Journal/Summary.pdf A summary of journal price averages in various disciplines including mathematics as of 2010] (see also [http://www.mcafee.cc/Journal/ the parent site, which contains more detailed information]).
** [http://www.econ.ucsb.edu/~tedb/Journals/BundleContracts.html Big Deal Contract Project] - an analysis of journal bundling contracts, and the attempts by publishers such as Elsevier to prevent them from becoming public.
** [http://oad.simmons.edu/oadwiki/OA_journal_business_models Open access journal business models] (from the Open Access Directory)
** [http://www.mathunion.org/fileadmin/CEIC/bestpractice/bpfinal.pdf Best Current Practices for Journals], endorsed by the International Mathematical Union general assembly, August 16, 2010.
** [http://www.msri.org/attachments/workshops/587/MSRIfinalreport.pdf Mathematics journals: what is valued and what may change], Report of the workshop held at MSRI, Berkeley, California on February 14 – 16 2011.

* '''Miscellaneous links'''
** [http://www.math.umd.edu/research/crisis.html The Crisis in Scientific Publishing] - a collection of links hosted by the University of Maryland.
** [http://www.azimuthproject.org/azimuth/show/Academic+publishing Academic publishing] - a wiki collection of links at the Azimuth project.

== Elsevier mathematics journals ==

This list is taken from [http://www.elsevier.com/wps/find/P11.cws_home/mathjournals here]

* [http://www.elsevier.com/wps/find/journaldescription.cws_home/708310/ Acta Mathematica Scientia]
* [http://www.elsevier.com/locate/yaama Advances in Applied Mathematics]
* [http://www.elsevier.com/locate/advengsoft Advances in Engineering Software]
* [http://www.journals.elsevier.com/advances-in-mathematics/ Advances in Mathematics]
* [http://www.elsevier.com/locate/anihpc Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire]
* [http://www.elsevier.com/locate/apal Annals of Pure & Applied Logic]
* [http://www.elsevier.com/wps/find/journaldescription.cws_home/600714 Annales Scientifiques de l'École Normale Supérieure] (Until 2008)
** This journal is [http://www.math.ens.fr/edition/annales/ now published by the Société mathématique de France].
* [http://www.elsevier.com/locate/arcontrol Annual Reviews in Control]
* [http://www.journals.elsevier.com/applied-and-computational-harmonic-analysis/ Applied & Computional Harmonic Analysis]
** Ingrid Daubechies resigned her position as editor-in-chief in 2012, according to her statement on [http://thecostofknowledge.com the Elsevier boycott site].
* [http://www.elsevier.com/locate/apm Applied Mathematical Modelling]
* [http://www.elsevier.com/locate/amc Applied Mathematics & Computation]
* [http://www.journals.elsevier.com/applied-mathematics-letters/ Applied Mathematics Letters]
** [http://retractionwatch.wordpress.com/2011/06/13/applied-mathematics-letters-posts-apology-for-retracting-intelligent-design-friendly-paper/ Applied Mathematics Letters posts apology for retracting Intelligent Design-friendly paper], Retraction Watch, 13 June 2011.
** [http://www.timeshighereducation.co.uk/story.asp?sectioncode=26&storycode=416514&c=1 Second thoughts result in payout], Paul Jump, Times Higher Education, 16 June 2011.
* [http://www.elsevier.com/locate/apnum Applied Numerical Mathematics]
* [http://www.elsevier.com/locate/artint Artificial Intelligence]
* [http://www.elsevier.com/locate/automatica Automatica]
* [http://www.elsevier.com/locate/btt Biometric Technology Today]
* [http://www.elsevier.com/locate/biosystems Biosystems]
* [http://www.elsevier.com/locate/bulsci Bulletin des Sciences Mathématiques]
* [http://www.journals.elsevier.com/chaos-solitons-and-fractals/ Chaos, Solitons & Fractals]
** There was a significant amount of controversy regarding the quality control at this journal during the tenure of a past editor-in-chief, who stepped down in 2009. Unfortunately, most of the primary reporting on this has been taken down due to ongoing litigation.
** [http://en.wikipedia.org/wiki/Elsevier#Chaos.2C_Solitons_.26_Fractals The Wikipedia section on this issue]
** [http://sbseminar.wordpress.com/2008/11/30/laffaire-el-naschie/ L’affaire El Naschie], Secret Blogging Seminar, November 30, 2008.
** [http://www.ima.umn.edu/~arnold/siam-columns/integrity-under-attack.pdf Integrity under attack: The State of Scholarly Publishing], Douglas Arnold, SIAM news, December 2009.
** [http://www.bbc.co.uk/news/science-environment-15697636 Nature journal libel case begins], Pallab Ghosh, BBC News, November 11, 2011.
* [http://www.elsevier.com/locate/cnsns Communications in Nonlinear Science and Numerical Simulation]
* [http://www.elsevier.com/wps/find/journaldescription.cws_home/600301/description#description Comptes Rendus Mathematique]
* [http://www.elsevier.com/locate/comgeo Computational Geometry]
* [http://www.elsevier.com/locate/csda Computational Statistics & Data Analysis]
* [http://www.elsevier.com/locate/cma Computer Methods in Applied Mechanics and Engineering]
* [http://www.journals.elsevier.com/computers-and-mathematics-with-applications Computers & Mathematics with Applications]
** [http://www.sciencedirect.com/science/article/pii/S0898122109005070 A computer application in mathematics], M. Sivasubramanian, S. Kalimuthu, in Computers and Mathematics with Applications, vol. 59 (2010) pp. 296-297. (This article is discussed in [http://blog.mathunion.org/journals/?no_cache=1&tx_t3blog_pi1%5BblogList%5D%5BshowUid%5D=30&tx_t3blog_pi1%5BblogList%5D%5Byear%5D=2012&tx_t3blog_pi1%5BblogList%5D%5Bmonth%5D=02&tx_t3blog_pi1%5BblogList%5D%5Bday%5D=05&cHash=a2d6424f899302a7ea3b75b9bb591802 this blog post] on the IMU mathematics journal blog, and is also available [http://www.math.hkbu.edu.hk/~ttang/newspaper/funnyarticle11.pdf here].)
** The editorial board [http://about.elsevier.com/pdf/LetterFromEditor.pdf was replaced in 2012].
* [http://www.elsevier.com/locate/conengprac Control Engineering Practice]
* [http://www.elsevier.com/locate/difgeo Differential Geometry and its Applications]
* [http://www.elsevier.com/locate/dam Discrete Applied Mathematics]
* [http://www.elsevier.com/locate/disc Discrete Mathematics]
* [http://www.elsevier.com/locate/disopt Discrete Optimization]
* [http://www.elsevier.com/locate/endm Electronic Notes in Discrete Mathematics]
* [http://www.elsevier.com/locate/entcs Electronic Notes in Theoretical Computer Science]
* [http://www.elsevier.com/locate/enganabound Engineering Analysis with Boundary Elements]
* [http://www.elsevier.com/locate/engappai Engineering Applications of Artificial Intelligence]
* [http://www.elsevier.com/locate/ejc European Journal of Combinatorics]
** Gunther Ziegler [http://www.scilogs.de/wblogs/blog/mathematik-im-alltag/allgemein/2012-02-19/boykottiert-elsevier-ich-boykottiere-elsevier resigned his position] as an editor of this journal in 2012.
* [http://www.elsevier.com/locate/ejor European Journal of Operational Research]
* [http://www.elsevier.com/locate/expomath Expositiones Mathematicae]
* [http://www.elsevier.com/locate/ffa Finite Fields and their Applications]
* [http://www.elsevier.com/locate/fss Fuzzy Sets and Systems]
* [http://www.elsevier.com/locate/hm Historia Mathematica]
* [http://www.elsevier.com/locate/indag Indagationes Mathematicae]
* [http://www.elsevier.com/locate/ins Information Sciences]
* [http://www.elsevier.com/locate/ijforecast International Journal of Forecasting]
* [http://www.elsevier.com/locate/nlm International Journal of Non-Linear Mechanics]
* [http://www.elsevier.com/locate/matpur Journal de Mathématiques Pures et Appliquées]
* [http://www.elsevier.com/locate/yjabr Journal of Algebra]
* [http://www.sciencedirect.com/science/journal/01966774 Journal of Algorithms]
** [http://www.cs.colorado.edu/~hal/jalg.html Editorial board resignation], December 13, 2003.
** [http://www.cs.colorado.edu/~hal/chronicle.txt Editorial Board of Scientific Journal Quits, Accusing Elsevier of Price-Gouging], Brock Read, the Chronicle of Higher Education, February 9, 2004.
* [http://www.elsevier.com/locate/jal Journal of Applied Logic]
* [http://www.elsevier.com/locate/jat Journal of Approximation Theory]
* [http://www.elsevier.com/locate/yjcta Journal of Combinatorial Theory, series A]
** Gunther Ziegler [http://www.scilogs.de/wblogs/blog/mathematik-im-alltag/allgemein/2012-02-19/boykottiert-elsevier-ich-boykottiere-elsevier resigned his position] as an editor of this journal in 2012.
* [http://www.elsevier.com/locate/yjctb Journal of Combinatorial Theory, series B]
* [http://www.elsevier.com/locate/jco Journal of Complexity]
* [http://www.elsevier.com/locate/cam Journal of Computational & Applied Mathematics]
* [http://www.elsevier.com/locate/jcss Journal of Computer and System Sciences]
* [http://www.elsevier.com/locate/yjdeq Journal of Differential Equations]
* [http://www.elsevier.com/locate/jda Journal of Discrete Algorithms]
* [http://www.elsevier.com/locate/jeconom Journal of Econometrics]
* [http://www.elsevier.com/locate/yjfan Journal of Functional Analysis]
* [http://www.elsevier.com/locate/geomphys Journal of Geometry and Physics]
* [http://www.elsevier.com/locate/jmaa Journal of Mathematical Analysis & Applications]
* [http://www.elsevier.com/locate/jmateco Journal of Mathematical Economics]
* [http://www.elsevier.com/locate/yjmva Journal of Multivariate Analysis]
* [http://www.elsevier.com/locate/jnt Journal of Number Theory] ** Marie-France Vigneras resigned her position as an editor in 2012, according to her statement on the Elsevier boycott site.
* [http://www.elsevier.com/locate/jprocont Journal of Process Control]
* [http://www.journals.elsevier.com/journal-of-pure-and-applied-algebra/ Journal of Pure & Applied Algebra]
* [http://www.elsevier.com/locate/jspi Journal of Statistical Planning & Inference]
* [http://www.elsevier.com/locate/fi Journal of the Franklin Institute]
* [http://www.elsevier.com/locate/jkss Journal of the Korean Statistical Society]
* [http://www.elsevier.com/locate/laa Linear Algebra and its Applications]
* [http://www.elsevier.com/locate/mcm Mathematical and Computer Modelling]
* [http://www.elsevier.com/locate/mbs Mathematical Biosciences]
* [http://www.elsevier.com/locate/mss Mathematical Social Science]
* [http://www.elsevier.com/locate/matcom Mathematics and Computers in Simulation]
* [http://www.elsevier.com/locate/neunet Neural Networks]
* [http://www.elsevier.com/locate/na Nonlinear Analysis]
** [http://www.sciencedirect.com/science/article/pii/S0362546X04000409 On the second part of Hilbert's 16th problem], E. Oxenhielm, Nonlinear Analysis 57 (1), April 2004.
*** [http://news.bbc.co.uk/2/hi/science/nature/3243736.stm Historic maths problem 'cracked'] David Whitehouse, BBC, November 27, 2003.
*** [http://tesugen.com/archives/03/12/elin-oxenhielm-update Elin Oxenhielm update], Peter Lindberg, December 3, 2003.
*** [http://www.nature.com/news/2003/031209/full/news031208-4.html Mathematicians dispute proof of century-old problem], John Whitfield, Nature, December 9, 2003.
*** [http://plus.maths.org/content/struggling-sixteen Struggling for sixteen], Rachel Thomas, Plus magazine, December 16, 2003.
*** The paper was eventually [http://www.sciencedirect.com/science/article/pii/S0362546X04000409 withdrawn from the journal by the editors].
** [http://www.sciencedirect.com/science/article/pii/S0362546X0500235X On some contradictory computations in multi-dimensional mathematics], L. Carvalho, Nonlinear Analysis 63 (5-7), November 2005, 725--734. (Claims that the change of variables formula is incorrect.)
*** [http://math.ucr.edu/home/baez/corfield/2006/03/new-bogdanoff-affair_114355412211228579.html A New Bogdanoff Affair?], David Corfield, March 28, 2006.
*** [http://www.sciencedirect.com/science/article/pii/S0362546X06004597 A comment on: ''On some contradictory computations in multi-dimensional mathematics''], E. Capelas de Oliveira, W. Rodrigues, Nonlinear Anal. 67 (7), October 2007, 2316–2320.
*** As of 2012, the original paper of Carvalho has not been retracted from the journal. (However, it is no longer listed as a publication on [http://www.icmc.usp.br/~andcarva/publicac.html Carvalho's web page].)
** [http://blog.mikael.johanssons.org/archive/2006/03/this-is-me-losing-all-faith-in-non-linear-analysis/ This is me losing all faith in Nonlinear Analysis], Mikael Johansson, March 28, 2006.
* [http://www.elsevier.com/locate/nahs Nonlinear Analysis: Hybrid Systems]
* [http://www.elsevier.com/locate/nonrwa Nonlinear Analysis: Real world applications]
* [http://www.elsevier.com/locate/orl Operations Research Letters]
* [http://www.elsevier.com/locate/pr Pattern Recognition]
* [http://www.elsevier.com/locate/physa Physica A: Statistical Mechanics and its Applications]
* [http://www.elsevier.com/locate/physd Physica D: Nonlinear Phenomena]
* [http://www.elsevier.com/locate/simpat Simulation Modelling Practice & Theory]
* [http://www.elsevier.com/locate/stamet Statistical Methodology]
* [http://www.elsevier.com/locate/stapro Statistics and Probability Letters]
* [http://www.elsevier.com/locate/spa Stochastic Processes and their Applications]
* [http://www.elsevier.com/locate/sysconle Systems & Control Letters]
* [http://www.sciencedirect.com/science/journal/00409383 Topology]
** [http://math.ucr.edu/home/baez/topology-letter.pdf Editorial board resignation letter, 10 August 2006]
** [http://www.nysun.com/arts/rebellion-erupts-over-journals-of-academia/42317/ A Rebellion Erupts Over Journals Of Academia], Gary Shapiro, New York Sun, 26 October, 2006.
** [http://www.ams.org/notices/200705/comm-toped-web.pdf Jumping Ship: Topology editorial board resigns], Allyn Jackson, Notices of the American Mathematical Society, May 2007.
** [http://en.wikipedia.org/wiki/Topology_(journal) Wikipedia page on the journal]
** This journal was [http://www.info.sciverse.com/techsupport/journals/jnldiscontinued.htm discontinued in 2012].
* [http://www.journals.elsevier.com/topology-and-its-applications/ Topology & its Applications]
** In 2001, a group of editors of this journal [http://www.uflib.ufl.edu/oa/2009/posters/constitutional-declarationsdeniselgposter2-1.pdf resigned] to form [http://www.msp.warwick.ac.uk/agt/2012/12-01/ Algebraic & Geometric Topology].

== Open Access journals ==

* These lists are taken from the [http://www.doaj.org/ Directory of Open Access Journals] (limited to peer-reviewed journals).
** Perhaps someone could spell out or cut/paste the DOAJ lists below, like the Elsevier list above.

* In [http://www.doaj.org/doaj?func=subject&cpid=58&uiLanguage=en mathematics]

* In [http://www.doaj.org/doaj?func=subject&cpid=59&uiLanguage=en statistics]

* In [http://www.doaj.org/doaj?func=subject&cpid=114&uiLanguage=en computer science], e.g.
** [http://www.jair.org/ Journal of Artificial Intelligence Research]
** [http://www.lmcs-online.org Logical Methods in Computer Science]
** [http://jmlr.csail.mit.edu/ Journal of Machine Learning Research]
** [http://theoryofcomputing.org/ Theory of Computing]
** [http://www.jucs.org/ Journal of Universal Computer Science]
** [http://cjtcs.cs.uchicago.edu/ Chicago Journal of Theoretical Computer Science]

* In [http://www.doaj.org/doaj?func=subject&cpid=49&uiLanguage=en physics], e.g.
** [http://prx.aps.org/ Physical Review X]
** [http://iopscience.iop.org/1367-2630/ The New Journal of Physics]

== Mathematics journal price tables ==

The following tables list the ten most expensive mathematics journals by volume list price (as of 2008), and (for comparison) the ten mathematics journals with the highest impact factor (as of 2000). One should caution that due to complicated (and, in some cases, [http://www.econ.ucsb.edu/~tedb/Journals/BundleContracts.html deliberately obscured]) bundling agreements, the actual price of subscriptions to many journals (including Elsevier journals) may differ somewhat from the official list price. Nevertheless, these tables should convey the rough order of magnitude, at least, of journal costs from publisher to publisher.

Data is drawn from [http://www.mathematik.uni-bielefeld.de/~rehmann/BIB/AMS/Price_per_Volume.html this set of 2007 journal price data] and [http://in-cites.com/research/2001/oct_15_2001-2.html this list of 2000 ISI impact factors]. All prices in US dollars.

=== Top ten mathematics journals by volume list price ===

{|
|Title
|Publisher
|Price/volume
|Price/page
|-
|J. Math. Sci. (New York)
|Springer
|9998
|1.38
|-
|Theoret. Comput. Sci.
|Elsevier
|6551
|1.02
|-
|J. Math. Anal. Appl.
|Academic Press/Elsevier
|6362
|0.36
|-
|J. Algebra
|Academic Press/Elsevier
|5736
|0.51
|-
|Nonlinear Anal.
|Elsevier
|5426
|0.84
|-
|Discrete Math.
|Elsevier
|5269
|1.63
|-
|Appl. Math. Comput.
|Elsevier
|5250
|0.38
|-
|Math. Methods Appl. Sci.
|Wiley/Teubner
|4995
|2.09
|-
|Linear Algebra Appl.
|Elsevier
|4885
|0.94
|-
|Math. Nachr.
|Wiley/VCH Verlag
|4795
|2.58
|}

=== Top ten mathematics journals by impact factor ===

{|
|Title
|Publisher
|Price/volume
|Price/page
|-
|Bull. Amer. Math. Soc.
|American Mathematical Society
|418
|0.64
|-
|Acta Mathematica
|Institut Mittag-Leffler
|392
|0.65
|-
|J. Amer. Math. Soc.
|American Mathematical Society
|287
|0.24
|-
|Comm. Pure Appl. Math.
|Wiley
|3205
|1.74
|-
|Inventiones Mathemat.
|Springer-Verlag
|3232
|1.21
|-
|Annals of Mathematics
|Princeton University Press
|260
|0.13
|-
|Advances in Mathematics
|Elsevier/Academic Press
|3221
|0.41
|-
|Mem. Amer. Math. Soc.
|American Mathematical Society
|N/A
|N/A
|-
|Commun. Contemp. Math.
|World Scientific
|483
|0.51
|-
|Geom. Func. Anal.
|Springer/Birkhauser
|1185
|0.88
|}

== Data from libraries ==

Pricing data from libraries is often hard to come by (for instance, many bundling contracts come with confidentiality agreements). More links in this section would be greatly appreciated.

* [http://www.bibliothek.kit.edu/cms/english/most-expensive-journals%20.php Here is a list of the 10 most expensive journals subscribed to by the Karlsruhe Institute of Technology] as of 2010/2011. 8 of the 10 are published by Elsevier.
* [http://libraries.mit.edu/sites/scholarly/mit-open-access/open-access-at-mit/mit-open-access-policy/publishers-and-the-mit-faculty-open-access-policy/elsevier-fact-sheet/ Elsevier Fact Sheet], MIT libraries. MIT avoids bundling in order to obtain flexibility in its subscriptions, but pays Elsevier almost $2 million/year for its journals.
* [http://www.purdueexponent.org/campus/article_19f1031d-0396-5b21-870a-c7f9f6ca91bc.html According to this news article], Purdue pays Elsevier $2.3 million/year for digital access to its journals, with price increases of approximately 5 percent per year.
* The [http://www.econ.ucsb.edu/~tedb/Journals/BundleContracts.html Bundle Contract Project] seeks to collect bundling contracts from commercial publishers.

Journal publishing reform

2012-02-23T08:53:01Z

Gowers: /* Reactions from blogs */

[[Image:elsevier_poster.jpg|right|300px|Credit: Michael Eisen]]

This is a collection of links to information, opinion, activism, and other issues concerning the practices of research journal publishers (particularly in the mathematical sciences). Further contributions are welcome.

== The cost of knowledge ==

[http://thecostofknowledge.com/ The cost of knowledge] is a web page at which one may register a protest against the practices of Elsevier by pledging not to submit a paper to an Elsevier journal, not to referee for an Elsevier journal, not to join an editorial board of an Elsevier journal, or some combination of the three. This site was inspired by the following blog post:

* [http://gowers.wordpress.com/2012/01/21/elsevier-my-part-in-its-downfall/ Elsevier - my part in its downfall], Timothy Gowers, January 21, 2012.

A more detailed statement of purpose of the boycott, can be [http://gowers.files.wordpress.com/2012/02/elsevierstatementfinal.pdf found here]. It is written and signed by [http://en.wikipedia.org/wiki/Scott_Aaronson Scott Aaronson], [http://en.wikipedia.org/wiki/Douglas_N._Arnold Douglas N. Arnold], [http://en.wikipedia.org/wiki/Artur_Ávila Artur Ávila], [http://en.wikipedia.org/wiki/John_C._Baez John Baez], [http://www-m3.ma.tum.de/Allgemeines/FolkmarBornemann Folkmar Bornemann], [http://en.wikipedia.org/wiki/Danny_Calegari Danny Calegari], [http://research.microsoft.com/en-us/um/people/cohn/ Henry Cohn], [http://en.wikipedia.org/wiki/Ingrid_Daubechies Ingrid Daubechies], [http://en.wikipedia.org/wiki/Jordan_Ellenberg Jordan Ellenberg], [http://www.math.uchicago.edu/~emerton/ Matthew Emerton], [http://wavelets.ens.fr/EQUIPE/marie.htm Marie Farge], [http://en.wikipedia.org/wiki/David_Gabai David Gabai], [http://en.wikipedia.org/wiki/Timothy_Gowers Timothy Gowers], [http://en.wikipedia.org/wiki/Ben_J._Green Ben Green], [http://de.wikipedia.org/wiki/Martin_Grötschel Martin Grötschel], [http://en.wikipedia.org/wiki/Michael_Harris_%28mathematician%29 Michael Harris], [http://en.wikipedia.org/wiki/Fr%C3%A9d%C3%A9ric_H%C3%A9lein Frédéric Hélein], [http://en.wikipedia.org/wiki/Robion_Kirby Rob Kirby], [http://en.wikipedia.org/wiki/Vincent_Lafforgue Vincent Lafforgue], [http://en.wikipedia.org/wiki/Greg_Lawler Gregory F. Lawler], [http://en.wikipedia.org/wiki/Randall_J._LeVeque Randall J. LeVeque], [http://en.wikipedia.org/wiki/Laszlo_lovasz Laszlo Lovasz], [http://www.math.umn.edu/~olver/ Peter J. Olver], [http://www.maths.qmul.ac.uk/~olof/ Olof Sisask], [http://en.wikipedia.org/wiki/Terence_tao Terence Tao], [http://en.wikipedia.org/wiki/Richard_Taylor_%28mathematician%29 Richard Taylor], [http://en.wikipedia.org/wiki/Bernard_Teissier Bernard Teissier], [http://en.wikipedia.org/wiki/Burt_Totaro Burt Totaro], [http://en.wikipedia.org/wiki/Lloyd_Trefethen Lloyd N. Trefethen], [http://kyokan.ms.u-tokyo.ac.jp/~tsuboi/ Takashi Tsuboi], [http://en.wikipedia.org/wiki/Marie-France_Vign%C3%A9ras Marie-France Vigneras], [http://en.wikipedia.org/wiki/Wendelin_Werner Wendelin Werner], [http://math.uchicago.edu/~wilkinso/ Amie Wilkinson], and [http://page.mi.fu-berlin.de/gmziegler/ Gunter M. Ziegler].

See also [http://blog.thecostofknowledge.com/ the blog associated to the cost of knowledge site]. A poster for the protest may be [http://math.ucr.edu/home/baez/elsevier_boycott_poster.pdf found here].

There have since been many reactions to this protest:

=== Reactions from blogs ===

* [http://gowers.wordpress.com/2012/01/23/httpthecostofknowledge-com/ The cost of knowledge], Timothy Gowers, January 23, 2012.
* [http://johncarlosbaez.wordpress.com/2012/01/26/ban-elsevier/ Ban Elsevier], John Baez, January 26, 2012.
* [http://www.scottaaronson.com/blog/?p=891 Boycott Elsevier!], Scott Aaronson, January 26, 2012.
* [http://terrytao.wordpress.com/2012/01/26/the-cost-of-knowledge/ The cost of knowledge], Terence Tao, January 26, 2012.
* [http://dabacon.org/pontiff/?p=5982 Why boycott Elsevier?], Adam Harrow, January 27, 2012.
* [http://cameroncounts.wordpress.com/2012/01/29/publishers-wars/ Publisher's wars], Peter Cameron, January 29, 2012.
* [http://gowers.wordpress.com/2012/01/29/whats-wrong-with-electronic-journals/ What's wrong with electronic journals], Tim Gowers, January 29, 2012.
* [http://sbseminar.wordpress.com/2012/01/30/thinking-about-elsevier-replacements/ Thinking about Elsevier replacements], David Speyer, January 30, 2012.
* [http://blogs.lse.ac.uk/impactofsocialsciences/2012/02/01/stand-down-journal-referee/ Comfort is the death knell of academia: why I’m standing down as a journal referee], Matthew Todd, LSE Impact Blog, February 1, 2012.
* [http://www.scilogs.de/wblogs/blog/detritus/sonstiges/2012-02-01/boykottiert-elsevier-unterst-tzt-open-access Boykottiert Elsevier! Unterstützt Open Access!], Martin Ballaschk, February 1, 2012. (German)
* [http://scholarlykitchen.sspnet.org/2012/02/02/mysteries-of-the-elsevier-boycott Mysteries of the Elsevier Boycott], Rick Anderson, February 2, 2012.
** [http://breakingculture.tumblr.com/post/17112742228/unraveling-boycott-mysteries Unraveling (some of) the mysteries of the Elsevier Boycott], Sean Johnson Andrews, February 6, 2012.
** [http://www.against-the-grain.com/2012/02/multigrain-discussion-another-response-to-the-elsevier-boycott/ Multigrain Discussion: Another Response to the Elsevier Boycott], Chuck Hamaker, February 14, 2012.
* [http://scholarlykitchen.sspnet.org/2012/02/02/the-elsevier-boycott-does-it-make-sense The Elsevier Boycott — Does It Make Sense?], Kent Anderson, February 2, 2012.
* [http://www.michaeleisen.org/blog/?p=890 You are Elsevier: time to overcome our fears and kill subscription journals], Michael Eisen, February 3, 2012.
** [http://scienceblogs.com/denialism/2012/02/eisen_calls_for_elsevier_boyco.php Eisen calls for Elsevier Boycott - but can we all go OA?], Mark Hoofnagle, February 6, 2012.
* [http://stochastictrend.blogspot.com/2012/02/in-defence-of-elsevier.html In Defence of Elsevier], David Stern, February 4, 2012.
* [http://blog.mathunion.org/journals/?no_cache=1&tx_t3blog_pi1%5BblogList%5D%5BshowUid%5D=30&tx_t3blog_pi1%5BblogList%5D%5Byear%5D=2012&tx_t3blog_pi1%5BblogList%5D%5Bmonth%5D=02&tx_t3blog_pi1%5BblogList%5D%5Bday%5D=05&cHash=a2d6424f899302a7ea3b75b9bb591802 More reasons to support the Elsevier boycott], Doug Arnold, IMU blog on mathematical journals, February 5, 2012.
* [http://gowers.wordpress.com/2012/02/08/a-more-formal-statement-about-mathematical-publishing/ A more formal statement about mathematical publishing], Timothy Gowers, February 8, 2012.
* [http://scientopia.org/blogs/drugmonkey/2012/02/08/explaining-resistance-to-the-elsevier-boycott-practicalities/ Explaining resistance to the Elsevier boycott: Practicalities.], DrugMonkey, February 8, 2012.
* [http://neurodojo.blogspot.com/2012/02/whens-scientists-and-published.html When scientists’ and publishers’ motivations align], Zen Faulkes, February 9, 2012.
* [https://etechlib.wordpress.com/2012/02/11/about-the-elsevier-controversy-and-essential-science/ About the Elsevier Controversy and Essential Science], PF Anderson, February 11, 2012.
* [http://www.science3point0.com/palphy/2012/02/12/journal-mega-bundles-thecostofknowledge/ Journal mega-bundles & TheCostOfKnowledge], Ross Mounce, February 12, 2012.
* [http://mathbabe.org/2012/02/13/mathematics-has-an-occupy-moment/ Mathematics has an Occupy moment], Cathy O'Neil, February 13, 2012.
* [http://svpow.wordpress.com/2012/02/13/a-window-of-opportunity-for-elsevier/ A window of opportunity for Elsevier], Mike Taylor, February 13, 2012.
* [http://mhpbooks.com/49648/5000-profs-join-boycott-of-elsevier-publications-in-international-academic-spring/ 5,000 profs join boycott of Elsevier publications in international “academic spring”], Dennis Johnson, February 14, 2012.
* [http://blogs.lse.ac.uk/impactofsocialsciences/2012/02/15/after-elsevier-boycott-green-open-access What comes after the Elsevier boycott? The answer might be found by following the ‘Green’ road to open access], Neil Stewart, LSE Impact Blog, February 15, 2012.
* [http://mhpbooks.com/50115/whats-next-in-the-elsevier-boycott/ What’s next in the Elsevier boycott?], Dennis Johnson, Melville House, February 16, 2012.
* [http://lj.libraryjournal.com/2012/02/opinion/barbara-fister/joining-the-movement-a-call-to-action-peer-to-peer-review/ Joining the Movement: A Call to Action | Peer to Peer Review] Barbara Fister, Library Journal, February 16, 2012
* [http://www.scilogs.de/wblogs/blog/mathematik-im-alltag/allgemein/2012-02-19/boykottiert-elsevier-ich-boykottiere-elsevier Boykottiert Elsevier! Ich boykottiere Elsevier!], Gunter Ziegler, February 19, 2012. (German)
* [http://burttotaro.wordpress.com/2012/02/19/i-am-not-a-radical-but-i-am-boycotting-elsevier/ I am not a radical, but I am boycotting Elsevier], Burt Totaro, February 19, 2012.
* [http://audsandens.blogspot.com/2012/02/taking-control-more-reasons-for.html Taking Control: More Reasons for the Elsevier Boycott], Aaron Barlow, February 20, 2012.
* [http://www.weeklyweinersmith.com/?p=211 The Elsevier Boycott], Zach and Kelly Wienersmith, February 21, 2012. (Podcast)
* [http://scienceblogs.com/webeasties/2012/02/the_future_of_science_pub.php The Future of Science Publishing], Kevin Bonham, February 21, 2012.
* [http://blogs.lse.ac.uk/impactofsocialsciences/2012/02/22/elsevier-price-boycotters-untruth/ Elsevier have a right to price their journals as they see fit, but they must be honest in their reasoning and not attack boycotters with untruths], Tim Leunig, LSE Impact blog, February 22, 2012.

=== News aggregators ===

* [http://news.ycombinator.com/item?id=3494340 Fields medalist Tim Gowers: Elsevier — my part in its downfall], Hacker News, January 21, 2012
* [http://www.reddit.com/r/math/comments/oqirf/one_mathematicians_stance_against_elsevier/ One mathematician's stance against Elsevier], Reddit, January 22, 2012.
* [http://news.ycombinator.com/item?id=3501561 The Cost of Knowledge: Researchers taking a stand against Elsevier], Hacker News, January 23, 2012.
* [http://science.slashdot.org/story/12/01/27/1322234/scientists-organize-elsevier-boycott Scientists organize Elsevier boycott], Slashdot, January 27, 2012.
* [http://www.metafilter.com/112178/Scientists-boycott-Elsevier Scientists boycott Elsevier], Metafilter, January 29, 2012.
* [http://www.reddit.com/r/math/comments/pepuo/thanks_to_angry_mathematicians_elseviers/ Thanks to angry mathematicians, Elsevier's publishing model might be about to go up in smoke], Reddit, February 7, 2012.

=== Coverage by the media ===

* [http://www.theregister.co.uk/2012/01/28/scientists_boycott_elsevier/ Blog blast births boffin boycott of publisher Elsevier], Iain Thomson, the Register, January 28, 2012.
* [http://www.forbes.com/sites/timworstall/2012/01/28/elseviers-publishing-model-might-be-about-to-go-up-in-smoke/ Elsevier's Publishing Model Might be About to Go Up in Smoke], Tim Worstall, Forbes, January 28, 2012.
* [http://www.wired.com/wiredscience/2012/01/testify-the-open-science-movement-catches-fire/ Testify: The Open-Science Movement Catches Fire] David Dobbs, Wired, January 30, 2012.
* [http://chronicle.com/blogs/wiredcampus/elsevier-publishing-boycott-gathers-steam-among-academics/35216 Elsevier Publishing Boycott Gathers Steam Among Academics], Josh Fischman, The Chronicle of Higher Education, January 30, 2012.
* [http://www.techdirt.com/articles/20120130/13030217589/will-academics-boycott-elsevier-be-tipping-point-open-access-another-embarrassing-flop.shtml Will Academics' Boycott Of Elsevier Be The Tipping Point For Open Access -- Or Another Embarrassing Flop?], Glyn Moody, Techdirt, January 31, 2012.
* [http://boingboing.net/2012/01/31/scientists-boycott-elsevier-ov.html Scientists and scholars boycott Elsevier over bad business practices and copyright maximalism], Cory Doctorow, Boingboing, January 31, 2012.
* [http://lj.libraryjournal.com/2012/01/publishing/petition-targeting-elseviers-business-practices-begins-to-snowball/ Petition Targeting Elsevier’s Business Practices Begins to Snowball], Michael Kelley, Library Journal, January 31, 2012.
* [http://www.thebookseller.com/news/academics-call-boycott-elsevier.html Academics call for boycott of Elsevier], Charlotte Williams, The Bookseller, January 31, 2012.
* [http://chronicle.com/article/As-Journal-Boycott-Grows/130600/ As Journal Boycott Grows, Elsevier Defends Its Practices], Josh Fischman, The Chronicle of Higher Education, January 31, 2012.
* [http://arstechnica.com/science/news/2012/01/researchers-boycott-publisher-will-they-embrace-instant-publishing.ars Researchers boycott publisher; will they embrace instant publishing?], John Timmer, Ars Technica, January 31, 2012.
* [http://www.elmundo.es/elmundosalud/2012/01/30/noticias/1327952591.html Boicot científico a Elsevier], Cristina de Martos, El Mundo, January 31, 2012. (Spanish)
* [http://nos.nl/op3/artikel/335992-elsevier-in-de-clinch-met-wetenschappers.html Elsevier in de clinch met wetenschappers], NOS News, January 31, 2012. (Dutch)
* [http://news.sciencemag.org/scienceinsider/2012/02/thousands-of-scientists-vow-to-b.html Thousands of Scientists Vow to Boycott Elsevier to Protest Journal Prices], Jop de Vrieze, Science Insider, February 1, 2012.
* [http://www.mmm-online.com/elsevier-begins-outreach-as-push-back-on-publisher-threatens-to-widen/article/225855/ Elsevier begins outreach as push-back on publisher threatens to widen], Deborah Weinstein, Medical Marketing & Media, February 1, 2012.
* [http://www.care2.com/causes/scientists-fight-for-open-access-for-their-research.html Scientists Fight For Open Access For Research], Kristina Chew, Care2, February 1, 2012.
* [http://www.bloomberg.com/news/2012-02-01/samsung-csr-nfl-elsevier-motorola-intellectual-property.html Samsung, CSR, NFL, Elsevier, Motorola: Intellectual Property], Victoria Slind-Flor, Bloomberg, February 1, 2012. (Brief mention only.)
* [http://mediadecoder.blogs.nytimes.com/2012/02/01/the-breakfast-meeting-a-week-of-negative-ads-and-new-chief-at-sony/ The Breakfast Meeting: A Week of Negative Ads, and New Chief at Sony], Noam Cohen, New York Times, February 1, 2012. (Brief mention only.)
* [http://www.guardian.co.uk/science/2012/feb/02/academics-boycott-publisher-elsevier Scientists sign petition to boycott academic publisher Elsevier], Alison Flood, the Guardian, February 2, 2012.
* [http://blogues.cyberpresse.ca/sciences/2012/02/02/fronde-contre-les-revues-savantes-delsevier/ Étonnante fronde de chercheurs contre les revues savantes d’Elsevier], Jean-François Cliche, le Soleil, February 2, 2012. (French)
* [http://www.wired.com/wiredscience/2012/02/is-the-open-science-revolution-for-real/ Is the Open Science Revolution For Real?], David Dobbs, Wired, February 3, 2012.
* [http://www.economist.com/node/21545974 The price of information], the Economist, February 4, 2012.
* [http://archiv.twoday.net/stories/64967798/ Zum Elsevier-Boykott], Klaus Graf, Archivalia, February 5, 2012. (German)
* [http://paidcontent.org/article/419-academics-revolt-against-elseviers-journal-pricing/ Academics Revolt Against Elsevier’s Journal Pricing], Robert Andrews, PaidContent, February 6, 2012.
* [http://theconversation.edu.au/spread-the-word-scientists-are-tearing-down-publishers-walls-5098 Spread the word: scientists are tearing down publishers' walls], Alex Holcombe, the Conversation, February 7, 2012.
* [http://www2.ljworld.com/news/2012/feb/07/heard-hill-university-senate-considering-boycottin/ Heard on the Hill: University Senate considering boycotting publisher Elsevier; newspaper readership program popular at other places, too; KUMC researcher mentioned in LA Times story on Alzheimer’s], Andy Hyland, LJWorld, February 7, 2012.
* [http://hon.jp/news/modules/rsnavi/showarticle.php?id=3082 欧米圏で“学術の春”運動始まる、電子ジャーナル出版大手Elsevierに対し学者たちのボイコット運動が急拡大], editorial, hon.jp Daywatch, Feb 7, 2012. (Japanese)
* [http://the-scientist.com/2012/02/07/occupy-elsevier/ Occupy Elsevier?], Bob Grant, the Scientist, February 7, 2012.
* [http://www.theaustralian.com.au/higher-education/academics-boycott-publisher-elsevier/story-e6frgcjx-1226265110496?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+TheAustralianHigherEducationNews+%28The+Australian+%7C+Higher+Education%29&utm_content=Google+Reader Academics boycott publisher Elsevier], Bernard Lane, the Australian, February 8, 2012.
* [http://latimesblogs.latimes.com/jacketcopy/2012/02/wed-book-news-bezos-the-elsevier-boycott-and-more.html Wednesday book news: Bezos, the Elsevier boycott and more], Carolyn Kellogg, Los Angeles Times, February 8, 2012. (Brief mention only.)
* [http://www.guardian.co.uk/higher-education-network/blog/2012/feb/08/open-access-journals-elsvier-boycott Open access journals: are we asking the right questions?], Martin Paul Eve, the Guardian, February 8, 2012.
* [http://www.varsity.co.uk/news/4370 The Academic Spring], Patrick O'Grady, Varsity, February 8, 2012.
* [http://www.timeshighereducation.co.uk/story.asp?sectioncode=26&storycode=418952 Elsevier defends stance on anti-open-access bill], John Gill, Times Higher Education, February 9, 2012.
* [http://www.nature.com/news/elsevier-boycott-gathers-pace-1.10010 Elsevier boycott gathers pace], John Whitfield, Nature, February 9, 2012.
* [http://www.wired.com/wiredscience/2012/02/open-science-revolt-occupies-congress/ Open Science Revolt Occupies Congress], David Dobbs, Wired, February 9, 2012.
* [http://blogs.independent.co.uk/2012/02/09/the-future-of-academic-publishing/ The future of academic publishing], Mike Taylor, the Independent, February 9, 2012.
* [http://www.tcs.cam.ac.uk/issue/news/cambridge-professor-leads-boycott-of-elsevier-publications/ Cambridge Professor leads boycott of Elsevier Publications], Emily Loud, the Cambridge Student Online, February 9, 2012.
* [http://www.utimes.pitt.edu/?p=19679 Protest launched against journal publisher], Kimberly Barlow, University Times, February 9, 2012.
* [http://jeps.efpsa.org/blog/2012/02/10/a-revolution-in-scientific-publishing/ A revolution in scientific publishing?], Sina Scherer, JEPS Bulletin, February 10, 2012.
* [http://libraries.mit.edu/sites/news/elsevier-boycott-grows/7785/ Elsevier Boycott Grows: MIT Faculty Speak About Participation], Ellen Duranceau, MIT Libraries News, February 10, 2012.
* [http://www1.folha.uol.com.br/ciencia/1046769-cientistas-boicotam-a-maior-editora-de-periodicos-do-mundo.shtml Cientistas boicotam a maior editora de periódicos do mundo], Sabine Righetti, Folha, February 10, 2012. (Portugese)
* [http://www.bostonglobe.com/opinion/2012/02/12/why-scientists-are-boycotting-publisher/9sCpDEP7BkkX1INfakn3NL/story.html Why scientists are boycotting a publisher], Gareth Cook, the Boston Globe, February 12, 2012.
** [http://bostonglobe.com/opinion/letters/2012/02/16/elsevier-committed-universal-access-content-sustainable-publishing-model/70QfCpSOvy0IUibSK6eCTL/story.html Elsevier committed to universal access to content, sustainable publishing model], Lynne Herndon (former CEO of Cell press), letter to the editor, the Boston Globe, February 16, 2012.
*** [http://quomodocumque.wordpress.com/2012/02/16/elseviers-sorry-defense-of-the-research-works-act/ Elsevier’s sorry defense of the Research Works Act], Jordan Ellenberg, February 16, 2012.
* [http://newsbreaks.infotoday.com/NewsBreaks/The-Cost-of-Knowledge-Versus-Elsevier--Signatures-and-Growing-80575.asp The Cost of Knowledge Versus Elsevier: 5,600 Signatures and Growing], Robin Peek, Information Today, February 13, 2012.
* [http://www.pourlascience.fr/ewb_pages/a/actualite-la-fronde-des-chercheurs-contre-i-elsevier-i-29118.php La fronde des chercheurs contre Elsevier], Maurice Mashaal, Pour la Science, February 13, 2012.
* [http://www.newscientist.com/article/dn21467-web-freedoms-fuel-academic-spring-journal-protest.html Web freedoms fuel 'academic spring' journal protest], Jacob Aron, New Scientist, February 13, 2012.
* [http://www.nytimes.com/2012/02/14/science/researchers-boycott-elsevier-journal-publisher.html Mathematicians Organize Boycott of a Publisher], Thomas Lin, New York Times, February 13, 2012.
* [http://motherjones.com/blue-marble/2012/02/science-uprising Science Uprising], Julia Whitty, Mother Jones, February 13, 2012.
* [http://www.kansan.com/news/2012/feb/13/professors-boycott/ Professors boycott prominent publishing company], Kelsey Cipolla, The University Daily Kansan, February 13, 2012.
* [http://www.purdueexponent.org/opinion/editorials/article_a6e96c79-5c95-54b8-bf85-eca8de6bb3db.html Monopoly on research publishing is unethical], Editorial, The Exponent, February 14, 2012.
* [http://today.duke.edu/2012/02/elsevierboycott Duke Scholars Join Boycott Against Elsevier], Ashley Yeager, Duke Today, February 14, 2012.
* [https://theconversation.edu.au/academics-line-up-to-boycott-worlds-biggest-journal-publisher-5384 Academics line up to boycott world’s biggest journal publisher], Justin Norrie, the Conversation, February 15, 2012.
* [http://www.ft.com/cms/s/0/2494fbc4-5873-11e1-9f28-00144feabdc0.html Reed chief hits back at critics of division], Salamander Davoudi, February 16, 2012.
* [http://www.abc.net.au/science/articles/2012/02/17/3433568.htm Academics boycott journal publisher], Eleanor Bell, ABC news, February 17, 2012.
* [http://www.onthemedia.org/2012/feb/17/trouble-elsevier-leading-academic-publisher/ Trouble for Elsevier, the leading academic publisher], Rick Karr, On the media, NPR, February 17, 2012. (Audio)
** [http://crookedtimber.org/2012/02/21/some-questions-for-elsevier/ Some questions for Elsevier], Harry Brighouse, Crooked Timber, February 21, 2012.
* [http://www.smh.com.au/national/education/academics-join-world-fight-against-publisher-20120220-1tjk6.html Academics join world fight against publisher], Nicky Phillips, Sydney Morning Herald, February 21, 2012.
* [http://blogs.discovermagazine.com/crux/2012/02/21/its-not-academic-how-publishers-are-squelching-science-communication/ It’s Not Academic: How Publishers Are Squelching Science Communication], Michael Taylor, Discover Magazine, February 21, 2012.

=== Open letters to Elsevier ===

* [http://math.berkeley.edu/~kirby/elsevier.html Letter to Elsevier], Rob Kirby, December 30, 1997.
* [http://www.library.yale.edu/~llicense/ListArchives/0310/msg00048.html Call for Boycott of Cell Press Journals], Peter Walter and Keith Yamomoto, October 19, 2003.
** [http://genomebiology.com/2003/4/10/spotlight-20031024-02 Researchers boycott Cell Press], Alison McCook, Genome Biology, October 24, 2003.
* [http://www.cs.colorado.edu/~hal/jalg.html Journal of Algorithms editorial board resignation], December 13, 2003.
* [http://math.ucr.edu/home/baez/topology-letter.pdf Topology editorial board resignation letter], August 10, 2006.
* [http://idiolect.org.uk/elsevier/docs/academics_openletter.pdf Arms fairs and academics], 138 signatories, February 28, 2007.
* [http://idiolect.org.uk/notes/?p=643 An open letter to Elsevier and all those involved in the IEHG], Keith Halfacree, April 10, 2007.
* [http://www.coar-repositories.org/news/coar-writes-open-letter-as-reaction-to-elseviers-practices/ Open Letter to Elsevier], Norbert Lossau, Chair of the Executive Board, Confederation of Open Access Repositories, February 6, 2012.
* [https://plus.google.com/105282922684661032446/posts/WCZqgPVehmx Letter to Elsevier], Cynthia Parr, February 10, 2012.
* [http://darwin.eeb.uconn.edu/uncommon-ground/2012/02/declining-elsevier.html Declining elsevier], Kent Holsinger, February 10, 2012.
* [http://occamstypewriter.org/scurry/2012/02/12/an-open-letter-to-elsevier/ An Open Letter to Elsevier], Stephen Curry, February 12, 2012.
* [http://svpow.wordpress.com/2012/02/15/a-response-to-one-elsevier-employee-and-an-open-letter-to-the-rest/ A response to one Elsevier employee, and an open letter to the rest], Matt Wedel, February 15, 2012.
* [http://fakeelsevier.wordpress.com/2012/02/19/dear-elsevier-employees-with-love-from-fakeelsevier/ Dear Elsevier employees, with love, from @FakeElsevier], FakeElsevier, February 19, 2012.

=== Responses by Elsevier ===

* [http://gowers.wordpress.com/2012/01/21/elsevier-my-part-in-its-downfall/#comment-14679 A response by David Clark at Elsevier], January 23, 2012.
* [http://www.elsevier.com/wps/find/intro.cws_home/elsevieropenletter An open letter to the research community: journal prices, discounts, and access], Elsevier, undated as of Feb 6, 2012.
** [http://bjoern.brembs.net/news.php?item.833.11 Against Own Assertion, Elsevier Doubled Price For Access], Bjorn Brembs, February 11, 2012.
* [http://www.epjournal.net/blog/2012/02/elsevier-and-evolution-human-behavior/ Elsevier and Evolution & Human Behavior], Robert Kurzban (co-editor-in-chief of the Elsevier journal Evolution & Human Behavior), February 6, 2012.
* [http://poynder.blogspot.com/2012/02/elseviers-alicia-wise-on-rwa-west-wing.html Elsevier’s Alicia Wise on the RWA, the West Wing, and Universal Access], Richard Poynder, February 9, 2012.

=== Other coverage ===

* [http://www.arl.org/sparc/media/prime-time-for-public-access.shtml Prime Time for Public Access], Heather Joseph, Executive Director, SPARC, February 9, 2012.
* [http://www.openaire.eu/en/news-a-events/news/343-elseviers-practices-opposing-open-access Elsevier’s practices opposing open access], Open Access Infrastructure for Research in Europe, February 16, 2012.
* [http://en.wikipedia.org/wiki/The_Cost_of_Knowledge The wikipedia page] for this protest.

See also [http://scienceblogs.com/confessions/2012/02/around_the_web_research_works.php this list of links], which is focused more around the Research Works Act, but also contains many links regarding the boycott, as well as [http://www.math.ntnu.no/~stacey/Mathforge/Math2.0 Math 2.0], a discussion forum for all topics related to the future of mathematical publishing.

== Other pledges, boycotts, and petitions ==

* [http://www.researchwithoutwalls.org/ Research Without Walls]
* [http://www.openaccesspledge.com/ Open Access Pledge]
* [http://www-fourier.ujf-grenoble.fr/petitions/index.php?petition=3 Appel pour des négociations équilibrées avec les éditeurs de revues scientifiques] - a petition concerning the bundling and pricing practices of Springer
* [http://www.thepetitionsite.com/207/support-the-open-access-movement-stop-the-research-works-act/?cid=FB_TAF A petition to stop the Research Works Act]
* [http://www.taxpayeraccess.org/action/FRPAA2012.shtml Call to action: Tell Congress you support the Bipartisan Federal Research Public Access Act (H.R. 4004 and S. 2096)], Alliance for taxpayer access, February 9, 2012.

* See these tag libraries from the [http://oad.simmons.edu/oadwiki/OA_tracking_project Open Access Tracking Project] (more comprehensive after April 2009 than before):
** [http://www.connotea.org/tag/oa.boycotts oa.boycotts]
** [http://www.connotea.org/tag/oa.declarations oa.declarations]
** [http://www.connotea.org/tag/oa.petitions oa.petitions]
** [http://www.connotea.org/tag/oa.pledges oa.pledges]

== Other blog posts, letters, and opinion pieces ==
* [http://math.berkeley.edu/~kirby/journals.html Comparative price of math journals], Rob Kirby, May 27, 1997.
** [http://math.berkeley.edu/~kirby/elsevier.html Open letter to Elsevier], Rob Kirby, December 30, 1997.
** [http://math.berkeley.edu/~kirby/jp00.html 2000 data update]
* [http://www.ams.org/notices/200007/forum-birman.pdf Scientific Publishing: A Mathematician’s Viewpoint], Joan Birman, Notices of the American Mathematical Society, 770-774, July 2000.
* [http://homepages.cwi.nl/~apt/ps/cacm01.pdf One More Revolution to Make: Free Scientific Publishing], Krzysztof R. Apt, Communications of ACM, 44(5), pp. 25-28, 2001.
* [http://www.nieuwarchief.nl/serie5/deel02/sep2001/pdf/apt.pdf Towards free access to scientific literature], Krzysztof R. Apt, Nieuw Archief voor Wiskunde, 5/2 nr. 3, September 2001, pp. 251-255.
* [http://stromme.uib.no/kuperberg.pdf Scholarly Mathematical Communication at a Crossroads], Greg Kuperberg, Nieuw Arch. Wisk., (5) 3 no.3, September 2002.
* [http://people.ccmr.cornell.edu/~ginsparg/blurb/pg02pr.html Can Peer Review be better Focused?], Paul Ginsparg, March 2003.
* [http://www.ams.org/notices/200402/commentary.pdf Fleeced?], Rob Kirby, Notices of the American Mathematical Society, 161-162, February 2004.
* [http://www.ams.org/notices/200405/commentary.pdf We can make a change], Gerard van der Geer, Notices of the American Mathematical Society, May 2004.
* [http://www.math.columbia.edu/~neumann/journal.html What we can do about journal pricing], Walter Neumann, September 2005.
** The discussions mentioned in that email led to the [http://web.archive.org/web/20110525195311/http://members.cox.net/banffprotocol/ Banff protocol] (web site now only available through web archive).
* [http://www.scottaaronson.com/writings/journal.html Review of The Access Principle by John Willinsky], Scott Aaronson, 2006
* [http://digitalstrategies.blogspot.com/2008/06/scientific-publication-in-internet-era.html Scientific Publishing in the Internet Era] Efthymios Constantinides June 17, 2008
* [http://arstechnica.com/science/news/2008/11/elsevier-beyond-the-pale-of-scientific-respectability.ars Publishing economics harm science's credibility], Chris Lee, Ars Technica, November 2008.
* [http://www.ima.umn.edu/~arnold/siam-columns/integrity-under-attack.pdf Integrity under attack: The State of Scholarly Publishing], Douglas Arnold, SIAM news, December 2009.
* [http://scholarlykitchen.sspnet.org/2010/01/04/why-hasnt-scientific-publishing-been-disrupted-already/ Why Hasn’t Scientific Publishing Been Disrupted Already?], Michael Clarke, January 4, 2010.
* [http://math.ucr.edu/home/baez/journals.html What We Can Do About Science Journals], John Baez, January 24, 2011.
* [http://blog.mathunion.org/journals/?no_cache=1&tx_t3blog_pi1%5BblogList%5D%5BshowUid%5D=17&tx_t3blog_pi1%5BblogList%5D%5Byear%5D=2011&tx_t3blog_pi1%5BblogList%5D%5Bmonth%5D=12&tx_t3blog_pi1%5BblogList%5D%5Bday%5D=07&cHash=bb9177d8192db5b5756aca088ea79677 What might be done about high prices of journals?], IMU blog on mathematical journals, July 12, 2011.
* [http://www.monbiot.com/2011/08/29/the-lairds-of-learning/ The lairds of learning] George Monbiot, August 29, 2011.
** [http://sedgemore.com/2011/09/serials-crisis-and-corn-laws/ Serials crisis and corn laws], Francis Sedgemore, September 7, 2011.
* [http://www.guardian.co.uk/commentisfree/2011/aug/29/academic-publishers-murdoch-socialist Academic publishers make Murdoch look like a socialist], George Monbiot, the Guardian, August 29, 2011.
* [http://www.timeshighereducation.co.uk/story.asp?storycode=417576 Peers, review your actions], Michael Taylor, Times Higher Education, September 29, 2011.
* [http://gowers.wordpress.com/2011/10/31/how-might-we-get-to-a-new-model-of-mathematical-publishing/ How might we get to a new model of mathematical publishing?], Timothy Gowers, October 31, 2011.
** [http://gowers.wordpress.com/2011/11/03/a-more-modest-proposal/ A more modest proposal], Timothy Gowers, November 3, 2011.
** [http://boolesrings.org/krautzberger/2011/11/26/the-recent-publishing-debate-a-timeline/ A timeline of the debate initiated by this post], Peter Krautzberger, November 26, 2011.
* [http://www.nytimes.com/2012/01/11/opinion/research-bought-then-paid-for.html Research Bought, Then Paid For], Michael B. Eisen, New York Times opinion piece, January 10, 2012
** [http://www.nytimes.com/2012/01/23/opinion/should-research-be-more-freely-available.html?_r=1 Should Research Be More Freely Available?], Jeffrey M. Drazen (Editor in Chief of The New England Journal of Medicine), Gene D. Sprouse (treasurer of [http://www.aps.org APS]), and Joseph W. Serene (publisher at [http://www.aps.org APS]), letters to the New York Times, January 23, 2012.
* [http://www.guardian.co.uk/science/2012/jan/16/academic-publishers-enemies-science?CMP=twt_fd Academic publishers have become the enemies of science], Mike Taylor, the Guardian, January 16, 2011.
** [http://www.guardian.co.uk/science/2012/jan/27/academic-publishers-enemies-science-wrong Branding academic publishers 'enemies of science' is offensive and wrong], Graham Taylor, January 27, 2011.
** [http://nelh.blogspot.com/2012/02/elsevier-double-dipping-and-nhs.html Elsevier, double-dipping, and the NHS], Ben Toth, February 11, 2012.
* [http://www.michaeleisen.org/blog/?p=873 Nature’s shiny sounding copout on open access], Michael Eisen, January 26, 2012.
* [http://svpow.wordpress.com/2012/01/27/publishers-invent-a-whole-new-form-of-evil-suing-their-customers/ Publishers invent a whole new form of evil: suing their customers], Mike Taylor, SV-POW, January 27, 2012.
* [http://occamstypewriter.org/scurry/2012/01/28/why-i-chose-to-decline-an-invitation-to-review-by-elsevier/ Why I chose to decline an invitation to review by Elsevier], Stephen Curry, January 28, 2012.
* [http://sbseminar.wordpress.com/2012/02/01/journals-and-the-arxiv/ Journals and the arXiv], Scott Morrison, February 1, 2012.
* [http://occupypublishing.blogspot.com.au/2012/02/scientific-journals-in-e-publishing-age.html scientific journals in the e-publishing age], Phillip Thrift, February 1, 2012.
* [http://gowers.wordpress.com/2012/02/02/abstract-thoughts-about-online-review-systems Abstract thoughts about online review systems], Tim Gowers, February 2, 2012.
* [http://cameronneylon.net/blog/the-research-works-act-and-the-breakdown-of-mutual-incomprehension/ The Research Works Act and the breakdown of mutual incomprehension], Cameron Neylon, February 3, 2012.
* [http://sbseminar.wordpress.com/2012/02/09/a-forum-on-mathematical-publishing/ A forum on mathematical publishing], Scott Morrison, February 9, 2012.
* [http://vort.org/2012/02/09/moral-imperative-open-science/ The moral imperative for Open Science], Russell Neches, February 9, 2012.
* [http://johncarlosbaez.wordpress.com/2012/02/10/the-federal-research-public-access-act/ The Federal Research Public Access Act], John Baez, February 10, 2012.
* [http://www.guardian.co.uk/science/blog/2012/feb/10/parable-farmers-teleporting-duplicator The parable of the farmers and the Teleporting Duplicator], Michael Taylor, the Guardian, February 10, 2012.
* [http://svpow.wordpress.com/2012/02/11/why-isnt-anyone-publishing-open-access-articles-in-elsevier-journals/ Why isn’t anyone publishing open-access articles in Elsevier journals?], Mike Taylor, February 11, 2012.
* [http://michaelnielsen.org/blog/how-you-can-help-the-federal-research-public-access-act-frpaa-become-law/ How you can help the Federal Research Public Access Act (FRPAA) become law], Michael Nielsen (interviewing Heather Joseph), February 14, 2012.
* [http://lisnews.org/elsevier_filters_recommendation_engine_to_show_elsevier_titles_only Elsevier Filters Recommendation Engine to Show Elsevier Titles Only], LISNews, February 14, 2012.
* [http://techcrunch.com/2012/02/15/the-dangerous-research-works-act/ The Dangerous “Research Works Act”], Richard Price, TechCrunch, February 15, 2012.
* [http://www.ethlife.ethz.ch/archive_articles/120217_bibliothek_neubauer/index_EN A thorn in the side for science publishers], Wolfram Neubauer, February 17, 2012.
** [http://johncarlosbaez.wordpress.com/2012/02/20/elsevier-and-springer-sue-university-library/ Elsevier and Springer Sue University Library], John Baez, February 20, 2012.

== Media ==

* [http://www.nature.com/nature/journal/v445/n7126/full/445347a.html PR's 'pit bull' takes on open access], Jim Giles, Nature, January 25, 2007. Summary: A coalition of scientific publishers (including Elsevier, Wiley, and the American Chemical Society) organises to oppose open access.
* [http://www.guardian.co.uk/business/2008/may/30/armstrade.weaponstechnology Reed Elsevier makes its final farewell to arms], Katie Allen, the Guardian, 30 May 2008. Summary: Reed Elsevier was until 2009 organizing arms trade fairs.
** [http://www.acme-journal.org/vol8/Stafford09.pdf Lessons from the Campaign against Elsevier "We won, but how did we win?"], Tom Stafford, ACME: An International E-Journal for Critical Geographies 2009, 8 (3), 494-504.
** [http://www.caat.org.uk/issues/armsfairs/reedelsevier.php Campaign success: Reed Elsevier sells international arms fairs], Campaign against arms trade, March 9, 2009.
* [http://classic.the-scientist.com/blog/display/55679/ Elsevier Published 6 Fake Journals], Bob Grant, The Scientist, May 7, 2009. Summary: Elsevier was paid by unnamed pharmaceutical companies to publish six journals that looked like independent peer-reviewed medical journals, but which were not.
** [http://en.wikipedia.org/wiki/Australasian_Journal_of_Bone_%26_Joint_Medicine The wikipedia page on these six journals].
** The Elsevier fake-journal tally eventually rose to [http://www.earlham.edu/~peters/fos/2009/06/elsevier-fake-journal-tally-now-9.html nine].
** [http://www.guardian.co.uk/commentisfree/2009/may/09/bad-science-medical-journals-companies The danger of drugs... and data], Ben Goldacre, the Guardian, May 8, 2009.
** [http://www.elsevier.com/wps/find/authored_newsitem.cws_home/companynews05_01203 Elsevier press release on this incident], May 7, 2009.
* [http://www.insidehighered.com/news/2009/06/23/elsevier Elsevier Won't Pay for Praise], Scott Jashik, Inside Higher Ed, June 23, 2009. Summary: Elsevier suspends its practice of offering Amazon gift cards to anyone who would give their textbooks a five-star rating.

== Other Information ==

* '''On Elsevier'''
** [http://www.reed-elsevier.com/mediacentre/pressreleases/Documents/2010/Reed%20Elsevier%202009%20Results%20Announcement%2017%20February%202010%20FINAL.pdf Reed Elsevier's 2009 report] Elsevier reported a profit of 1.1 billion dollars on revenue of 3.2 billion dollars.
** [http://en.wikipedia.org/wiki/Elsevier#Criticism_and_controversies Criticism and controversies of Elsevier] (Wikipedia)
** [http://gizmodo.com/5870241 Elsevier support for the Stop Online Piracy Act (SOPA)] (Gizmodo)
*** [http://en.wikipedia.org/wiki/List_of_organizations_that_support_the_Stop_Online_Piracy_Act List of organizations with official stances on the Stop Online Piracy Act] (Wikipedia)
** [http://www.michaeleisen.org/blog/?p=846 Elsevier support for the Research Works Act (RWA)] (Michael Nielsen)
*** [http://poynder.blogspot.com/2012/01/elsevier-needs-to-get-out-more.html Elsevier needs to get out more] (Richard Poynder)
*** [http://freethoughtblogs.com/pharyngula/2012/01/16/elsevier-evil/ Elsevier = evil] (Phyrangula)
*** [http://www.michaeleisen.org/blog/?p=807 Elsevier-funded NY Congresswoman Carolyn Maloney Wants to Deny Americans Access to Taxpayer Funded Research] (Michael Eisen)
**** [http://www.michaeleisen.org/blog/?p=807#comment-52048 A response by Tom Reller] (Vice President and Head of Global Corporate Relations at Elsevier)
*** Note however that the editorial board of [http://www.thelancet.com/ the Lancet], a very prestigious medical journal published by Elsevier, has [http://www.thelancet.com/journals/lancet/article/PIIS0140-6736(12)60125-1/fulltext come out strongly against the Research Works Act].
*** [http://www.elsevier.com/wps/find/intro.cws_home/elsevierstatement A message to the research community: Elsevier, access, and the Research Works Act], Elsevier, undated as of Feb 6 2012.
** [http://www.whitehouse.gov/sites/default/files/microsites/ostp/scholarly-pubs-%28%23168%29%20Elsevier%20submission.pdf Elsevier submission to the Office of Science and Technology Policy on open access], January 2012.
*** [http://openaccess.kb.se/?p=637 Elsevier tries to block institutional OA mandates], Jan Hagerlid, January 31, 2012.
** [http://www.researchinformation.info/riaut03elsevier.html Why commercial publishers are good for research], Arie Jongejan, CEO Science & Technology, Elsevier, Autumn 2003.
** [http://www.elsevier.com/wps/find/authorsview.authors/preprints Elsevier's policy on authors making their papers available on preprint servers] (Short version: Elsevier allows draft versions of papers to be placed on public servers such as the arXiv, and revised versions of papers to be placed on personal or institutional pages, but final versions of papers are only permitted at the journal site itself.)

* '''Stock analyses of Elsevier and other publishers'''
** [http://www.econ.ucsb.edu/~tedb/Journals/morganstanley.pdf Scientific Publishing: Knowledge is Power], Morgan Stanley, September 20, 2002.
** [http://dl.dropbox.com/u/4398178/Reciprocal%20Space%20Files/001-BR-EndoftheBigDeal-2011.pdf Reed Elsevier: The inevitable crunch point – downgrading to under perform because of growing concerns on Elsevier], Bernstein Research, March 10, 2011.
** [http://dl.dropbox.com/u/4398178/Reciprocal%20Space%20Files/002-BR-ElsevierNegotiations-2011.pdf Reed Elsevier, Bringing down the house – Why Elsevier is vulnerable in its upcoming Big Deal negotiations], Bernstein Research, March 29, 2011.
** [http://dl.dropbox.com/u/4398178/Reciprocal%20Space%20Files/003-BR-ReedCostofKnowledge-2012.pdf Occupy Elsevier], Bernstein Research, February 6, 2012.
** [https://plus.google.com/117663015413546257905/posts/1xRiEyWnipc Noise around boycott against Elsevier offers short term trading opportunity], Exane Paribas, February 7, 2012.
*** [http://cameronneylon.net/blog/a-tale-of-two-analysts/ A tale of two analysts], Cameron Neylon, February 15, 2012.

* '''On open access'''
** [http://en.wikipedia.org/wiki/Open_access Open Access]
** [http://oad.simmons.edu Open Access Directory]
** [http://www.earlham.edu/~peters/fos/overview.htm Open Access Overview] (Peter Suber)

* '''On scholarly journals'''
** [http://www.unc.edu/scholcomdig/whitepapers/panitch-michalak.html The serials crisis] Judith Panitch and Sarah Michalak, A White Paper for the UNC-Chapel Hill Scholarly Communications Convocation, January, 2005.
** [http://www.ams.org/membership/mem-journal-survey AMS Journal Price Survey]
*** [http://www.mathematik.uni-bielefeld.de/~rehmann/BIB/AMS/Publisher.html Math Journal Price Survey], from 2008 data.
** [http://en.wikipedia.org/wiki/Serials_crisis Journal subscription prices have increased far more rapidly than either inflation or spending on research]
** [http://www.mcafee.cc/Journal/Summary.pdf A summary of journal price averages in various disciplines including mathematics as of 2010] (see also [http://www.mcafee.cc/Journal/ the parent site, which contains more detailed information]).
** [http://www.econ.ucsb.edu/~tedb/Journals/BundleContracts.html Big Deal Contract Project] - an analysis of journal bundling contracts, and the attempts by publishers such as Elsevier to prevent them from becoming public.
** [http://oad.simmons.edu/oadwiki/OA_journal_business_models Open access journal business models] (from the Open Access Directory)
** [http://www.mathunion.org/fileadmin/CEIC/bestpractice/bpfinal.pdf Best Current Practices for Journals], endorsed by the International Mathematical Union general assembly, August 16, 2010.
** [http://www.msri.org/attachments/workshops/587/MSRIfinalreport.pdf Mathematics journals: what is valued and what may change], Report of the workshop held at MSRI, Berkeley, California on February 14 – 16 2011.

* '''Miscellaneous links'''
** [http://www.math.umd.edu/research/crisis.html The Crisis in Scientific Publishing] - a collection of links hosted by the University of Maryland.
** [http://www.azimuthproject.org/azimuth/show/Academic+publishing Academic publishing] - a wiki collection of links at the Azimuth project.

== Elsevier mathematics journals ==

This list is taken from [http://www.elsevier.com/wps/find/P11.cws_home/mathjournals here]

* [http://www.elsevier.com/wps/find/journaldescription.cws_home/708310/ Acta Mathematica Scientia]
* [http://www.elsevier.com/locate/yaama Advances in Applied Mathematics]
* [http://www.elsevier.com/locate/advengsoft Advances in Engineering Software]
* [http://www.journals.elsevier.com/advances-in-mathematics/ Advances in Mathematics]
* [http://www.elsevier.com/locate/anihpc Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire]
* [http://www.elsevier.com/locate/apal Annals of Pure & Applied Logic]
* [http://www.elsevier.com/wps/find/journaldescription.cws_home/600714 Annales Scientifiques de l'École Normale Supérieure] (Until 2008)
** This journal is [http://www.math.ens.fr/edition/annales/ now published by the Société mathématique de France].
* [http://www.elsevier.com/locate/arcontrol Annual Reviews in Control]
* [http://www.journals.elsevier.com/applied-and-computational-harmonic-analysis/ Applied & Computional Harmonic Analysis]
** Ingrid Daubechies resigned her position as editor-in-chief in 2012, according to her statement on [http://thecostofknowledge.com the Elsevier boycott site].
* [http://www.elsevier.com/locate/apm Applied Mathematical Modelling]
* [http://www.elsevier.com/locate/amc Applied Mathematics & Computation]
* [http://www.journals.elsevier.com/applied-mathematics-letters/ Applied Mathematics Letters]
** [http://retractionwatch.wordpress.com/2011/06/13/applied-mathematics-letters-posts-apology-for-retracting-intelligent-design-friendly-paper/ Applied Mathematics Letters posts apology for retracting Intelligent Design-friendly paper], Retraction Watch, 13 June 2011.
** [http://www.timeshighereducation.co.uk/story.asp?sectioncode=26&storycode=416514&c=1 Second thoughts result in payout], Paul Jump, Times Higher Education, 16 June 2011.
* [http://www.elsevier.com/locate/apnum Applied Numerical Mathematics]
* [http://www.elsevier.com/locate/artint Artificial Intelligence]
* [http://www.elsevier.com/locate/automatica Automatica]
* [http://www.elsevier.com/locate/btt Biometric Technology Today]
* [http://www.elsevier.com/locate/biosystems Biosystems]
* [http://www.elsevier.com/locate/bulsci Bulletin des Sciences Mathématiques]
* [http://www.journals.elsevier.com/chaos-solitons-and-fractals/ Chaos, Solitons & Fractals]
** There was a significant amount of controversy regarding the quality control at this journal during the tenure of a past editor-in-chief, who stepped down in 2009. Unfortunately, most of the primary reporting on this has been taken down due to ongoing litigation.
** [http://en.wikipedia.org/wiki/Elsevier#Chaos.2C_Solitons_.26_Fractals The Wikipedia section on this issue]
** [http://sbseminar.wordpress.com/2008/11/30/laffaire-el-naschie/ L’affaire El Naschie], Secret Blogging Seminar, November 30, 2008.
** [http://www.ima.umn.edu/~arnold/siam-columns/integrity-under-attack.pdf Integrity under attack: The State of Scholarly Publishing], Douglas Arnold, SIAM news, December 2009.
** [http://www.bbc.co.uk/news/science-environment-15697636 Nature journal libel case begins], Pallab Ghosh, BBC News, November 11, 2011.
* [http://www.elsevier.com/locate/cnsns Communications in Nonlinear Science and Numerical Simulation]
* [http://www.elsevier.com/wps/find/journaldescription.cws_home/600301/description#description Comptes Rendus Mathematique]
* [http://www.elsevier.com/locate/comgeo Computational Geometry]
* [http://www.elsevier.com/locate/csda Computational Statistics & Data Analysis]
* [http://www.elsevier.com/locate/cma Computer Methods in Applied Mechanics and Engineering]
* [http://www.journals.elsevier.com/computers-and-mathematics-with-applications Computers & Mathematics with Applications]
** [http://www.sciencedirect.com/science/article/pii/S0898122109005070 A computer application in mathematics], M. Sivasubramanian, S. Kalimuthu, in Computers and Mathematics with Applications, vol. 59 (2010) pp. 296-297. (This article is discussed in [http://blog.mathunion.org/journals/?no_cache=1&tx_t3blog_pi1%5BblogList%5D%5BshowUid%5D=30&tx_t3blog_pi1%5BblogList%5D%5Byear%5D=2012&tx_t3blog_pi1%5BblogList%5D%5Bmonth%5D=02&tx_t3blog_pi1%5BblogList%5D%5Bday%5D=05&cHash=a2d6424f899302a7ea3b75b9bb591802 this blog post] on the IMU mathematics journal blog, and is also available [http://www.math.hkbu.edu.hk/~ttang/newspaper/funnyarticle11.pdf here].)
** The editorial board [http://about.elsevier.com/pdf/LetterFromEditor.pdf was replaced in 2012].
* [http://www.elsevier.com/locate/conengprac Control Engineering Practice]
* [http://www.elsevier.com/locate/difgeo Differential Geometry and its Applications]
* [http://www.elsevier.com/locate/dam Discrete Applied Mathematics]
* [http://www.elsevier.com/locate/disc Discrete Mathematics]
* [http://www.elsevier.com/locate/disopt Discrete Optimization]
* [http://www.elsevier.com/locate/endm Electronic Notes in Discrete Mathematics]
* [http://www.elsevier.com/locate/entcs Electronic Notes in Theoretical Computer Science]
* [http://www.elsevier.com/locate/enganabound Engineering Analysis with Boundary Elements]
* [http://www.elsevier.com/locate/engappai Engineering Applications of Artificial Intelligence]
* [http://www.elsevier.com/locate/ejc European Journal of Combinatorics]
** Gunther Ziegler [http://www.scilogs.de/wblogs/blog/mathematik-im-alltag/allgemein/2012-02-19/boykottiert-elsevier-ich-boykottiere-elsevier resigned his position] as an editor of this journal in 2012.
* [http://www.elsevier.com/locate/ejor European Journal of Operational Research]
* [http://www.elsevier.com/locate/expomath Expositiones Mathematicae]
* [http://www.elsevier.com/locate/ffa Finite Fields and their Applications]
* [http://www.elsevier.com/locate/fss Fuzzy Sets and Systems]
* [http://www.elsevier.com/locate/hm Historia Mathematica]
* [http://www.elsevier.com/locate/indag Indagationes Mathematicae]
* [http://www.elsevier.com/locate/ins Information Sciences]
* [http://www.elsevier.com/locate/ijforecast International Journal of Forecasting]
* [http://www.elsevier.com/locate/nlm International Journal of Non-Linear Mechanics]
* [http://www.elsevier.com/locate/matpur Journal de Mathématiques Pures et Appliquées]
* [http://www.elsevier.com/locate/yjabr Journal of Algebra]
* [http://www.sciencedirect.com/science/journal/01966774 Journal of Algorithms]
** [http://www.cs.colorado.edu/~hal/jalg.html Editorial board resignation], December 13, 2003.
** [http://www.cs.colorado.edu/~hal/chronicle.txt Editorial Board of Scientific Journal Quits, Accusing Elsevier of Price-Gouging], Brock Read, the Chronicle of Higher Education, February 9, 2004.
* [http://www.elsevier.com/locate/jal Journal of Applied Logic]
* [http://www.elsevier.com/locate/jat Journal of Approximation Theory]
* [http://www.elsevier.com/locate/yjcta Journal of Combinatorial Theory, series A]
** Gunther Ziegler [http://www.scilogs.de/wblogs/blog/mathematik-im-alltag/allgemein/2012-02-19/boykottiert-elsevier-ich-boykottiere-elsevier resigned his position] as an editor of this journal in 2012.
* [http://www.elsevier.com/locate/yjctb Journal of Combinatorial Theory, series B]
* [http://www.elsevier.com/locate/jco Journal of Complexity]
* [http://www.elsevier.com/locate/cam Journal of Computational & Applied Mathematics]
* [http://www.elsevier.com/locate/jcss Journal of Computer and System Sciences]
* [http://www.elsevier.com/locate/yjdeq Journal of Differential Equations]
* [http://www.elsevier.com/locate/jda Journal of Discrete Algorithms]
* [http://www.elsevier.com/locate/jeconom Journal of Econometrics]
* [http://www.elsevier.com/locate/yjfan Journal of Functional Analysis]
* [http://www.elsevier.com/locate/geomphys Journal of Geometry and Physics]
* [http://www.elsevier.com/locate/jmaa Journal of Mathematical Analysis & Applications]
* [http://www.elsevier.com/locate/jmateco Journal of Mathematical Economics]
* [http://www.elsevier.com/locate/yjmva Journal of Multivariate Analysis]
* [http://www.elsevier.com/locate/jnt Journal of Number Theory]
* [http://www.elsevier.com/locate/jprocont Journal of Process Control]
* [http://www.journals.elsevier.com/journal-of-pure-and-applied-algebra/ Journal of Pure & Applied Algebra]
* [http://www.elsevier.com/locate/jspi Journal of Statistical Planning & Inference]
* [http://www.elsevier.com/locate/fi Journal of the Franklin Institute]
* [http://www.elsevier.com/locate/jkss Journal of the Korean Statistical Society]
* [http://www.elsevier.com/locate/laa Linear Algebra and its Applications]
* [http://www.elsevier.com/locate/mcm Mathematical and Computer Modelling]
* [http://www.elsevier.com/locate/mbs Mathematical Biosciences]
* [http://www.elsevier.com/locate/mss Mathematical Social Science]
* [http://www.elsevier.com/locate/matcom Mathematics and Computers in Simulation]
* [http://www.elsevier.com/locate/neunet Neural Networks]
* [http://www.elsevier.com/locate/na Nonlinear Analysis]
** [http://www.sciencedirect.com/science/article/pii/S0362546X04000409 On the second part of Hilbert's 16th problem], E. Oxenhielm, Nonlinear Analysis 57 (1), April 2004.
*** [http://news.bbc.co.uk/2/hi/science/nature/3243736.stm Historic maths problem 'cracked'] David Whitehouse, BBC, November 27, 2003.
*** [http://tesugen.com/archives/03/12/elin-oxenhielm-update Elin Oxenhielm update], Peter Lindberg, December 3, 2003.
*** [http://www.nature.com/news/2003/031209/full/news031208-4.html Mathematicians dispute proof of century-old problem], John Whitfield, Nature, December 9, 2003.
*** [http://plus.maths.org/content/struggling-sixteen Struggling for sixteen], Rachel Thomas, Plus magazine, December 16, 2003.
*** The paper was eventually [http://www.sciencedirect.com/science/article/pii/S0362546X04000409 withdrawn from the journal by the editors].
** [http://www.sciencedirect.com/science/article/pii/S0362546X0500235X On some contradictory computations in multi-dimensional mathematics], L. Carvalho, Nonlinear Analysis 63 (5-7), November 2005, 725--734. (Claims that the change of variables formula is incorrect.)
*** [http://math.ucr.edu/home/baez/corfield/2006/03/new-bogdanoff-affair_114355412211228579.html A New Bogdanoff Affair?], David Corfield, March 28, 2006.
*** [http://www.sciencedirect.com/science/article/pii/S0362546X06004597 A comment on: ''On some contradictory computations in multi-dimensional mathematics''], E. Capelas de Oliveira, W. Rodrigues, Nonlinear Anal. 67 (7), October 2007, 2316–2320.
*** As of 2012, the original paper of Carvalho has not been retracted from the journal. (However, it is no longer listed as a publication on [http://www.icmc.usp.br/~andcarva/publicac.html Carvalho's web page].)
** [http://blog.mikael.johanssons.org/archive/2006/03/this-is-me-losing-all-faith-in-non-linear-analysis/ This is me losing all faith in Nonlinear Analysis], Mikael Johansson, March 28, 2006.
* [http://www.elsevier.com/locate/nahs Nonlinear Analysis: Hybrid Systems]
* [http://www.elsevier.com/locate/nonrwa Nonlinear Analysis: Real world applications]
* [http://www.elsevier.com/locate/orl Operations Research Letters]
* [http://www.elsevier.com/locate/pr Pattern Recognition]
* [http://www.elsevier.com/locate/physa Physica A: Statistical Mechanics and its Applications]
* [http://www.elsevier.com/locate/physd Physica D: Nonlinear Phenomena]
* [http://www.elsevier.com/locate/simpat Simulation Modelling Practice & Theory]
* [http://www.elsevier.com/locate/stamet Statistical Methodology]
* [http://www.elsevier.com/locate/stapro Statistics and Probability Letters]
* [http://www.elsevier.com/locate/spa Stochastic Processes and their Applications]
* [http://www.elsevier.com/locate/sysconle Systems & Control Letters]
* [http://www.sciencedirect.com/science/journal/00409383 Topology]
** [http://math.ucr.edu/home/baez/topology-letter.pdf Editorial board resignation letter, 10 August 2006]
** [http://www.nysun.com/arts/rebellion-erupts-over-journals-of-academia/42317/ A Rebellion Erupts Over Journals Of Academia], Gary Shapiro, New York Sun, 26 October, 2006.
** [http://www.ams.org/notices/200705/comm-toped-web.pdf Jumping Ship: Topology editorial board resigns], Allyn Jackson, Notices of the American Mathematical Society, May 2007.
** [http://en.wikipedia.org/wiki/Topology_(journal) Wikipedia page on the journal]
** This journal was [http://www.info.sciverse.com/techsupport/journals/jnldiscontinued.htm discontinued in 2012].
* [http://www.journals.elsevier.com/topology-and-its-applications/ Topology & its Applications]
** In 2001, a group of editors of this journal [http://www.uflib.ufl.edu/oa/2009/posters/constitutional-declarationsdeniselgposter2-1.pdf resigned] to form [http://www.msp.warwick.ac.uk/agt/2012/12-01/ Algebraic & Geometric Topology].

== Open Access journals ==

* These lists are taken from the [http://www.doaj.org/ Directory of Open Access Journals] (limited to peer-reviewed journals).
** Perhaps someone could spell out or cut/paste the DOAJ lists below, like the Elsevier list above.

* In [http://www.doaj.org/doaj?func=subject&cpid=58&uiLanguage=en mathematics]

* In [http://www.doaj.org/doaj?func=subject&cpid=59&uiLanguage=en statistics]

* In [http://www.doaj.org/doaj?func=subject&cpid=114&uiLanguage=en computer science], e.g.
** [http://www.jair.org/ Journal of Artificial Intelligence Research]
** [http://www.lmcs-online.org Logical Methods in Computer Science]
** [http://jmlr.csail.mit.edu/ Journal of Machine Learning Research]
** [http://theoryofcomputing.org/ Theory of Computing]
** [http://www.jucs.org/ Journal of Universal Computer Science]
** [http://cjtcs.cs.uchicago.edu/ Chicago Journal of Theoretical Computer Science]

* In [http://www.doaj.org/doaj?func=subject&cpid=49&uiLanguage=en physics], e.g.
** [http://prx.aps.org/ Physical Review X]
** [http://iopscience.iop.org/1367-2630/ The New Journal of Physics]

== Mathematics journal price tables ==

The following tables list the ten most expensive mathematics journals by volume list price (as of 2008), and (for comparison) the ten mathematics journals with the highest impact factor (as of 2000). One should caution that due to complicated (and, in some cases, [http://www.econ.ucsb.edu/~tedb/Journals/BundleContracts.html deliberately obscured]) bundling agreements, the actual price of subscriptions to many journals (including Elsevier journals) may differ somewhat from the official list price. Nevertheless, these tables should convey the rough order of magnitude, at least, of journal costs from publisher to publisher.

Data is drawn from [http://www.mathematik.uni-bielefeld.de/~rehmann/BIB/AMS/Price_per_Volume.html this set of 2007 journal price data] and [http://in-cites.com/research/2001/oct_15_2001-2.html this list of 2000 ISI impact factors]. All prices in US dollars.

=== Top ten mathematics journals by volume list price ===

{|
|Title
|Publisher
|Price/volume
|Price/page
|-
|J. Math. Sci. (New York)
|Springer
|9998
|1.38
|-
|Theoret. Comput. Sci.
|Elsevier
|6551
|1.02
|-
|J. Math. Anal. Appl.
|Academic Press/Elsevier
|6362
|0.36
|-
|J. Algebra
|Academic Press/Elsevier
|5736
|0.51
|-
|Nonlinear Anal.
|Elsevier
|5426
|0.84
|-
|Discrete Math.
|Elsevier
|5269
|1.63
|-
|Appl. Math. Comput.
|Elsevier
|5250
|0.38
|-
|Math. Methods Appl. Sci.
|Wiley/Teubner
|4995
|2.09
|-
|Linear Algebra Appl.
|Elsevier
|4885
|0.94
|-
|Math. Nachr.
|Wiley/VCH Verlag
|4795
|2.58
|}

=== Top ten mathematics journals by impact factor ===

{|
|Title
|Publisher
|Price/volume
|Price/page
|-
|Bull. Amer. Math. Soc.
|American Mathematical Society
|418
|0.64
|-
|Acta Mathematica
|Institut Mittag-Leffler
|392
|0.65
|-
|J. Amer. Math. Soc.
|American Mathematical Society
|287
|0.24
|-
|Comm. Pure Appl. Math.
|Wiley
|3205
|1.74
|-
|Inventiones Mathemat.
|Springer-Verlag
|3232
|1.21
|-
|Annals of Mathematics
|Princeton University Press
|260
|0.13
|-
|Advances in Mathematics
|Elsevier/Academic Press
|3221
|0.41
|-
|Mem. Amer. Math. Soc.
|American Mathematical Society
|N/A
|N/A
|-
|Commun. Contemp. Math.
|World Scientific
|483
|0.51
|-
|Geom. Func. Anal.
|Springer/Birkhauser
|1185
|0.88
|}

== Data from libraries ==

Pricing data from libraries is often hard to come by (for instance, many bundling contracts come with confidentiality agreements). More links in this section would be greatly appreciated.

* [http://www.bibliothek.kit.edu/cms/english/most-expensive-journals%20.php Here is a list of the 10 most expensive journals subscribed to by the Karlsruhe Institute of Technology] as of 2010/2011. 8 of the 10 are published by Elsevier.
* [http://libraries.mit.edu/sites/scholarly/mit-open-access/open-access-at-mit/mit-open-access-policy/publishers-and-the-mit-faculty-open-access-policy/elsevier-fact-sheet/ Elsevier Fact Sheet], MIT libraries. MIT avoids bundling in order to obtain flexibility in its subscriptions, but pays Elsevier almost $2 million/year for its journals.
* [http://www.purdueexponent.org/campus/article_19f1031d-0396-5b21-870a-c7f9f6ca91bc.html According to this news article], Purdue pays Elsevier $2.3 million/year for digital access to its journals, with price increases of approximately 5 percent per year.
* The [http://www.econ.ucsb.edu/~tedb/Journals/BundleContracts.html Bundle Contract Project] seeks to collect bundling contracts from commercial publishers.

Journal publishing reform

2012-02-23T08:52:17Z

Gowers: /* Reactions from blogs */

[[Image:elsevier_poster.jpg|right|300px|Credit: Michael Eisen]]

This is a collection of links to information, opinion, activism, and other issues concerning the practices of research journal publishers (particularly in the mathematical sciences). Further contributions are welcome.

== The cost of knowledge ==

[http://thecostofknowledge.com/ The cost of knowledge] is a web page at which one may register a protest against the practices of Elsevier by pledging not to submit a paper to an Elsevier journal, not to referee for an Elsevier journal, not to join an editorial board of an Elsevier journal, or some combination of the three. This site was inspired by the following blog post:

* [http://gowers.wordpress.com/2012/01/21/elsevier-my-part-in-its-downfall/ Elsevier - my part in its downfall], Timothy Gowers, January 21, 2012.

A more detailed statement of purpose of the boycott, can be [http://gowers.files.wordpress.com/2012/02/elsevierstatementfinal.pdf found here]. It is written and signed by [http://en.wikipedia.org/wiki/Scott_Aaronson Scott Aaronson], [http://en.wikipedia.org/wiki/Douglas_N._Arnold Douglas N. Arnold], [http://en.wikipedia.org/wiki/Artur_Ávila Artur Ávila], [http://en.wikipedia.org/wiki/John_C._Baez John Baez], [http://www-m3.ma.tum.de/Allgemeines/FolkmarBornemann Folkmar Bornemann], [http://en.wikipedia.org/wiki/Danny_Calegari Danny Calegari], [http://research.microsoft.com/en-us/um/people/cohn/ Henry Cohn], [http://en.wikipedia.org/wiki/Ingrid_Daubechies Ingrid Daubechies], [http://en.wikipedia.org/wiki/Jordan_Ellenberg Jordan Ellenberg], [http://www.math.uchicago.edu/~emerton/ Matthew Emerton], [http://wavelets.ens.fr/EQUIPE/marie.htm Marie Farge], [http://en.wikipedia.org/wiki/David_Gabai David Gabai], [http://en.wikipedia.org/wiki/Timothy_Gowers Timothy Gowers], [http://en.wikipedia.org/wiki/Ben_J._Green Ben Green], [http://de.wikipedia.org/wiki/Martin_Grötschel Martin Grötschel], [http://en.wikipedia.org/wiki/Michael_Harris_%28mathematician%29 Michael Harris], [http://en.wikipedia.org/wiki/Fr%C3%A9d%C3%A9ric_H%C3%A9lein Frédéric Hélein], [http://en.wikipedia.org/wiki/Robion_Kirby Rob Kirby], [http://en.wikipedia.org/wiki/Vincent_Lafforgue Vincent Lafforgue], [http://en.wikipedia.org/wiki/Greg_Lawler Gregory F. Lawler], [http://en.wikipedia.org/wiki/Randall_J._LeVeque Randall J. LeVeque], [http://en.wikipedia.org/wiki/Laszlo_lovasz Laszlo Lovasz], [http://www.math.umn.edu/~olver/ Peter J. Olver], [http://www.maths.qmul.ac.uk/~olof/ Olof Sisask], [http://en.wikipedia.org/wiki/Terence_tao Terence Tao], [http://en.wikipedia.org/wiki/Richard_Taylor_%28mathematician%29 Richard Taylor], [http://en.wikipedia.org/wiki/Bernard_Teissier Bernard Teissier], [http://en.wikipedia.org/wiki/Burt_Totaro Burt Totaro], [http://en.wikipedia.org/wiki/Lloyd_Trefethen Lloyd N. Trefethen], [http://kyokan.ms.u-tokyo.ac.jp/~tsuboi/ Takashi Tsuboi], [http://en.wikipedia.org/wiki/Marie-France_Vign%C3%A9ras Marie-France Vigneras], [http://en.wikipedia.org/wiki/Wendelin_Werner Wendelin Werner], [http://math.uchicago.edu/~wilkinso/ Amie Wilkinson], and [http://page.mi.fu-berlin.de/gmziegler/ Gunter M. Ziegler].

See also [http://blog.thecostofknowledge.com/ the blog associated to the cost of knowledge site]. A poster for the protest may be [http://math.ucr.edu/home/baez/elsevier_boycott_poster.pdf found here].

There have since been many reactions to this protest:

=== Reactions from blogs ===

* [http://gowers.wordpress.com/2012/01/23/httpthecostofknowledge-com/ The cost of knowledge], Timothy Gowers, January 23, 2012.
* [http://johncarlosbaez.wordpress.com/2012/01/26/ban-elsevier/ Ban Elsevier], John Baez, January 26, 2012.
* [http://www.scottaaronson.com/blog/?p=891 Boycott Elsevier!], Scott Aaronson, January 26, 2012.
* [http://terrytao.wordpress.com/2012/01/26/the-cost-of-knowledge/ The cost of knowledge], Terence Tao, January 26, 2012.
* [http://dabacon.org/pontiff/?p=5982 Why boycott Elsevier?], Adam Harrow, January 27, 2012.
* [http://cameroncounts.wordpress.com/2012/01/29/publishers-wars/ Publisher's wars], Peter Cameron, January 29, 2012.
* [http://gowers.wordpress.com/2012/01/29/whats-wrong-with-electronic-journals/ What's wrong with electronic journals], Tim Gowers, January 29, 2012.
* [http://sbseminar.wordpress.com/2012/01/30/thinking-about-elsevier-replacements/ Thinking about Elsevier replacements], David Speyer, January 30, 2012.
* [http://blogs.lse.ac.uk/impactofsocialsciences/2012/02/01/stand-down-journal-referee/ Comfort is the death knell of academia: why I’m standing down as a journal referee], Matthew Todd, LSE Impact Blog, February 1, 2012.
* [http://www.scilogs.de/wblogs/blog/detritus/sonstiges/2012-02-01/boykottiert-elsevier-unterst-tzt-open-access Boykottiert Elsevier! Unterstützt Open Access!], Martin Ballaschk, February 1, 2012. (German)
* [http://scholarlykitchen.sspnet.org/2012/02/02/mysteries-of-the-elsevier-boycott Mysteries of the Elsevier Boycott], Rick Anderson, February 2, 2012.
** [http://breakingculture.tumblr.com/post/17112742228/unraveling-boycott-mysteries Unraveling (some of) the mysteries of the Elsevier Boycott], Sean Johnson Andrews, February 6, 2012.
** [http://www.against-the-grain.com/2012/02/multigrain-discussion-another-response-to-the-elsevier-boycott/ Multigrain Discussion: Another Response to the Elsevier Boycott], Chuck Hamaker, February 14, 2012.
* [http://scholarlykitchen.sspnet.org/2012/02/02/the-elsevier-boycott-does-it-make-sense The Elsevier Boycott — Does It Make Sense?], Kent Anderson, February 2, 2012.
* [http://www.michaeleisen.org/blog/?p=890 You are Elsevier: time to overcome our fears and kill subscription journals], Michael Eisen, February 3, 2012.
** [http://scienceblogs.com/denialism/2012/02/eisen_calls_for_elsevier_boyco.php Eisen calls for Elsevier Boycott - but can we all go OA?], Mark Hoofnagle, February 6, 2012.
* [http://stochastictrend.blogspot.com/2012/02/in-defence-of-elsevier.html In Defence of Elsevier], David Stern, February 4, 2012.
* [http://blog.mathunion.org/journals/?no_cache=1&tx_t3blog_pi1%5BblogList%5D%5BshowUid%5D=30&tx_t3blog_pi1%5BblogList%5D%5Byear%5D=2012&tx_t3blog_pi1%5BblogList%5D%5Bmonth%5D=02&tx_t3blog_pi1%5BblogList%5D%5Bday%5D=05&cHash=a2d6424f899302a7ea3b75b9bb591802 More reasons to support the Elsevier boycott], Doug Arnold, IMU blog on mathematical journals, February 5, 2012.
* [http://gowers.wordpress.com/2012/02/08/a-more-formal-statement-about-mathematical-publishing/ A more formal statement about mathematical publishing], Timothy Gowers, February 8, 2012.
* [http://scientopia.org/blogs/drugmonkey/2012/02/08/explaining-resistance-to-the-elsevier-boycott-practicalities/ Explaining resistance to the Elsevier boycott: Practicalities.], DrugMonkey, February 8, 2012.
* [http://neurodojo.blogspot.com/2012/02/whens-scientists-and-published.html When scientists’ and publishers’ motivations align], Zen Faulkes, February 9, 2012.
* [https://etechlib.wordpress.com/2012/02/11/about-the-elsevier-controversy-and-essential-science/ About the Elsevier Controversy and Essential Science], PF Anderson, February 11, 2012.
* [http://www.science3point0.com/palphy/2012/02/12/journal-mega-bundles-thecostofknowledge/ Journal mega-bundles & TheCostOfKnowledge], Ross Mounce, February 12, 2012.
* [http://mathbabe.org/2012/02/13/mathematics-has-an-occupy-moment/ Mathematics has an Occupy moment], Cathy O'Neil, February 13, 2012.
* [http://svpow.wordpress.com/2012/02/13/a-window-of-opportunity-for-elsevier/ A window of opportunity for Elsevier], Mike Taylor, February 13, 2012.
* [http://mhpbooks.com/49648/5000-profs-join-boycott-of-elsevier-publications-in-international-academic-spring/ 5,000 profs join boycott of Elsevier publications in international “academic spring”], Dennis Johnson, February 14, 2012.
* [http://blogs.lse.ac.uk/impactofsocialsciences/2012/02/15/after-elsevier-boycott-green-open-access What comes after the Elsevier boycott? The answer might be found by following the ‘Green’ road to open access], Neil Stewart, LSE Impact Blog, February 15, 2012.
* [http://mhpbooks.com/50115/whats-next-in-the-elsevier-boycott/ What’s next in the Elsevier boycott?], Dennis Johnson, Melville House, February 16, 2012.
* [http://lj.libraryjournal.com/2012/02/opinion/barbara-fister/joining-the-movement-a-call-to-action-peer-to-peer-review/ Joining the Movement: A Call to Action | Peer to Peer Review] Barbara Fister, Library Journal, February 16, 2012
* [http://www.scilogs.de/wblogs/blog/mathematik-im-alltag/allgemein/2012-02-19/boykottiert-elsevier-ich-boykottiere-elsevier Boykottiert Elsevier! Ich boykottiere Elsevier!], Gunter Ziegler, February 19, 2012. (German)
* [http://burttotaro.wordpress.com/2012/02/19/i-am-not-a-radical-but-i-am-boycotting-elsevier/ I am not a radical, but I am boycotting Elsevier], Burt Totaro, February 19, 2012.
* [http://audsandens.blogspot.com/2012/02/taking-control-more-reasons-for.html Taking Control: More Reasons for the Elsevier Boycott], Aaron Barlow, February 20, 2012.
* [http://www.weeklyweinersmith.com/?p=211 The Elsevier Boycott], Zach and Kelly Wienersmith, February 21, 2012. (Podcast)
* [http://scienceblogs.com/webeasties/2012/02/the_future_of_science_pub.php The Future of Science Publishing], Kevin Bonham, February 21, 2012.
* [http://blogs.lse.ac.uk/impactofsocialsciences/2012/02/22/elsevier-price-boycotters-untruth/ Elsevier have a right to price their journals as they see fit, but they must be honest in their reasoning and not attack boycotters with untruths], Tim Leunig, LSE, February 22, 2012.

=== News aggregators ===

* [http://news.ycombinator.com/item?id=3494340 Fields medalist Tim Gowers: Elsevier — my part in its downfall], Hacker News, January 21, 2012
* [http://www.reddit.com/r/math/comments/oqirf/one_mathematicians_stance_against_elsevier/ One mathematician's stance against Elsevier], Reddit, January 22, 2012.
* [http://news.ycombinator.com/item?id=3501561 The Cost of Knowledge: Researchers taking a stand against Elsevier], Hacker News, January 23, 2012.
* [http://science.slashdot.org/story/12/01/27/1322234/scientists-organize-elsevier-boycott Scientists organize Elsevier boycott], Slashdot, January 27, 2012.
* [http://www.metafilter.com/112178/Scientists-boycott-Elsevier Scientists boycott Elsevier], Metafilter, January 29, 2012.
* [http://www.reddit.com/r/math/comments/pepuo/thanks_to_angry_mathematicians_elseviers/ Thanks to angry mathematicians, Elsevier's publishing model might be about to go up in smoke], Reddit, February 7, 2012.

=== Coverage by the media ===

* [http://www.theregister.co.uk/2012/01/28/scientists_boycott_elsevier/ Blog blast births boffin boycott of publisher Elsevier], Iain Thomson, the Register, January 28, 2012.
* [http://www.forbes.com/sites/timworstall/2012/01/28/elseviers-publishing-model-might-be-about-to-go-up-in-smoke/ Elsevier's Publishing Model Might be About to Go Up in Smoke], Tim Worstall, Forbes, January 28, 2012.
* [http://www.wired.com/wiredscience/2012/01/testify-the-open-science-movement-catches-fire/ Testify: The Open-Science Movement Catches Fire] David Dobbs, Wired, January 30, 2012.
* [http://chronicle.com/blogs/wiredcampus/elsevier-publishing-boycott-gathers-steam-among-academics/35216 Elsevier Publishing Boycott Gathers Steam Among Academics], Josh Fischman, The Chronicle of Higher Education, January 30, 2012.
* [http://www.techdirt.com/articles/20120130/13030217589/will-academics-boycott-elsevier-be-tipping-point-open-access-another-embarrassing-flop.shtml Will Academics' Boycott Of Elsevier Be The Tipping Point For Open Access -- Or Another Embarrassing Flop?], Glyn Moody, Techdirt, January 31, 2012.
* [http://boingboing.net/2012/01/31/scientists-boycott-elsevier-ov.html Scientists and scholars boycott Elsevier over bad business practices and copyright maximalism], Cory Doctorow, Boingboing, January 31, 2012.
* [http://lj.libraryjournal.com/2012/01/publishing/petition-targeting-elseviers-business-practices-begins-to-snowball/ Petition Targeting Elsevier’s Business Practices Begins to Snowball], Michael Kelley, Library Journal, January 31, 2012.
* [http://www.thebookseller.com/news/academics-call-boycott-elsevier.html Academics call for boycott of Elsevier], Charlotte Williams, The Bookseller, January 31, 2012.
* [http://chronicle.com/article/As-Journal-Boycott-Grows/130600/ As Journal Boycott Grows, Elsevier Defends Its Practices], Josh Fischman, The Chronicle of Higher Education, January 31, 2012.
* [http://arstechnica.com/science/news/2012/01/researchers-boycott-publisher-will-they-embrace-instant-publishing.ars Researchers boycott publisher; will they embrace instant publishing?], John Timmer, Ars Technica, January 31, 2012.
* [http://www.elmundo.es/elmundosalud/2012/01/30/noticias/1327952591.html Boicot científico a Elsevier], Cristina de Martos, El Mundo, January 31, 2012. (Spanish)
* [http://nos.nl/op3/artikel/335992-elsevier-in-de-clinch-met-wetenschappers.html Elsevier in de clinch met wetenschappers], NOS News, January 31, 2012. (Dutch)
* [http://news.sciencemag.org/scienceinsider/2012/02/thousands-of-scientists-vow-to-b.html Thousands of Scientists Vow to Boycott Elsevier to Protest Journal Prices], Jop de Vrieze, Science Insider, February 1, 2012.
* [http://www.mmm-online.com/elsevier-begins-outreach-as-push-back-on-publisher-threatens-to-widen/article/225855/ Elsevier begins outreach as push-back on publisher threatens to widen], Deborah Weinstein, Medical Marketing & Media, February 1, 2012.
* [http://www.care2.com/causes/scientists-fight-for-open-access-for-their-research.html Scientists Fight For Open Access For Research], Kristina Chew, Care2, February 1, 2012.
* [http://www.bloomberg.com/news/2012-02-01/samsung-csr-nfl-elsevier-motorola-intellectual-property.html Samsung, CSR, NFL, Elsevier, Motorola: Intellectual Property], Victoria Slind-Flor, Bloomberg, February 1, 2012. (Brief mention only.)
* [http://mediadecoder.blogs.nytimes.com/2012/02/01/the-breakfast-meeting-a-week-of-negative-ads-and-new-chief-at-sony/ The Breakfast Meeting: A Week of Negative Ads, and New Chief at Sony], Noam Cohen, New York Times, February 1, 2012. (Brief mention only.)
* [http://www.guardian.co.uk/science/2012/feb/02/academics-boycott-publisher-elsevier Scientists sign petition to boycott academic publisher Elsevier], Alison Flood, the Guardian, February 2, 2012.
* [http://blogues.cyberpresse.ca/sciences/2012/02/02/fronde-contre-les-revues-savantes-delsevier/ Étonnante fronde de chercheurs contre les revues savantes d’Elsevier], Jean-François Cliche, le Soleil, February 2, 2012. (French)
* [http://www.wired.com/wiredscience/2012/02/is-the-open-science-revolution-for-real/ Is the Open Science Revolution For Real?], David Dobbs, Wired, February 3, 2012.
* [http://www.economist.com/node/21545974 The price of information], the Economist, February 4, 2012.
* [http://archiv.twoday.net/stories/64967798/ Zum Elsevier-Boykott], Klaus Graf, Archivalia, February 5, 2012. (German)
* [http://paidcontent.org/article/419-academics-revolt-against-elseviers-journal-pricing/ Academics Revolt Against Elsevier’s Journal Pricing], Robert Andrews, PaidContent, February 6, 2012.
* [http://theconversation.edu.au/spread-the-word-scientists-are-tearing-down-publishers-walls-5098 Spread the word: scientists are tearing down publishers' walls], Alex Holcombe, the Conversation, February 7, 2012.
* [http://www2.ljworld.com/news/2012/feb/07/heard-hill-university-senate-considering-boycottin/ Heard on the Hill: University Senate considering boycotting publisher Elsevier; newspaper readership program popular at other places, too; KUMC researcher mentioned in LA Times story on Alzheimer’s], Andy Hyland, LJWorld, February 7, 2012.
* [http://hon.jp/news/modules/rsnavi/showarticle.php?id=3082 欧米圏で“学術の春”運動始まる、電子ジャーナル出版大手Elsevierに対し学者たちのボイコット運動が急拡大], editorial, hon.jp Daywatch, Feb 7, 2012. (Japanese)
* [http://the-scientist.com/2012/02/07/occupy-elsevier/ Occupy Elsevier?], Bob Grant, the Scientist, February 7, 2012.
* [http://www.theaustralian.com.au/higher-education/academics-boycott-publisher-elsevier/story-e6frgcjx-1226265110496?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+TheAustralianHigherEducationNews+%28The+Australian+%7C+Higher+Education%29&utm_content=Google+Reader Academics boycott publisher Elsevier], Bernard Lane, the Australian, February 8, 2012.
* [http://latimesblogs.latimes.com/jacketcopy/2012/02/wed-book-news-bezos-the-elsevier-boycott-and-more.html Wednesday book news: Bezos, the Elsevier boycott and more], Carolyn Kellogg, Los Angeles Times, February 8, 2012. (Brief mention only.)
* [http://www.guardian.co.uk/higher-education-network/blog/2012/feb/08/open-access-journals-elsvier-boycott Open access journals: are we asking the right questions?], Martin Paul Eve, the Guardian, February 8, 2012.
* [http://www.varsity.co.uk/news/4370 The Academic Spring], Patrick O'Grady, Varsity, February 8, 2012.
* [http://www.timeshighereducation.co.uk/story.asp?sectioncode=26&storycode=418952 Elsevier defends stance on anti-open-access bill], John Gill, Times Higher Education, February 9, 2012.
* [http://www.nature.com/news/elsevier-boycott-gathers-pace-1.10010 Elsevier boycott gathers pace], John Whitfield, Nature, February 9, 2012.
* [http://www.wired.com/wiredscience/2012/02/open-science-revolt-occupies-congress/ Open Science Revolt Occupies Congress], David Dobbs, Wired, February 9, 2012.
* [http://blogs.independent.co.uk/2012/02/09/the-future-of-academic-publishing/ The future of academic publishing], Mike Taylor, the Independent, February 9, 2012.
* [http://www.tcs.cam.ac.uk/issue/news/cambridge-professor-leads-boycott-of-elsevier-publications/ Cambridge Professor leads boycott of Elsevier Publications], Emily Loud, the Cambridge Student Online, February 9, 2012.
* [http://www.utimes.pitt.edu/?p=19679 Protest launched against journal publisher], Kimberly Barlow, University Times, February 9, 2012.
* [http://jeps.efpsa.org/blog/2012/02/10/a-revolution-in-scientific-publishing/ A revolution in scientific publishing?], Sina Scherer, JEPS Bulletin, February 10, 2012.
* [http://libraries.mit.edu/sites/news/elsevier-boycott-grows/7785/ Elsevier Boycott Grows: MIT Faculty Speak About Participation], Ellen Duranceau, MIT Libraries News, February 10, 2012.
* [http://www1.folha.uol.com.br/ciencia/1046769-cientistas-boicotam-a-maior-editora-de-periodicos-do-mundo.shtml Cientistas boicotam a maior editora de periódicos do mundo], Sabine Righetti, Folha, February 10, 2012. (Portugese)
* [http://www.bostonglobe.com/opinion/2012/02/12/why-scientists-are-boycotting-publisher/9sCpDEP7BkkX1INfakn3NL/story.html Why scientists are boycotting a publisher], Gareth Cook, the Boston Globe, February 12, 2012.
** [http://bostonglobe.com/opinion/letters/2012/02/16/elsevier-committed-universal-access-content-sustainable-publishing-model/70QfCpSOvy0IUibSK6eCTL/story.html Elsevier committed to universal access to content, sustainable publishing model], Lynne Herndon (former CEO of Cell press), letter to the editor, the Boston Globe, February 16, 2012.
*** [http://quomodocumque.wordpress.com/2012/02/16/elseviers-sorry-defense-of-the-research-works-act/ Elsevier’s sorry defense of the Research Works Act], Jordan Ellenberg, February 16, 2012.
* [http://newsbreaks.infotoday.com/NewsBreaks/The-Cost-of-Knowledge-Versus-Elsevier--Signatures-and-Growing-80575.asp The Cost of Knowledge Versus Elsevier: 5,600 Signatures and Growing], Robin Peek, Information Today, February 13, 2012.
* [http://www.pourlascience.fr/ewb_pages/a/actualite-la-fronde-des-chercheurs-contre-i-elsevier-i-29118.php La fronde des chercheurs contre Elsevier], Maurice Mashaal, Pour la Science, February 13, 2012.
* [http://www.newscientist.com/article/dn21467-web-freedoms-fuel-academic-spring-journal-protest.html Web freedoms fuel 'academic spring' journal protest], Jacob Aron, New Scientist, February 13, 2012.
* [http://www.nytimes.com/2012/02/14/science/researchers-boycott-elsevier-journal-publisher.html Mathematicians Organize Boycott of a Publisher], Thomas Lin, New York Times, February 13, 2012.
* [http://motherjones.com/blue-marble/2012/02/science-uprising Science Uprising], Julia Whitty, Mother Jones, February 13, 2012.
* [http://www.kansan.com/news/2012/feb/13/professors-boycott/ Professors boycott prominent publishing company], Kelsey Cipolla, The University Daily Kansan, February 13, 2012.
* [http://www.purdueexponent.org/opinion/editorials/article_a6e96c79-5c95-54b8-bf85-eca8de6bb3db.html Monopoly on research publishing is unethical], Editorial, The Exponent, February 14, 2012.
* [http://today.duke.edu/2012/02/elsevierboycott Duke Scholars Join Boycott Against Elsevier], Ashley Yeager, Duke Today, February 14, 2012.
* [https://theconversation.edu.au/academics-line-up-to-boycott-worlds-biggest-journal-publisher-5384 Academics line up to boycott world’s biggest journal publisher], Justin Norrie, the Conversation, February 15, 2012.
* [http://www.ft.com/cms/s/0/2494fbc4-5873-11e1-9f28-00144feabdc0.html Reed chief hits back at critics of division], Salamander Davoudi, February 16, 2012.
* [http://www.abc.net.au/science/articles/2012/02/17/3433568.htm Academics boycott journal publisher], Eleanor Bell, ABC news, February 17, 2012.
* [http://www.onthemedia.org/2012/feb/17/trouble-elsevier-leading-academic-publisher/ Trouble for Elsevier, the leading academic publisher], Rick Karr, On the media, NPR, February 17, 2012. (Audio)
** [http://crookedtimber.org/2012/02/21/some-questions-for-elsevier/ Some questions for Elsevier], Harry Brighouse, Crooked Timber, February 21, 2012.
* [http://www.smh.com.au/national/education/academics-join-world-fight-against-publisher-20120220-1tjk6.html Academics join world fight against publisher], Nicky Phillips, Sydney Morning Herald, February 21, 2012.
* [http://blogs.discovermagazine.com/crux/2012/02/21/its-not-academic-how-publishers-are-squelching-science-communication/ It’s Not Academic: How Publishers Are Squelching Science Communication], Michael Taylor, Discover Magazine, February 21, 2012.

=== Open letters to Elsevier ===

* [http://math.berkeley.edu/~kirby/elsevier.html Letter to Elsevier], Rob Kirby, December 30, 1997.
* [http://www.library.yale.edu/~llicense/ListArchives/0310/msg00048.html Call for Boycott of Cell Press Journals], Peter Walter and Keith Yamomoto, October 19, 2003.
** [http://genomebiology.com/2003/4/10/spotlight-20031024-02 Researchers boycott Cell Press], Alison McCook, Genome Biology, October 24, 2003.
* [http://www.cs.colorado.edu/~hal/jalg.html Journal of Algorithms editorial board resignation], December 13, 2003.
* [http://math.ucr.edu/home/baez/topology-letter.pdf Topology editorial board resignation letter], August 10, 2006.
* [http://idiolect.org.uk/elsevier/docs/academics_openletter.pdf Arms fairs and academics], 138 signatories, February 28, 2007.
* [http://idiolect.org.uk/notes/?p=643 An open letter to Elsevier and all those involved in the IEHG], Keith Halfacree, April 10, 2007.
* [http://www.coar-repositories.org/news/coar-writes-open-letter-as-reaction-to-elseviers-practices/ Open Letter to Elsevier], Norbert Lossau, Chair of the Executive Board, Confederation of Open Access Repositories, February 6, 2012.
* [https://plus.google.com/105282922684661032446/posts/WCZqgPVehmx Letter to Elsevier], Cynthia Parr, February 10, 2012.
* [http://darwin.eeb.uconn.edu/uncommon-ground/2012/02/declining-elsevier.html Declining elsevier], Kent Holsinger, February 10, 2012.
* [http://occamstypewriter.org/scurry/2012/02/12/an-open-letter-to-elsevier/ An Open Letter to Elsevier], Stephen Curry, February 12, 2012.
* [http://svpow.wordpress.com/2012/02/15/a-response-to-one-elsevier-employee-and-an-open-letter-to-the-rest/ A response to one Elsevier employee, and an open letter to the rest], Matt Wedel, February 15, 2012.
* [http://fakeelsevier.wordpress.com/2012/02/19/dear-elsevier-employees-with-love-from-fakeelsevier/ Dear Elsevier employees, with love, from @FakeElsevier], FakeElsevier, February 19, 2012.

=== Responses by Elsevier ===

* [http://gowers.wordpress.com/2012/01/21/elsevier-my-part-in-its-downfall/#comment-14679 A response by David Clark at Elsevier], January 23, 2012.
* [http://www.elsevier.com/wps/find/intro.cws_home/elsevieropenletter An open letter to the research community: journal prices, discounts, and access], Elsevier, undated as of Feb 6, 2012.
** [http://bjoern.brembs.net/news.php?item.833.11 Against Own Assertion, Elsevier Doubled Price For Access], Bjorn Brembs, February 11, 2012.
* [http://www.epjournal.net/blog/2012/02/elsevier-and-evolution-human-behavior/ Elsevier and Evolution & Human Behavior], Robert Kurzban (co-editor-in-chief of the Elsevier journal Evolution & Human Behavior), February 6, 2012.
* [http://poynder.blogspot.com/2012/02/elseviers-alicia-wise-on-rwa-west-wing.html Elsevier’s Alicia Wise on the RWA, the West Wing, and Universal Access], Richard Poynder, February 9, 2012.

=== Other coverage ===

* [http://www.arl.org/sparc/media/prime-time-for-public-access.shtml Prime Time for Public Access], Heather Joseph, Executive Director, SPARC, February 9, 2012.
* [http://www.openaire.eu/en/news-a-events/news/343-elseviers-practices-opposing-open-access Elsevier’s practices opposing open access], Open Access Infrastructure for Research in Europe, February 16, 2012.
* [http://en.wikipedia.org/wiki/The_Cost_of_Knowledge The wikipedia page] for this protest.

See also [http://scienceblogs.com/confessions/2012/02/around_the_web_research_works.php this list of links], which is focused more around the Research Works Act, but also contains many links regarding the boycott, as well as [http://www.math.ntnu.no/~stacey/Mathforge/Math2.0 Math 2.0], a discussion forum for all topics related to the future of mathematical publishing.

== Other pledges, boycotts, and petitions ==

* [http://www.researchwithoutwalls.org/ Research Without Walls]
* [http://www.openaccesspledge.com/ Open Access Pledge]
* [http://www-fourier.ujf-grenoble.fr/petitions/index.php?petition=3 Appel pour des négociations équilibrées avec les éditeurs de revues scientifiques] - a petition concerning the bundling and pricing practices of Springer
* [http://www.thepetitionsite.com/207/support-the-open-access-movement-stop-the-research-works-act/?cid=FB_TAF A petition to stop the Research Works Act]
* [http://www.taxpayeraccess.org/action/FRPAA2012.shtml Call to action: Tell Congress you support the Bipartisan Federal Research Public Access Act (H.R. 4004 and S. 2096)], Alliance for taxpayer access, February 9, 2012.

* See these tag libraries from the [http://oad.simmons.edu/oadwiki/OA_tracking_project Open Access Tracking Project] (more comprehensive after April 2009 than before):
** [http://www.connotea.org/tag/oa.boycotts oa.boycotts]
** [http://www.connotea.org/tag/oa.declarations oa.declarations]
** [http://www.connotea.org/tag/oa.petitions oa.petitions]
** [http://www.connotea.org/tag/oa.pledges oa.pledges]

== Other blog posts, letters, and opinion pieces ==
* [http://math.berkeley.edu/~kirby/journals.html Comparative price of math journals], Rob Kirby, May 27, 1997.
** [http://math.berkeley.edu/~kirby/elsevier.html Open letter to Elsevier], Rob Kirby, December 30, 1997.
** [http://math.berkeley.edu/~kirby/jp00.html 2000 data update]
* [http://www.ams.org/notices/200007/forum-birman.pdf Scientific Publishing: A Mathematician’s Viewpoint], Joan Birman, Notices of the American Mathematical Society, 770-774, July 2000.
* [http://homepages.cwi.nl/~apt/ps/cacm01.pdf One More Revolution to Make: Free Scientific Publishing], Krzysztof R. Apt, Communications of ACM, 44(5), pp. 25-28, 2001.
* [http://www.nieuwarchief.nl/serie5/deel02/sep2001/pdf/apt.pdf Towards free access to scientific literature], Krzysztof R. Apt, Nieuw Archief voor Wiskunde, 5/2 nr. 3, September 2001, pp. 251-255.
* [http://stromme.uib.no/kuperberg.pdf Scholarly Mathematical Communication at a Crossroads], Greg Kuperberg, Nieuw Arch. Wisk., (5) 3 no.3, September 2002.
* [http://people.ccmr.cornell.edu/~ginsparg/blurb/pg02pr.html Can Peer Review be better Focused?], Paul Ginsparg, March 2003.
* [http://www.ams.org/notices/200402/commentary.pdf Fleeced?], Rob Kirby, Notices of the American Mathematical Society, 161-162, February 2004.
* [http://www.ams.org/notices/200405/commentary.pdf We can make a change], Gerard van der Geer, Notices of the American Mathematical Society, May 2004.
* [http://www.math.columbia.edu/~neumann/journal.html What we can do about journal pricing], Walter Neumann, September 2005.
** The discussions mentioned in that email led to the [http://web.archive.org/web/20110525195311/http://members.cox.net/banffprotocol/ Banff protocol] (web site now only available through web archive).
* [http://www.scottaaronson.com/writings/journal.html Review of The Access Principle by John Willinsky], Scott Aaronson, 2006
* [http://digitalstrategies.blogspot.com/2008/06/scientific-publication-in-internet-era.html Scientific Publishing in the Internet Era] Efthymios Constantinides June 17, 2008
* [http://arstechnica.com/science/news/2008/11/elsevier-beyond-the-pale-of-scientific-respectability.ars Publishing economics harm science's credibility], Chris Lee, Ars Technica, November 2008.
* [http://www.ima.umn.edu/~arnold/siam-columns/integrity-under-attack.pdf Integrity under attack: The State of Scholarly Publishing], Douglas Arnold, SIAM news, December 2009.
* [http://scholarlykitchen.sspnet.org/2010/01/04/why-hasnt-scientific-publishing-been-disrupted-already/ Why Hasn’t Scientific Publishing Been Disrupted Already?], Michael Clarke, January 4, 2010.
* [http://math.ucr.edu/home/baez/journals.html What We Can Do About Science Journals], John Baez, January 24, 2011.
* [http://blog.mathunion.org/journals/?no_cache=1&tx_t3blog_pi1%5BblogList%5D%5BshowUid%5D=17&tx_t3blog_pi1%5BblogList%5D%5Byear%5D=2011&tx_t3blog_pi1%5BblogList%5D%5Bmonth%5D=12&tx_t3blog_pi1%5BblogList%5D%5Bday%5D=07&cHash=bb9177d8192db5b5756aca088ea79677 What might be done about high prices of journals?], IMU blog on mathematical journals, July 12, 2011.
* [http://www.monbiot.com/2011/08/29/the-lairds-of-learning/ The lairds of learning] George Monbiot, August 29, 2011.
** [http://sedgemore.com/2011/09/serials-crisis-and-corn-laws/ Serials crisis and corn laws], Francis Sedgemore, September 7, 2011.
* [http://www.guardian.co.uk/commentisfree/2011/aug/29/academic-publishers-murdoch-socialist Academic publishers make Murdoch look like a socialist], George Monbiot, the Guardian, August 29, 2011.
* [http://www.timeshighereducation.co.uk/story.asp?storycode=417576 Peers, review your actions], Michael Taylor, Times Higher Education, September 29, 2011.
* [http://gowers.wordpress.com/2011/10/31/how-might-we-get-to-a-new-model-of-mathematical-publishing/ How might we get to a new model of mathematical publishing?], Timothy Gowers, October 31, 2011.
** [http://gowers.wordpress.com/2011/11/03/a-more-modest-proposal/ A more modest proposal], Timothy Gowers, November 3, 2011.
** [http://boolesrings.org/krautzberger/2011/11/26/the-recent-publishing-debate-a-timeline/ A timeline of the debate initiated by this post], Peter Krautzberger, November 26, 2011.
* [http://www.nytimes.com/2012/01/11/opinion/research-bought-then-paid-for.html Research Bought, Then Paid For], Michael B. Eisen, New York Times opinion piece, January 10, 2012
** [http://www.nytimes.com/2012/01/23/opinion/should-research-be-more-freely-available.html?_r=1 Should Research Be More Freely Available?], Jeffrey M. Drazen (Editor in Chief of The New England Journal of Medicine), Gene D. Sprouse (treasurer of [http://www.aps.org APS]), and Joseph W. Serene (publisher at [http://www.aps.org APS]), letters to the New York Times, January 23, 2012.
* [http://www.guardian.co.uk/science/2012/jan/16/academic-publishers-enemies-science?CMP=twt_fd Academic publishers have become the enemies of science], Mike Taylor, the Guardian, January 16, 2011.
** [http://www.guardian.co.uk/science/2012/jan/27/academic-publishers-enemies-science-wrong Branding academic publishers 'enemies of science' is offensive and wrong], Graham Taylor, January 27, 2011.
** [http://nelh.blogspot.com/2012/02/elsevier-double-dipping-and-nhs.html Elsevier, double-dipping, and the NHS], Ben Toth, February 11, 2012.
* [http://www.michaeleisen.org/blog/?p=873 Nature’s shiny sounding copout on open access], Michael Eisen, January 26, 2012.
* [http://svpow.wordpress.com/2012/01/27/publishers-invent-a-whole-new-form-of-evil-suing-their-customers/ Publishers invent a whole new form of evil: suing their customers], Mike Taylor, SV-POW, January 27, 2012.
* [http://occamstypewriter.org/scurry/2012/01/28/why-i-chose-to-decline-an-invitation-to-review-by-elsevier/ Why I chose to decline an invitation to review by Elsevier], Stephen Curry, January 28, 2012.
* [http://sbseminar.wordpress.com/2012/02/01/journals-and-the-arxiv/ Journals and the arXiv], Scott Morrison, February 1, 2012.
* [http://occupypublishing.blogspot.com.au/2012/02/scientific-journals-in-e-publishing-age.html scientific journals in the e-publishing age], Phillip Thrift, February 1, 2012.
* [http://gowers.wordpress.com/2012/02/02/abstract-thoughts-about-online-review-systems Abstract thoughts about online review systems], Tim Gowers, February 2, 2012.
* [http://cameronneylon.net/blog/the-research-works-act-and-the-breakdown-of-mutual-incomprehension/ The Research Works Act and the breakdown of mutual incomprehension], Cameron Neylon, February 3, 2012.
* [http://sbseminar.wordpress.com/2012/02/09/a-forum-on-mathematical-publishing/ A forum on mathematical publishing], Scott Morrison, February 9, 2012.
* [http://vort.org/2012/02/09/moral-imperative-open-science/ The moral imperative for Open Science], Russell Neches, February 9, 2012.
* [http://johncarlosbaez.wordpress.com/2012/02/10/the-federal-research-public-access-act/ The Federal Research Public Access Act], John Baez, February 10, 2012.
* [http://www.guardian.co.uk/science/blog/2012/feb/10/parable-farmers-teleporting-duplicator The parable of the farmers and the Teleporting Duplicator], Michael Taylor, the Guardian, February 10, 2012.
* [http://svpow.wordpress.com/2012/02/11/why-isnt-anyone-publishing-open-access-articles-in-elsevier-journals/ Why isn’t anyone publishing open-access articles in Elsevier journals?], Mike Taylor, February 11, 2012.
* [http://michaelnielsen.org/blog/how-you-can-help-the-federal-research-public-access-act-frpaa-become-law/ How you can help the Federal Research Public Access Act (FRPAA) become law], Michael Nielsen (interviewing Heather Joseph), February 14, 2012.
* [http://lisnews.org/elsevier_filters_recommendation_engine_to_show_elsevier_titles_only Elsevier Filters Recommendation Engine to Show Elsevier Titles Only], LISNews, February 14, 2012.
* [http://techcrunch.com/2012/02/15/the-dangerous-research-works-act/ The Dangerous “Research Works Act”], Richard Price, TechCrunch, February 15, 2012.
* [http://www.ethlife.ethz.ch/archive_articles/120217_bibliothek_neubauer/index_EN A thorn in the side for science publishers], Wolfram Neubauer, February 17, 2012.
** [http://johncarlosbaez.wordpress.com/2012/02/20/elsevier-and-springer-sue-university-library/ Elsevier and Springer Sue University Library], John Baez, February 20, 2012.

== Media ==

* [http://www.nature.com/nature/journal/v445/n7126/full/445347a.html PR's 'pit bull' takes on open access], Jim Giles, Nature, January 25, 2007. Summary: A coalition of scientific publishers (including Elsevier, Wiley, and the American Chemical Society) organises to oppose open access.
* [http://www.guardian.co.uk/business/2008/may/30/armstrade.weaponstechnology Reed Elsevier makes its final farewell to arms], Katie Allen, the Guardian, 30 May 2008. Summary: Reed Elsevier was until 2009 organizing arms trade fairs.
** [http://www.acme-journal.org/vol8/Stafford09.pdf Lessons from the Campaign against Elsevier "We won, but how did we win?"], Tom Stafford, ACME: An International E-Journal for Critical Geographies 2009, 8 (3), 494-504.
** [http://www.caat.org.uk/issues/armsfairs/reedelsevier.php Campaign success: Reed Elsevier sells international arms fairs], Campaign against arms trade, March 9, 2009.
* [http://classic.the-scientist.com/blog/display/55679/ Elsevier Published 6 Fake Journals], Bob Grant, The Scientist, May 7, 2009. Summary: Elsevier was paid by unnamed pharmaceutical companies to publish six journals that looked like independent peer-reviewed medical journals, but which were not.
** [http://en.wikipedia.org/wiki/Australasian_Journal_of_Bone_%26_Joint_Medicine The wikipedia page on these six journals].
** The Elsevier fake-journal tally eventually rose to [http://www.earlham.edu/~peters/fos/2009/06/elsevier-fake-journal-tally-now-9.html nine].
** [http://www.guardian.co.uk/commentisfree/2009/may/09/bad-science-medical-journals-companies The danger of drugs... and data], Ben Goldacre, the Guardian, May 8, 2009.
** [http://www.elsevier.com/wps/find/authored_newsitem.cws_home/companynews05_01203 Elsevier press release on this incident], May 7, 2009.
* [http://www.insidehighered.com/news/2009/06/23/elsevier Elsevier Won't Pay for Praise], Scott Jashik, Inside Higher Ed, June 23, 2009. Summary: Elsevier suspends its practice of offering Amazon gift cards to anyone who would give their textbooks a five-star rating.

== Other Information ==

* '''On Elsevier'''
** [http://www.reed-elsevier.com/mediacentre/pressreleases/Documents/2010/Reed%20Elsevier%202009%20Results%20Announcement%2017%20February%202010%20FINAL.pdf Reed Elsevier's 2009 report] Elsevier reported a profit of 1.1 billion dollars on revenue of 3.2 billion dollars.
** [http://en.wikipedia.org/wiki/Elsevier#Criticism_and_controversies Criticism and controversies of Elsevier] (Wikipedia)
** [http://gizmodo.com/5870241 Elsevier support for the Stop Online Piracy Act (SOPA)] (Gizmodo)
*** [http://en.wikipedia.org/wiki/List_of_organizations_that_support_the_Stop_Online_Piracy_Act List of organizations with official stances on the Stop Online Piracy Act] (Wikipedia)
** [http://www.michaeleisen.org/blog/?p=846 Elsevier support for the Research Works Act (RWA)] (Michael Nielsen)
*** [http://poynder.blogspot.com/2012/01/elsevier-needs-to-get-out-more.html Elsevier needs to get out more] (Richard Poynder)
*** [http://freethoughtblogs.com/pharyngula/2012/01/16/elsevier-evil/ Elsevier = evil] (Phyrangula)
*** [http://www.michaeleisen.org/blog/?p=807 Elsevier-funded NY Congresswoman Carolyn Maloney Wants to Deny Americans Access to Taxpayer Funded Research] (Michael Eisen)
**** [http://www.michaeleisen.org/blog/?p=807#comment-52048 A response by Tom Reller] (Vice President and Head of Global Corporate Relations at Elsevier)
*** Note however that the editorial board of [http://www.thelancet.com/ the Lancet], a very prestigious medical journal published by Elsevier, has [http://www.thelancet.com/journals/lancet/article/PIIS0140-6736(12)60125-1/fulltext come out strongly against the Research Works Act].
*** [http://www.elsevier.com/wps/find/intro.cws_home/elsevierstatement A message to the research community: Elsevier, access, and the Research Works Act], Elsevier, undated as of Feb 6 2012.
** [http://www.whitehouse.gov/sites/default/files/microsites/ostp/scholarly-pubs-%28%23168%29%20Elsevier%20submission.pdf Elsevier submission to the Office of Science and Technology Policy on open access], January 2012.
*** [http://openaccess.kb.se/?p=637 Elsevier tries to block institutional OA mandates], Jan Hagerlid, January 31, 2012.
** [http://www.researchinformation.info/riaut03elsevier.html Why commercial publishers are good for research], Arie Jongejan, CEO Science & Technology, Elsevier, Autumn 2003.
** [http://www.elsevier.com/wps/find/authorsview.authors/preprints Elsevier's policy on authors making their papers available on preprint servers] (Short version: Elsevier allows draft versions of papers to be placed on public servers such as the arXiv, and revised versions of papers to be placed on personal or institutional pages, but final versions of papers are only permitted at the journal site itself.)

* '''Stock analyses of Elsevier and other publishers'''
** [http://www.econ.ucsb.edu/~tedb/Journals/morganstanley.pdf Scientific Publishing: Knowledge is Power], Morgan Stanley, September 20, 2002.
** [http://dl.dropbox.com/u/4398178/Reciprocal%20Space%20Files/001-BR-EndoftheBigDeal-2011.pdf Reed Elsevier: The inevitable crunch point – downgrading to under perform because of growing concerns on Elsevier], Bernstein Research, March 10, 2011.
** [http://dl.dropbox.com/u/4398178/Reciprocal%20Space%20Files/002-BR-ElsevierNegotiations-2011.pdf Reed Elsevier, Bringing down the house – Why Elsevier is vulnerable in its upcoming Big Deal negotiations], Bernstein Research, March 29, 2011.
** [http://dl.dropbox.com/u/4398178/Reciprocal%20Space%20Files/003-BR-ReedCostofKnowledge-2012.pdf Occupy Elsevier], Bernstein Research, February 6, 2012.
** [https://plus.google.com/117663015413546257905/posts/1xRiEyWnipc Noise around boycott against Elsevier offers short term trading opportunity], Exane Paribas, February 7, 2012.
*** [http://cameronneylon.net/blog/a-tale-of-two-analysts/ A tale of two analysts], Cameron Neylon, February 15, 2012.

* '''On open access'''
** [http://en.wikipedia.org/wiki/Open_access Open Access]
** [http://oad.simmons.edu Open Access Directory]
** [http://www.earlham.edu/~peters/fos/overview.htm Open Access Overview] (Peter Suber)

* '''On scholarly journals'''
** [http://www.unc.edu/scholcomdig/whitepapers/panitch-michalak.html The serials crisis] Judith Panitch and Sarah Michalak, A White Paper for the UNC-Chapel Hill Scholarly Communications Convocation, January, 2005.
** [http://www.ams.org/membership/mem-journal-survey AMS Journal Price Survey]
*** [http://www.mathematik.uni-bielefeld.de/~rehmann/BIB/AMS/Publisher.html Math Journal Price Survey], from 2008 data.
** [http://en.wikipedia.org/wiki/Serials_crisis Journal subscription prices have increased far more rapidly than either inflation or spending on research]
** [http://www.mcafee.cc/Journal/Summary.pdf A summary of journal price averages in various disciplines including mathematics as of 2010] (see also [http://www.mcafee.cc/Journal/ the parent site, which contains more detailed information]).
** [http://www.econ.ucsb.edu/~tedb/Journals/BundleContracts.html Big Deal Contract Project] - an analysis of journal bundling contracts, and the attempts by publishers such as Elsevier to prevent them from becoming public.
** [http://oad.simmons.edu/oadwiki/OA_journal_business_models Open access journal business models] (from the Open Access Directory)
** [http://www.mathunion.org/fileadmin/CEIC/bestpractice/bpfinal.pdf Best Current Practices for Journals], endorsed by the International Mathematical Union general assembly, August 16, 2010.
** [http://www.msri.org/attachments/workshops/587/MSRIfinalreport.pdf Mathematics journals: what is valued and what may change], Report of the workshop held at MSRI, Berkeley, California on February 14 – 16 2011.

* '''Miscellaneous links'''
** [http://www.math.umd.edu/research/crisis.html The Crisis in Scientific Publishing] - a collection of links hosted by the University of Maryland.
** [http://www.azimuthproject.org/azimuth/show/Academic+publishing Academic publishing] - a wiki collection of links at the Azimuth project.

== Elsevier mathematics journals ==

This list is taken from [http://www.elsevier.com/wps/find/P11.cws_home/mathjournals here]

* [http://www.elsevier.com/wps/find/journaldescription.cws_home/708310/ Acta Mathematica Scientia]
* [http://www.elsevier.com/locate/yaama Advances in Applied Mathematics]
* [http://www.elsevier.com/locate/advengsoft Advances in Engineering Software]
* [http://www.journals.elsevier.com/advances-in-mathematics/ Advances in Mathematics]
* [http://www.elsevier.com/locate/anihpc Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire]
* [http://www.elsevier.com/locate/apal Annals of Pure & Applied Logic]
* [http://www.elsevier.com/wps/find/journaldescription.cws_home/600714 Annales Scientifiques de l'École Normale Supérieure] (Until 2008)
** This journal is [http://www.math.ens.fr/edition/annales/ now published by the Société mathématique de France].
* [http://www.elsevier.com/locate/arcontrol Annual Reviews in Control]
* [http://www.journals.elsevier.com/applied-and-computational-harmonic-analysis/ Applied & Computional Harmonic Analysis]
** Ingrid Daubechies resigned her position as editor-in-chief in 2012, according to her statement on [http://thecostofknowledge.com the Elsevier boycott site].
* [http://www.elsevier.com/locate/apm Applied Mathematical Modelling]
* [http://www.elsevier.com/locate/amc Applied Mathematics & Computation]
* [http://www.journals.elsevier.com/applied-mathematics-letters/ Applied Mathematics Letters]
** [http://retractionwatch.wordpress.com/2011/06/13/applied-mathematics-letters-posts-apology-for-retracting-intelligent-design-friendly-paper/ Applied Mathematics Letters posts apology for retracting Intelligent Design-friendly paper], Retraction Watch, 13 June 2011.
** [http://www.timeshighereducation.co.uk/story.asp?sectioncode=26&storycode=416514&c=1 Second thoughts result in payout], Paul Jump, Times Higher Education, 16 June 2011.
* [http://www.elsevier.com/locate/apnum Applied Numerical Mathematics]
* [http://www.elsevier.com/locate/artint Artificial Intelligence]
* [http://www.elsevier.com/locate/automatica Automatica]
* [http://www.elsevier.com/locate/btt Biometric Technology Today]
* [http://www.elsevier.com/locate/biosystems Biosystems]
* [http://www.elsevier.com/locate/bulsci Bulletin des Sciences Mathématiques]
* [http://www.journals.elsevier.com/chaos-solitons-and-fractals/ Chaos, Solitons & Fractals]
** There was a significant amount of controversy regarding the quality control at this journal during the tenure of a past editor-in-chief, who stepped down in 2009. Unfortunately, most of the primary reporting on this has been taken down due to ongoing litigation.
** [http://en.wikipedia.org/wiki/Elsevier#Chaos.2C_Solitons_.26_Fractals The Wikipedia section on this issue]
** [http://sbseminar.wordpress.com/2008/11/30/laffaire-el-naschie/ L’affaire El Naschie], Secret Blogging Seminar, November 30, 2008.
** [http://www.ima.umn.edu/~arnold/siam-columns/integrity-under-attack.pdf Integrity under attack: The State of Scholarly Publishing], Douglas Arnold, SIAM news, December 2009.
** [http://www.bbc.co.uk/news/science-environment-15697636 Nature journal libel case begins], Pallab Ghosh, BBC News, November 11, 2011.
* [http://www.elsevier.com/locate/cnsns Communications in Nonlinear Science and Numerical Simulation]
* [http://www.elsevier.com/wps/find/journaldescription.cws_home/600301/description#description Comptes Rendus Mathematique]
* [http://www.elsevier.com/locate/comgeo Computational Geometry]
* [http://www.elsevier.com/locate/csda Computational Statistics & Data Analysis]
* [http://www.elsevier.com/locate/cma Computer Methods in Applied Mechanics and Engineering]
* [http://www.journals.elsevier.com/computers-and-mathematics-with-applications Computers & Mathematics with Applications]
** [http://www.sciencedirect.com/science/article/pii/S0898122109005070 A computer application in mathematics], M. Sivasubramanian, S. Kalimuthu, in Computers and Mathematics with Applications, vol. 59 (2010) pp. 296-297. (This article is discussed in [http://blog.mathunion.org/journals/?no_cache=1&tx_t3blog_pi1%5BblogList%5D%5BshowUid%5D=30&tx_t3blog_pi1%5BblogList%5D%5Byear%5D=2012&tx_t3blog_pi1%5BblogList%5D%5Bmonth%5D=02&tx_t3blog_pi1%5BblogList%5D%5Bday%5D=05&cHash=a2d6424f899302a7ea3b75b9bb591802 this blog post] on the IMU mathematics journal blog, and is also available [http://www.math.hkbu.edu.hk/~ttang/newspaper/funnyarticle11.pdf here].)
** The editorial board [http://about.elsevier.com/pdf/LetterFromEditor.pdf was replaced in 2012].
* [http://www.elsevier.com/locate/conengprac Control Engineering Practice]
* [http://www.elsevier.com/locate/difgeo Differential Geometry and its Applications]
* [http://www.elsevier.com/locate/dam Discrete Applied Mathematics]
* [http://www.elsevier.com/locate/disc Discrete Mathematics]
* [http://www.elsevier.com/locate/disopt Discrete Optimization]
* [http://www.elsevier.com/locate/endm Electronic Notes in Discrete Mathematics]
* [http://www.elsevier.com/locate/entcs Electronic Notes in Theoretical Computer Science]
* [http://www.elsevier.com/locate/enganabound Engineering Analysis with Boundary Elements]
* [http://www.elsevier.com/locate/engappai Engineering Applications of Artificial Intelligence]
* [http://www.elsevier.com/locate/ejc European Journal of Combinatorics]
** Gunther Ziegler [http://www.scilogs.de/wblogs/blog/mathematik-im-alltag/allgemein/2012-02-19/boykottiert-elsevier-ich-boykottiere-elsevier resigned his position] as an editor of this journal in 2012.
* [http://www.elsevier.com/locate/ejor European Journal of Operational Research]
* [http://www.elsevier.com/locate/expomath Expositiones Mathematicae]
* [http://www.elsevier.com/locate/ffa Finite Fields and their Applications]
* [http://www.elsevier.com/locate/fss Fuzzy Sets and Systems]
* [http://www.elsevier.com/locate/hm Historia Mathematica]
* [http://www.elsevier.com/locate/indag Indagationes Mathematicae]
* [http://www.elsevier.com/locate/ins Information Sciences]
* [http://www.elsevier.com/locate/ijforecast International Journal of Forecasting]
* [http://www.elsevier.com/locate/nlm International Journal of Non-Linear Mechanics]
* [http://www.elsevier.com/locate/matpur Journal de Mathématiques Pures et Appliquées]
* [http://www.elsevier.com/locate/yjabr Journal of Algebra]
* [http://www.sciencedirect.com/science/journal/01966774 Journal of Algorithms]
** [http://www.cs.colorado.edu/~hal/jalg.html Editorial board resignation], December 13, 2003.
** [http://www.cs.colorado.edu/~hal/chronicle.txt Editorial Board of Scientific Journal Quits, Accusing Elsevier of Price-Gouging], Brock Read, the Chronicle of Higher Education, February 9, 2004.
* [http://www.elsevier.com/locate/jal Journal of Applied Logic]
* [http://www.elsevier.com/locate/jat Journal of Approximation Theory]
* [http://www.elsevier.com/locate/yjcta Journal of Combinatorial Theory, series A]
** Gunther Ziegler [http://www.scilogs.de/wblogs/blog/mathematik-im-alltag/allgemein/2012-02-19/boykottiert-elsevier-ich-boykottiere-elsevier resigned his position] as an editor of this journal in 2012.
* [http://www.elsevier.com/locate/yjctb Journal of Combinatorial Theory, series B]
* [http://www.elsevier.com/locate/jco Journal of Complexity]
* [http://www.elsevier.com/locate/cam Journal of Computational & Applied Mathematics]
* [http://www.elsevier.com/locate/jcss Journal of Computer and System Sciences]
* [http://www.elsevier.com/locate/yjdeq Journal of Differential Equations]
* [http://www.elsevier.com/locate/jda Journal of Discrete Algorithms]
* [http://www.elsevier.com/locate/jeconom Journal of Econometrics]
* [http://www.elsevier.com/locate/yjfan Journal of Functional Analysis]
* [http://www.elsevier.com/locate/geomphys Journal of Geometry and Physics]
* [http://www.elsevier.com/locate/jmaa Journal of Mathematical Analysis & Applications]
* [http://www.elsevier.com/locate/jmateco Journal of Mathematical Economics]
* [http://www.elsevier.com/locate/yjmva Journal of Multivariate Analysis]
* [http://www.elsevier.com/locate/jnt Journal of Number Theory]
* [http://www.elsevier.com/locate/jprocont Journal of Process Control]
* [http://www.journals.elsevier.com/journal-of-pure-and-applied-algebra/ Journal of Pure & Applied Algebra]
* [http://www.elsevier.com/locate/jspi Journal of Statistical Planning & Inference]
* [http://www.elsevier.com/locate/fi Journal of the Franklin Institute]
* [http://www.elsevier.com/locate/jkss Journal of the Korean Statistical Society]
* [http://www.elsevier.com/locate/laa Linear Algebra and its Applications]
* [http://www.elsevier.com/locate/mcm Mathematical and Computer Modelling]
* [http://www.elsevier.com/locate/mbs Mathematical Biosciences]
* [http://www.elsevier.com/locate/mss Mathematical Social Science]
* [http://www.elsevier.com/locate/matcom Mathematics and Computers in Simulation]
* [http://www.elsevier.com/locate/neunet Neural Networks]
* [http://www.elsevier.com/locate/na Nonlinear Analysis]
** [http://www.sciencedirect.com/science/article/pii/S0362546X04000409 On the second part of Hilbert's 16th problem], E. Oxenhielm, Nonlinear Analysis 57 (1), April 2004.
*** [http://news.bbc.co.uk/2/hi/science/nature/3243736.stm Historic maths problem 'cracked'] David Whitehouse, BBC, November 27, 2003.
*** [http://tesugen.com/archives/03/12/elin-oxenhielm-update Elin Oxenhielm update], Peter Lindberg, December 3, 2003.
*** [http://www.nature.com/news/2003/031209/full/news031208-4.html Mathematicians dispute proof of century-old problem], John Whitfield, Nature, December 9, 2003.
*** [http://plus.maths.org/content/struggling-sixteen Struggling for sixteen], Rachel Thomas, Plus magazine, December 16, 2003.
*** The paper was eventually [http://www.sciencedirect.com/science/article/pii/S0362546X04000409 withdrawn from the journal by the editors].
** [http://www.sciencedirect.com/science/article/pii/S0362546X0500235X On some contradictory computations in multi-dimensional mathematics], L. Carvalho, Nonlinear Analysis 63 (5-7), November 2005, 725--734. (Claims that the change of variables formula is incorrect.)
*** [http://math.ucr.edu/home/baez/corfield/2006/03/new-bogdanoff-affair_114355412211228579.html A New Bogdanoff Affair?], David Corfield, March 28, 2006.
*** [http://www.sciencedirect.com/science/article/pii/S0362546X06004597 A comment on: ''On some contradictory computations in multi-dimensional mathematics''], E. Capelas de Oliveira, W. Rodrigues, Nonlinear Anal. 67 (7), October 2007, 2316–2320.
*** As of 2012, the original paper of Carvalho has not been retracted from the journal. (However, it is no longer listed as a publication on [http://www.icmc.usp.br/~andcarva/publicac.html Carvalho's web page].)
** [http://blog.mikael.johanssons.org/archive/2006/03/this-is-me-losing-all-faith-in-non-linear-analysis/ This is me losing all faith in Nonlinear Analysis], Mikael Johansson, March 28, 2006.
* [http://www.elsevier.com/locate/nahs Nonlinear Analysis: Hybrid Systems]
* [http://www.elsevier.com/locate/nonrwa Nonlinear Analysis: Real world applications]
* [http://www.elsevier.com/locate/orl Operations Research Letters]
* [http://www.elsevier.com/locate/pr Pattern Recognition]
* [http://www.elsevier.com/locate/physa Physica A: Statistical Mechanics and its Applications]
* [http://www.elsevier.com/locate/physd Physica D: Nonlinear Phenomena]
* [http://www.elsevier.com/locate/simpat Simulation Modelling Practice & Theory]
* [http://www.elsevier.com/locate/stamet Statistical Methodology]
* [http://www.elsevier.com/locate/stapro Statistics and Probability Letters]
* [http://www.elsevier.com/locate/spa Stochastic Processes and their Applications]
* [http://www.elsevier.com/locate/sysconle Systems & Control Letters]
* [http://www.sciencedirect.com/science/journal/00409383 Topology]
** [http://math.ucr.edu/home/baez/topology-letter.pdf Editorial board resignation letter, 10 August 2006]
** [http://www.nysun.com/arts/rebellion-erupts-over-journals-of-academia/42317/ A Rebellion Erupts Over Journals Of Academia], Gary Shapiro, New York Sun, 26 October, 2006.
** [http://www.ams.org/notices/200705/comm-toped-web.pdf Jumping Ship: Topology editorial board resigns], Allyn Jackson, Notices of the American Mathematical Society, May 2007.
** [http://en.wikipedia.org/wiki/Topology_(journal) Wikipedia page on the journal]
** This journal was [http://www.info.sciverse.com/techsupport/journals/jnldiscontinued.htm discontinued in 2012].
* [http://www.journals.elsevier.com/topology-and-its-applications/ Topology & its Applications]
** In 2001, a group of editors of this journal [http://www.uflib.ufl.edu/oa/2009/posters/constitutional-declarationsdeniselgposter2-1.pdf resigned] to form [http://www.msp.warwick.ac.uk/agt/2012/12-01/ Algebraic & Geometric Topology].

== Open Access journals ==

* These lists are taken from the [http://www.doaj.org/ Directory of Open Access Journals] (limited to peer-reviewed journals).
** Perhaps someone could spell out or cut/paste the DOAJ lists below, like the Elsevier list above.

* In [http://www.doaj.org/doaj?func=subject&cpid=58&uiLanguage=en mathematics]

* In [http://www.doaj.org/doaj?func=subject&cpid=59&uiLanguage=en statistics]

* In [http://www.doaj.org/doaj?func=subject&cpid=114&uiLanguage=en computer science], e.g.
** [http://www.jair.org/ Journal of Artificial Intelligence Research]
** [http://www.lmcs-online.org Logical Methods in Computer Science]
** [http://jmlr.csail.mit.edu/ Journal of Machine Learning Research]
** [http://theoryofcomputing.org/ Theory of Computing]
** [http://www.jucs.org/ Journal of Universal Computer Science]
** [http://cjtcs.cs.uchicago.edu/ Chicago Journal of Theoretical Computer Science]

* In [http://www.doaj.org/doaj?func=subject&cpid=49&uiLanguage=en physics], e.g.
** [http://prx.aps.org/ Physical Review X]
** [http://iopscience.iop.org/1367-2630/ The New Journal of Physics]

== Mathematics journal price tables ==

The following tables list the ten most expensive mathematics journals by volume list price (as of 2008), and (for comparison) the ten mathematics journals with the highest impact factor (as of 2000). One should caution that due to complicated (and, in some cases, [http://www.econ.ucsb.edu/~tedb/Journals/BundleContracts.html deliberately obscured]) bundling agreements, the actual price of subscriptions to many journals (including Elsevier journals) may differ somewhat from the official list price. Nevertheless, these tables should convey the rough order of magnitude, at least, of journal costs from publisher to publisher.

Data is drawn from [http://www.mathematik.uni-bielefeld.de/~rehmann/BIB/AMS/Price_per_Volume.html this set of 2007 journal price data] and [http://in-cites.com/research/2001/oct_15_2001-2.html this list of 2000 ISI impact factors]. All prices in US dollars.

=== Top ten mathematics journals by volume list price ===

{|
|Title
|Publisher
|Price/volume
|Price/page
|-
|J. Math. Sci. (New York)
|Springer
|9998
|1.38
|-
|Theoret. Comput. Sci.
|Elsevier
|6551
|1.02
|-
|J. Math. Anal. Appl.
|Academic Press/Elsevier
|6362
|0.36
|-
|J. Algebra
|Academic Press/Elsevier
|5736
|0.51
|-
|Nonlinear Anal.
|Elsevier
|5426
|0.84
|-
|Discrete Math.
|Elsevier
|5269
|1.63
|-
|Appl. Math. Comput.
|Elsevier
|5250
|0.38
|-
|Math. Methods Appl. Sci.
|Wiley/Teubner
|4995
|2.09
|-
|Linear Algebra Appl.
|Elsevier
|4885
|0.94
|-
|Math. Nachr.
|Wiley/VCH Verlag
|4795
|2.58
|}

=== Top ten mathematics journals by impact factor ===

{|
|Title
|Publisher
|Price/volume
|Price/page
|-
|Bull. Amer. Math. Soc.
|American Mathematical Society
|418
|0.64
|-
|Acta Mathematica
|Institut Mittag-Leffler
|392
|0.65
|-
|J. Amer. Math. Soc.
|American Mathematical Society
|287
|0.24
|-
|Comm. Pure Appl. Math.
|Wiley
|3205
|1.74
|-
|Inventiones Mathemat.
|Springer-Verlag
|3232
|1.21
|-
|Annals of Mathematics
|Princeton University Press
|260
|0.13
|-
|Advances in Mathematics
|Elsevier/Academic Press
|3221
|0.41
|-
|Mem. Amer. Math. Soc.
|American Mathematical Society
|N/A
|N/A
|-
|Commun. Contemp. Math.
|World Scientific
|483
|0.51
|-
|Geom. Func. Anal.
|Springer/Birkhauser
|1185
|0.88
|}

== Data from libraries ==

Pricing data from libraries is often hard to come by (for instance, many bundling contracts come with confidentiality agreements). More links in this section would be greatly appreciated.

* [http://www.bibliothek.kit.edu/cms/english/most-expensive-journals%20.php Here is a list of the 10 most expensive journals subscribed to by the Karlsruhe Institute of Technology] as of 2010/2011. 8 of the 10 are published by Elsevier.
* [http://libraries.mit.edu/sites/scholarly/mit-open-access/open-access-at-mit/mit-open-access-policy/publishers-and-the-mit-faculty-open-access-policy/elsevier-fact-sheet/ Elsevier Fact Sheet], MIT libraries. MIT avoids bundling in order to obtain flexibility in its subscriptions, but pays Elsevier almost $2 million/year for its journals.
* [http://www.purdueexponent.org/campus/article_19f1031d-0396-5b21-870a-c7f9f6ca91bc.html According to this news article], Purdue pays Elsevier $2.3 million/year for digital access to its journals, with price increases of approximately 5 percent per year.
* The [http://www.econ.ucsb.edu/~tedb/Journals/BundleContracts.html Bundle Contract Project] seeks to collect bundling contracts from commercial publishers.

Journal publishing reform

2012-02-16T23:30:57Z

Gowers: /* Reactions from blogs */

This is a collection of links to information, opinion, activism, and other issues concerning the practices of research journal publishers (particularly in the mathematical sciences). Further contributions are welcome.

== The cost of knowledge ==

[http://thecostofknowledge.com/ The cost of knowledge] is a web page at which one may register a protest against the practices of Elsevier by pledging not to submit a paper to an Elsevier journal, not to referee for an Elsevier journal, not to join an editorial board of an Elsevier journal, or some combination of the three. This site was inspired by the following blog post:

* [http://gowers.wordpress.com/2012/01/21/elsevier-my-part-in-its-downfall/ Elsevier - my part in its downfall], Timothy Gowers, January 21, 2012.

A more detailed statement of purpose of the boycott, can be [http://gowers.files.wordpress.com/2012/02/elsevierstatementfinal.pdf found here]. It is written and signed by Scott Aaronson, Douglas N. Arnold, Artur Avila, John Baez, Folkmar Bornemann, Danny Calegari, Henry Cohn, Ingrid Daubechies, Jordan Ellenberg, Matthew Emerton, Marie Farge, David Gabai, Timothy Gowers, Ben Green, Martin Grotschel, Michael Harris, Frederic Helein, Rob Kirby, Vincent Lafforgue, Gregory F. Lawler, Randall J. LeVeque, Laszlo Lovasz, Peter J. Olver, Olof Sisask, Terence Tao, Richard Taylor, Bernard Teissier, Burt Totaro, Lloyd N. Trefethen, Takashi Tsuboi, Marie-France Vigneras, Wendelin Werner, Amie Wilkinson, and Gunter M. Ziegler.

There have since been many reactions to this protest:

=== Reactions from blogs ===

* [http://gowers.wordpress.com/2012/01/23/httpthecostofknowledge-com/ The cost of knowledge], Timothy Gowers, January 23, 2012.
* [http://johncarlosbaez.wordpress.com/2012/01/26/ban-elsevier/ Ban Elsevier], John Baez, January 26, 2012.
* [http://www.scottaaronson.com/blog/?p=891 Boycott Elsevier!], Scott Aaronson, January 26, 2012.
* [http://terrytao.wordpress.com/2012/01/26/the-cost-of-knowledge/ The cost of knowledge], Terence Tao, January 26, 2012.
* [http://dabacon.org/pontiff/?p=5982 Why boycott Elsevier?], Adam Harrow, January 27, 2012.
* [http://cameroncounts.wordpress.com/2012/01/29/publishers-wars/ Publisher's wars], Peter Cameron, January 29, 2012.
* [http://gowers.wordpress.com/2012/01/29/whats-wrong-with-electronic-journals/ What's wrong with electronic journals], Tim Gowers, January 29, 2012.
* [http://sbseminar.wordpress.com/2012/01/30/thinking-about-elsevier-replacements/ Thinking about Elsevier replacements], David Speyer, January 30, 2012.
* [http://blogs.lse.ac.uk/impactofsocialsciences/2012/02/01/stand-down-journal-referee/ Comfort is the death knell of academia: why I’m standing down as a journal referee], Matthew Todd, LSE Impact Blog, February 1, 2012.
* [http://scholarlykitchen.sspnet.org/2012/02/02/mysteries-of-the-elsevier-boycott Mysteries of the Elsevier Boycott], Rick Anderson, February 2, 2012.
** [http://breakingculture.tumblr.com/post/17112742228/unraveling-boycott-mysteries Unraveling (some of) the mysteries of the Elsevier Boycott], Sean Johnson Andrews, February 6, 2012.
** [http://www.against-the-grain.com/2012/02/multigrain-discussion-another-response-to-the-elsevier-boycott/ Multigrain Discussion: Another Response to the Elsevier Boycott], Chuck Hamaker], February 14, 2012.
* [http://scholarlykitchen.sspnet.org/2012/02/02/the-elsevier-boycott-does-it-make-sense The Elsevier Boycott — Does It Make Sense?], Kent Anderson, February 2, 2012.
* [http://www.michaeleisen.org/blog/?p=890 You are Elsevier: time to overcome our fears and kill subscription journals], Michael Eisen, February 3, 2012.
** [http://scienceblogs.com/denialism/2012/02/eisen_calls_for_elsevier_boyco.php Eisen calls for Elsevier Boycott - but can we all go OA?], Mark Hoofnagle, February 6, 2012.
* [http://stochastictrend.blogspot.com/2012/02/in-defence-of-elsevier.html In Defence of Elsevier], David Stern, February 4, 2012.
* [http://blog.mathunion.org/journals/?no_cache=1&tx_t3blog_pi1%5BblogList%5D%5BshowUid%5D=30&tx_t3blog_pi1%5BblogList%5D%5Byear%5D=2012&tx_t3blog_pi1%5BblogList%5D%5Bmonth%5D=02&tx_t3blog_pi1%5BblogList%5D%5Bday%5D=05&cHash=a2d6424f899302a7ea3b75b9bb591802 More reasons to support the Elsevier boycott], Doug Arnold, IMU blog on mathematical journals, February 5, 2012.
* [http://gowers.wordpress.com/2012/02/08/a-more-formal-statement-about-mathematical-publishing/ A more formal statement about mathematical publishing], Timothy Gowers, February 8, 2012.
* [http://scientopia.org/blogs/drugmonkey/2012/02/08/explaining-resistance-to-the-elsevier-boycott-practicalities/ Explaining resistance to the Elsevier boycott: Practicalities.], DrugMonkey, February 8, 2012.
* [http://neurodojo.blogspot.com/2012/02/whens-scientists-and-published.html When scientists’ and publishers’ motivations align], Zen Faulkes, February 9, 2012.
* [https://etechlib.wordpress.com/2012/02/11/about-the-elsevier-controversy-and-essential-science/ About the Elsevier Controversy and Essential Science], PF Anderson, February 11, 2012.
* [http://www.science3point0.com/palphy/2012/02/12/journal-mega-bundles-thecostofknowledge/ Journal mega-bundles & TheCostOfKnowledge], Ross Mounce, February 12, 2012.
* [http://mathbabe.org/2012/02/13/mathematics-has-an-occupy-moment/ The future of academic publishing], Cathy O'Neil, February 13, 2012.
* [http://svpow.wordpress.com/2012/02/13/a-window-of-opportunity-for-elsevier/ A window of opportunity for Elsevier], Mike Taylor, February 13, 2012.
* [http://mhpbooks.com/49648/5000-profs-join-boycott-of-elsevier-publications-in-international-academic-spring/ 5,000 profs join boycott of Elsevier publications in international “academic spring”], Dennis Johnson, February 14, 2012.
* [http://blogs.lse.ac.uk/impactofsocialsciences/2012/02/15/after-elsevier-boycott-green-open-access What comes after the Elsevier boycott? The answer might be found by following the ‘Green’ road to open access], Neil Stewart, LSE Impact Blog, February 15, 2012.
* [http://mhpbooks.com/50115/whats-next-in-the-elsevier-boycott/ What’s next in the Elsevier boycott?], Dennis Johnson, Melville House, February 16, 2012.
* [http://lj.libraryjournal.com/2012/02/opinion/barbara-fister/joining-the-movement-a-call-to-action-peer-to-peer-review/ Joining the Movement: A Call to Action | Peer to Peer Review] Barbara Fister, Library Journal, February 16th, 2012

=== News aggregators ===

* [http://news.ycombinator.com/item?id=3494340 Fields medalist Tim Gowers: Elsevier — my part in its downfall], Hacker News, January 21, 2012
* [http://www.reddit.com/r/math/comments/oqirf/one_mathematicians_stance_against_elsevier/ One mathematician's stance against Elsevier], Reddit, January 22, 2012.
* [http://news.ycombinator.com/item?id=3501561 The Cost of Knowledge: Researchers taking a stand against Elsevier], Hacker News, January 23, 2012.
* [http://science.slashdot.org/story/12/01/27/1322234/scientists-organize-elsevier-boycott Scientists organize Elsevier boycott], Slashdot, January 27, 2012.
* [http://www.metafilter.com/112178/Scientists-boycott-Elsevier Scientists boycott Elsevier], Metafilter, January 29, 2012.
* [http://www.reddit.com/r/math/comments/pepuo/thanks_to_angry_mathematicians_elseviers/ Thanks to angry mathematicians, Elsevier's publishing model might be about to go up in smoke], Reddit, February 7, 2012.

=== Coverage by the media ===

* [http://www.theregister.co.uk/2012/01/28/scientists_boycott_elsevier/ Blog blast births boffin boycott of publisher Elsevier], Iain Thomson, the Register, January 28, 2012.
* [http://www.forbes.com/sites/timworstall/2012/01/28/elseviers-publishing-model-might-be-about-to-go-up-in-smoke/ Elsevier's Publishing Model Might be About to Go Up in Smoke], Tim Worstall, Forbes, January 28, 2012.
* [http://www.wired.com/wiredscience/2012/01/testify-the-open-science-movement-catches-fire/ Testify: The Open-Science Movement Catches Fire] David Dobbs, Wired, January 30, 2012.
* [http://chronicle.com/blogs/wiredcampus/elsevier-publishing-boycott-gathers-steam-among-academics/35216 Elsevier Publishing Boycott Gathers Steam Among Academics], Josh Fischman, The Chronicle of Higher Education, January 30, 2012.
* [http://www.techdirt.com/articles/20120130/13030217589/will-academics-boycott-elsevier-be-tipping-point-open-access-another-embarrassing-flop.shtml Will Academics' Boycott Of Elsevier Be The Tipping Point For Open Access -- Or Another Embarrassing Flop?], Glyn Moody, Techdirt, January 31, 2012.
* [http://boingboing.net/2012/01/31/scientists-boycott-elsevier-ov.html Scientists and scholars boycott Elsevier over bad business practices and copyright maximalism], Cory Doctorow, Boingboing, January 31, 2012.
* [http://lj.libraryjournal.com/2012/01/publishing/petition-targeting-elseviers-business-practices-begins-to-snowball/ Petition Targeting Elsevier’s Business Practices Begins to Snowball], Michael Kelley, Library Journal, January 31, 2012.
* [http://www.thebookseller.com/news/academics-call-boycott-elsevier.html Academics call for boycott of Elsevier], Charlotte Williams, The Bookseller, January 31, 2012.
* [http://chronicle.com/article/As-Journal-Boycott-Grows/130600/ As Journal Boycott Grows, Elsevier Defends Its Practices], Josh Fischman, The Chronicle of Higher Education, January 31, 2012.
* [http://arstechnica.com/science/news/2012/01/researchers-boycott-publisher-will-they-embrace-instant-publishing.ars Researchers boycott publisher; will they embrace instant publishing?], John Timmer, Ars Technica, January 31, 2012.
* [http://www.elmundo.es/elmundosalud/2012/01/30/noticias/1327952591.html Boicot científico a Elsevier], Cristina de Martos, El Mundo, January 31, 2012. (Spanish)
* [http://nos.nl/op3/artikel/335992-elsevier-in-de-clinch-met-wetenschappers.html Elsevier in de clinch met wetenschappers], NOS News, January 31, 2012. (Dutch)
* [http://news.sciencemag.org/scienceinsider/2012/02/thousands-of-scientists-vow-to-b.html Thousands of Scientists Vow to Boycott Elsevier to Protest Journal Prices], Jop de Vrieze, Science Insider, February 1, 2012.
* [http://www.mmm-online.com/elsevier-begins-outreach-as-push-back-on-publisher-threatens-to-widen/article/225855/ Elsevier begins outreach as push-back on publisher threatens to widen], Deborah Weinstein, Medical Marketing & Media, February 1, 2012.
* [http://www.care2.com/causes/scientists-fight-for-open-access-for-their-research.html Scientists Fight For Open Access For Research], Kristina Chew, Care2, February 1, 2012.
* [http://www.bloomberg.com/news/2012-02-01/samsung-csr-nfl-elsevier-motorola-intellectual-property.html Samsung, CSR, NFL, Elsevier, Motorola: Intellectual Property], Victoria Slind-Flor, Bloomberg, February 1, 2012. (Brief mention only.)
* [http://mediadecoder.blogs.nytimes.com/2012/02/01/the-breakfast-meeting-a-week-of-negative-ads-and-new-chief-at-sony/ The Breakfast Meeting: A Week of Negative Ads, and New Chief at Sony], Noam Cohen, New York Times, February 1, 2012. (Brief mention only.)
* [http://www.guardian.co.uk/science/2012/feb/02/academics-boycott-publisher-elsevier Scientists sign petition to boycott academic publisher Elsevier], Alison Flood, the Guardian, February 2, 2012.
* [http://blogues.cyberpresse.ca/sciences/2012/02/02/fronde-contre-les-revues-savantes-delsevier/ Étonnante fronde de chercheurs contre les revues savantes d’Elsevier], Jean-François Cliche, le Soleil, February 2, 2012. (French)
* [http://www.wired.com/wiredscience/2012/02/is-the-open-science-revolution-for-real/ Is the Open Science Revolution For Real?], David Dobbs, Wired, February 3, 2012.
* [http://www.economist.com/node/21545974 The price of information], the Economist, February 4, 2012.
* [http://archiv.twoday.net/stories/64967798/ Zum Elsevier-Boykott], Klaus Graf, Archivalia, February 5, 2012. (German)
* [http://paidcontent.org/article/419-academics-revolt-against-elseviers-journal-pricing/ Academics Revolt Against Elsevier’s Journal Pricing], Robert Andrews, PaidContent, February 6, 2012.
* [http://theconversation.edu.au/spread-the-word-scientists-are-tearing-down-publishers-walls-5098 Spread the word: scientists are tearing down publishers' walls], Alex Holcombe, the Conversation, February 7, 2012.
* [http://www2.ljworld.com/news/2012/feb/07/heard-hill-university-senate-considering-boycottin/ Heard on the Hill: University Senate considering boycotting publisher Elsevier; newspaper readership program popular at other places, too; KUMC researcher mentioned in LA Times story on Alzheimer’s], Andy Hyland, LJWorld, February 7, 2012.
* [http://hon.jp/news/modules/rsnavi/showarticle.php?id=3082 欧米圏で“学術の春”運動始まる、電子ジャーナル出版大手Elsevierに対し学者たちのボイコット運動が急拡大], editorial, hon.jp Daywatch, Feb 7, 2012. (Japanese)
* [http://the-scientist.com/2012/02/07/occupy-elsevier/ Occupy Elsevier?], Bob Grant, the Scientist, February 7, 2012.
* [http://www.theaustralian.com.au/higher-education/academics-boycott-publisher-elsevier/story-e6frgcjx-1226265110496?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+TheAustralianHigherEducationNews+%28The+Australian+%7C+Higher+Education%29&utm_content=Google+Reader Academics boycott publisher Elsevier], Bernard Lane, the Australian, February 8, 2012.
* [http://latimesblogs.latimes.com/jacketcopy/2012/02/wed-book-news-bezos-the-elsevier-boycott-and-more.html Wednesday book news: Bezos, the Elsevier boycott and more], Carolyn Kellogg, Los Angeles Times, February 8, 2012. (Brief mention only.)
* [http://www.guardian.co.uk/higher-education-network/blog/2012/feb/08/open-access-journals-elsvier-boycott Open access journals: are we asking the right questions?], Martin Paul Eve, the Guardian, February 8, 2012.
* [http://www.varsity.co.uk/news/4370 The Academic Spring], Patrick O'Grady, Varsity, February 8, 2012.
* [http://www.timeshighereducation.co.uk/story.asp?sectioncode=26&storycode=418952 Elsevier defends stance on anti-open-access bill], John Gill, Times Higher Education, February 9, 2012.
* [http://www.nature.com/news/elsevier-boycott-gathers-pace-1.10010 Elsevier boycott gathers pace], John Whitfield, Nature, February 9, 2012.
* [http://www.wired.com/wiredscience/2012/02/open-science-revolt-occupies-congress/ Open Science Revolt Occupies Congress], David Dobbs, Wired, February 9, 2012.
* [http://blogs.independent.co.uk/2012/02/09/the-future-of-academic-publishing/ The future of academic publishing], Mike Taylor, the Independent, February 9, 2012.
* [http://www.tcs.cam.ac.uk/issue/news/cambridge-professor-leads-boycott-of-elsevier-publications/ Cambridge Professor leads boycott of Elsevier Publications], Emily Loud, the Cambridge Student Online, February 9, 2012.
* [http://www.utimes.pitt.edu/?p=19679 Protest launched against journal publisher], Kimberly Barlow, University Times, February 9, 2012.
* [http://jeps.efpsa.org/blog/2012/02/10/a-revolution-in-scientific-publishing/ A revolution in scientific publishing?], Sina Scherer, JEPS Bulletin, February 10, 2012.
* [http://libraries.mit.edu/sites/news/elsevier-boycott-grows/7785/ Elsevier Boycott Grows: MIT Faculty Speak About Participation], Ellen Duranceau, MIT Libraries News, February 10, 2012.
* [http://www1.folha.uol.com.br/ciencia/1046769-cientistas-boicotam-a-maior-editora-de-periodicos-do-mundo.shtml Cientistas boicotam a maior editora de periódicos do mundo], Sabine Righetti, Folha, February 10, 2012. (Portugese)
* [http://www.bostonglobe.com/opinion/2012/02/12/why-scientists-are-boycotting-publisher/9sCpDEP7BkkX1INfakn3NL/story.html Why scientists are boycotting a publisher], Gareth Cook, the Boston Globe, February 12, 2012.
** [http://bostonglobe.com/opinion/letters/2012/02/16/elsevier-committed-universal-access-content-sustainable-publishing-model/70QfCpSOvy0IUibSK6eCTL/story.html Elsevier committed to universal access to content, sustainable publishing model], Lynne Herndon (former CEO of Cell press), letter to the editor, the Boston Globe, February 16, 2012.
* [http://newsbreaks.infotoday.com/NewsBreaks/The-Cost-of-Knowledge-Versus-Elsevier--Signatures-and-Growing-80575.asp The Cost of Knowledge Versus Elsevier: 5,600 Signatures and Growing], Robin Peek, Information Today, February 13, 2012.
* [http://www.pourlascience.fr/ewb_pages/a/actualite-la-fronde-des-chercheurs-contre-i-elsevier-i-29118.php La fronde des chercheurs contre Elsevier], Maurice Mashaal, Pour la Science, February 13, 2012.
* [http://www.newscientist.com/article/dn21467-web-freedoms-fuel-academic-spring-journal-protest.html Web freedoms fuel 'academic spring' journal protest], Jacob Aron, New Scientist, February 13, 2012.
* [http://www.nytimes.com/2012/02/14/science/researchers-boycott-elsevier-journal-publisher.html Mathematicians Organize Boycott of a Publisher], Thomas Lin, New York Times, February 13, 2012.
* [http://motherjones.com/blue-marble/2012/02/science-uprising Science Uprising], Julia Whitty, Mother Jones, February 13, 2012.
* [http://www.kansan.com/news/2012/feb/13/professors-boycott/ Professors boycott prominent publishing company], Kelsey Cipolla, The University Daily Kansan, February 13, 2012.
* [http://www.purdueexponent.org/opinion/editorials/article_a6e96c79-5c95-54b8-bf85-eca8de6bb3db.html Monopoly on research publishing is unethical], Editorial, The Exponent, February 14, 2012.
* [http://today.duke.edu/2012/02/elsevierboycott Duke Scholars Join Boycott Against Elsevier], Ashley Yeager, Duke Today, February 14, 2012.
* [https://theconversation.edu.au/academics-line-up-to-boycott-worlds-biggest-journal-publisher-5384 Academics line up to boycott world’s biggest journal publisher], Justin Norrie, the Conversation, February 15, 2012.

=== Open letters to Elsevier ===

* [http://math.berkeley.edu/~kirby/elsevier.html Letter to Elsevier], Rob Kirby, December 30, 1997.
* [http://www.library.yale.edu/~llicense/ListArchives/0310/msg00048.html Call for Boycott of Cell Press Journals], Peter Walter and Keith Yamomoto, October 19, 2003.
** [http://genomebiology.com/2003/4/10/spotlight-20031024-02 Researchers boycott Cell Press], Alison McCook, Genome Biology, October 24, 2003.
* [http://www.cs.colorado.edu/~hal/jalg.html Journal of Algorithms editorial board resignation], December 13, 2003.
* [http://math.ucr.edu/home/baez/topology-letter.pdf Topology editorial board resignation letter], August 10, 2006.
* [http://idiolect.org.uk/elsevier/docs/academics_openletter.pdf Arms fairs and academics], 138 signatories, February 28, 2007.
* [http://idiolect.org.uk/notes/?p=643 An open letter to Elsevier and all those involved in the IEHG], Keith Halfacree, April 10, 2007.
* [http://www.coar-repositories.org/news/coar-writes-open-letter-as-reaction-to-elseviers-practices/ Open Letter to Elsevier], Norbert Lossau, Chair of the Executive Board, Confederation of Open Access Repositories, February 6, 2012.
* [https://plus.google.com/105282922684661032446/posts/WCZqgPVehmx Letter to Elsevier], Cynthia Parr, February 10, 2012.
* [http://darwin.eeb.uconn.edu/uncommon-ground/2012/02/declining-elsevier.html Declining elsevier], Kent Holsinger, February 10, 2012.
* [http://occamstypewriter.org/scurry/2012/02/12/an-open-letter-to-elsevier/ An Open Letter to Elsevier], Stephen Curry, February 12, 2012.
* [http://svpow.wordpress.com/2012/02/15/a-response-to-one-elsevier-employee-and-an-open-letter-to-the-rest/ A response to one Elsevier employee, and an open letter to the rest], Matt Wedel, February 15, 2012.

=== Responses by Elsevier ===

* [http://gowers.wordpress.com/2012/01/21/elsevier-my-part-in-its-downfall/#comment-14679 A response by David Clark at Elsevier], January 23, 2012.
* [http://www.elsevier.com/wps/find/intro.cws_home/elsevieropenletter An open letter to the research community: journal prices, discounts, and access], Elsevier, undated as of Feb 6, 2012.
** [http://bjoern.brembs.net/news.php?item.833.11 Against Own Assertion, Elsevier Doubled Price For Access], Bjorn Brembs, February 11, 2012.
* [http://www.epjournal.net/blog/2012/02/elsevier-and-evolution-human-behavior/ Elsevier and Evolution & Human Behavior], Robert Kurzban (co-editor-in-chief of the Elsevier journal Evolution & Human Behavior), February 6, 2012.
* [http://poynder.blogspot.com/2012/02/elseviers-alicia-wise-on-rwa-west-wing.html Elsevier’s Alicia Wise on the RWA, the West Wing, and Universal Access], Richard Poynder, February 9, 2012.

=== Other coverage ===

* [http://www.arl.org/sparc/media/prime-time-for-public-access.shtml Prime Time for Public Access], Heather Joseph, Executive Director, SPARC, February 9, 2012.
* [http://en.wikipedia.org/wiki/The_Cost_of_Knowledge The wikipedia page] for this protest.

See also [http://scienceblogs.com/confessions/2012/02/around_the_web_research_works.php this list of links], which is focused more around the Research Works Act, but also contains many links regarding the boycott, as well as [http://www.math.ntnu.no/~stacey/Mathforge/Math2.0 Math 2.0], a discussion forum for all topics related to the future of mathematical publishing.

== Other pledges, boycotts, and petitions ==

* [http://www.researchwithoutwalls.org/ Research Without Walls]
* [http://www.openaccesspledge.com/ Open Access Pledge]
* [http://www-fourier.ujf-grenoble.fr/petitions/index.php?petition=3 Appel pour des négociations équilibrées avec les éditeurs de revues scientifiques] - a petition concerning the bundling and pricing practices of Springer
* [http://www.thepetitionsite.com/207/support-the-open-access-movement-stop-the-research-works-act/?cid=FB_TAF A petition to stop the Research Works Act]
* [http://www.taxpayeraccess.org/action/FRPAA2012.shtml Call to action: Tell Congress you support the Bipartisan Federal Research Public Access Act (H.R. 4004 and S. 2096)], Alliance for taxpayer access, February 9, 2012.

* See these tag libraries from the [http://oad.simmons.edu/oadwiki/OA_tracking_project Open Access Tracking Project] (more comprehensive after April 2009 than before):
** [http://www.connotea.org/tag/oa.boycotts oa.boycotts]
** [http://www.connotea.org/tag/oa.declarations oa.declarations]
** [http://www.connotea.org/tag/oa.petitions oa.petitions]
** [http://www.connotea.org/tag/oa.pledges oa.pledges]

== Other blog posts, letters, and opinion pieces ==
* [http://math.berkeley.edu/~kirby/journals.html Comparative price of math journals], Rob Kirby, May 27, 1997.
** [http://math.berkeley.edu/~kirby/elsevier.html Open letter to Elsevier], Rob Kirby, December 30, 1997.
** [http://math.berkeley.edu/~kirby/jp00.html 2000 data update]
* [http://www.ams.org/notices/200007/forum-birman.pdf Scientific Publishing: A Mathematician’s Viewpoint], Joan Birman, Notices of the American Mathematical Society, 770-774, July 2000.
* [http://homepages.cwi.nl/~apt/ps/cacm01.pdf One More Revolution to Make: Free Scientific Publishing], Krzysztof R. Apt, Communications of ACM, 44(5), pp. 25-28, 2001.
* [http://www.nieuwarchief.nl/serie5/deel02/sep2001/pdf/apt.pdf Towards free access to scientific literature], Krzysztof R. Apt, Nieuw Archief voor Wiskunde, 5/2 nr. 3, September 2001, pp. 251-255.
* [http://stromme.uib.no/kuperberg.pdf Scholarly Mathematical Communication at a Crossroads], Greg Kuperberg, Nieuw Arch. Wisk., (5) 3 no.3, September 2002.
* [http://people.ccmr.cornell.edu/~ginsparg/blurb/pg02pr.html Can Peer Review be better Focused?], Paul Ginsparg, March 2003.
* [http://www.ams.org/notices/200402/commentary.pdf Fleeced?], Rob Kirby, Notices of the American Mathematical Society, 161-162, February 2004.
* [http://www.ams.org/notices/200405/commentary.pdf We can make a change], Gerard van der Geer, Notices of the American Mathematical Society, May 2004.
* [http://www.math.columbia.edu/~neumann/journal.html What we can do about journal pricing], Walter Neumann, September 2005.
** The discussions mentioned in that email led to the [http://web.archive.org/web/20110525195311/http://members.cox.net/banffprotocol/ Banff protocol] (web site now only available through web archive).
* [http://www.scottaaronson.com/writings/journal.html Review of The Access Principle by John Willinsky], Scott Aaronson, 2006
* [http://digitalstrategies.blogspot.com/2008/06/scientific-publication-in-internet-era.html Scientific Publishing in the Internet Era] Efthymios Constantinides June 17, 2008
* [http://arstechnica.com/science/news/2008/11/elsevier-beyond-the-pale-of-scientific-respectability.ars Publishing economics harm science's credibility], Chris Lee, Ars Technica, November 2008.
* [http://www.ima.umn.edu/~arnold/siam-columns/integrity-under-attack.pdf Integrity under attack: The State of Scholarly Publishing], Douglas Arnold, SIAM news, December 2009.
* [http://scholarlykitchen.sspnet.org/2010/01/04/why-hasnt-scientific-publishing-been-disrupted-already/ Why Hasn’t Scientific Publishing Been Disrupted Already?], Michael Clarke, January 4, 2010.
* [http://math.ucr.edu/home/baez/journals.html What We Can Do About Science Journals], John Baez, January 24, 2011.
* [http://blog.mathunion.org/journals/?no_cache=1&tx_t3blog_pi1%5BblogList%5D%5BshowUid%5D=17&tx_t3blog_pi1%5BblogList%5D%5Byear%5D=2011&tx_t3blog_pi1%5BblogList%5D%5Bmonth%5D=12&tx_t3blog_pi1%5BblogList%5D%5Bday%5D=07&cHash=bb9177d8192db5b5756aca088ea79677 What might be done about high prices of journals?], IMU blog on mathematical journals, July 12, 2011.
* [http://www.monbiot.com/2011/08/29/the-lairds-of-learning/ The lairds of learning] George Monbiot, August 29, 2011.
** [http://sedgemore.com/2011/09/serials-crisis-and-corn-laws/ Serials crisis and corn laws], Francis Sedgemore, September 7, 2011.
* [http://www.guardian.co.uk/commentisfree/2011/aug/29/academic-publishers-murdoch-socialist Academic publishers make Murdoch look like a socialist], George Monbiot, the Guardian, August 29, 2011.
* [http://www.timeshighereducation.co.uk/story.asp?storycode=417576 Peers, review your actions], Michael Taylor, Times Higher Education, September 29, 2011.
* [http://gowers.wordpress.com/2011/10/31/how-might-we-get-to-a-new-model-of-mathematical-publishing/ How might we get to a new model of mathematical publishing?], Timothy Gowers, October 31, 2011.
** [http://gowers.wordpress.com/2011/11/03/a-more-modest-proposal/ A more modest proposal], Timothy Gowers, November 3, 2011.
** [http://boolesrings.org/krautzberger/2011/11/26/the-recent-publishing-debate-a-timeline/ A timeline of the debate initiated by this post], Peter Krautzberger, November 26, 2011.
* [http://www.nytimes.com/2012/01/11/opinion/research-bought-then-paid-for.html Research Bought, Then Paid For], Michael B. Eisen, New York Times opinion piece, January 10, 2012
** [http://www.nytimes.com/2012/01/23/opinion/should-research-be-more-freely-available.html?_r=1 Should Research Be More Freely Available?], Jeffrey M. Drazen (Editor in Chief of The New England Journal of Medicine), Gene D. Sprouse (treasurer of [http://www.aps.org APS]), and Joseph W. Serene (publisher at [http://www.aps.org APS]), letters to the New York Times, January 23, 2012.
* [http://www.guardian.co.uk/science/2012/jan/16/academic-publishers-enemies-science?CMP=twt_fd Academic publishers have become the enemies of science], Mike Taylor, the Guardian, January 16, 2011.
** [http://www.guardian.co.uk/science/2012/jan/27/academic-publishers-enemies-science-wrong Branding academic publishers 'enemies of science' is offensive and wrong], Graham Taylor, January 27, 2011.
** [http://nelh.blogspot.com/2012/02/elsevier-double-dipping-and-nhs.html Elsevier, double-dipping, and the NHS], Ben Toth, February 11, 2012.
* [http://www.michaeleisen.org/blog/?p=873 Nature’s shiny sounding copout on open access], Michael Eisen, January 26, 2012.
* [http://svpow.wordpress.com/2012/01/27/publishers-invent-a-whole-new-form-of-evil-suing-their-customers/ Publishers invent a whole new form of evil: suing their customers], Mike Taylor, SV-POW, January 27, 2012.
* [http://occamstypewriter.org/scurry/2012/01/28/why-i-chose-to-decline-an-invitation-to-review-by-elsevier/ Why I chose to decline an invitation to review by Elsevier], Stephen Curry, January 28, 2012.
* [http://sbseminar.wordpress.com/2012/02/01/journals-and-the-arxiv/ Journals and the arXiv], Scott Morrison, February 1, 2012.
* [http://occupypublishing.blogspot.com.au/2012/02/scientific-journals-in-e-publishing-age.html scientific journals in the e-publishing age], Phillip Thrift, February 1, 2012.
* [http://gowers.wordpress.com/2012/02/02/abstract-thoughts-about-online-review-systems Abstract thoughts about online review systems], Tim Gowers, February 2, 2012.
* [http://cameronneylon.net/blog/the-research-works-act-and-the-breakdown-of-mutual-incomprehension/ The Research Works Act and the breakdown of mutual incomprehension], Cameron Neylon, February 3, 2012.
* [http://sbseminar.wordpress.com/2012/02/09/a-forum-on-mathematical-publishing/ A forum on mathematical publishing], Scott Morrison, February 9, 2012.
* [http://vort.org/2012/02/09/moral-imperative-open-science/ The moral imperative for Open Science], Russell Neches, February 9, 2012.
* [http://johncarlosbaez.wordpress.com/2012/02/10/the-federal-research-public-access-act/ The Federal Research Public Access Act], John Baez, February 10, 2012.
* [http://www.guardian.co.uk/science/blog/2012/feb/10/parable-farmers-teleporting-duplicator The parable of the farmers and the Teleporting Duplicator], Michael Taylor, the Guardian, February 10, 2012.
* [http://svpow.wordpress.com/2012/02/11/why-isnt-anyone-publishing-open-access-articles-in-elsevier-journals/ Why isn’t anyone publishing open-access articles in Elsevier journals?], Mike Taylor, February 11, 2012.
* [http://michaelnielsen.org/blog/how-you-can-help-the-federal-research-public-access-act-frpaa-become-law/ How you can help the Federal Research Public Access Act (FRPAA) become law], Michael Nielsen (interviewing Heather Joseph), February 14, 2012.
* [http://lisnews.org/elsevier_filters_recommendation_engine_to_show_elsevier_titles_only Elsevier Filters Recommendation Engine to Show Elsevier Titles Only], LISNews, February 14, 2012.
* [http://techcrunch.com/2012/02/15/the-dangerous-research-works-act/ The Dangerous “Research Works Act”], Richard Price, TechCrunch, February 15, 2012.

== Media ==

* [http://www.nature.com/nature/journal/v445/n7126/full/445347a.html PR's 'pit bull' takes on open access], Jim Giles, Nature, January 25, 2007. Summary: A coalition of scientific publishers (including Elsevier, Wiley, and the American Chemical Society) organises to oppose open access.
* [http://www.guardian.co.uk/business/2008/may/30/armstrade.weaponstechnology Reed Elsevier makes its final farewell to arms], Katie Allen, the Guardian, 30 May 2008. Summary: Reed Elsevier was until 2009 organizing arms trade fairs.
** [http://www.acme-journal.org/vol8/Stafford09.pdf Lessons from the Campaign against Elsevier "We won, but how did we win?"], Tom Stafford, ACME: An International E-Journal for Critical Geographies 2009, 8 (3), 494-504.
** [http://www.caat.org.uk/issues/armsfairs/reedelsevier.php Campaign success: Reed Elsevier sells international arms fairs], Campaign against arms trade, March 9, 2009.
* [http://classic.the-scientist.com/blog/display/55679/ Elsevier Published 6 Fake Journals], Bob Grant, The Scientist, May 7, 2009. Summary: Elsevier was paid by unnamed pharmaceutical companies to publish six journals that looked like independent peer-reviewed medical journals, but which were not.
** [http://en.wikipedia.org/wiki/Australasian_Journal_of_Bone_%26_Joint_Medicine The wikipedia page on these six journals].
** The Elsevier fake-journal tally eventually rose to [http://www.earlham.edu/~peters/fos/2009/06/elsevier-fake-journal-tally-now-9.html nine].
** [http://www.guardian.co.uk/commentisfree/2009/may/09/bad-science-medical-journals-companies The danger of drugs... and data], Ben Goldacre, the Guardian, May 8, 2009.
** [http://www.elsevier.com/wps/find/authored_newsitem.cws_home/companynews05_01203 Elsevier press release on this incident], May 7, 2009.
* [http://www.insidehighered.com/news/2009/06/23/elsevier Elsevier Won't Pay for Praise], Scott Jashik, Inside Higher Ed, June 23, 2009. Summary: Elsevier suspends its practice of offering Amazon gift cards to anyone who would give their textbooks a five-star rating.

== Other Information ==

* '''On Elsevier'''
** [http://www.reed-elsevier.com/mediacentre/pressreleases/Documents/2010/Reed%20Elsevier%202009%20Results%20Announcement%2017%20February%202010%20FINAL.pdf Reed Elsevier's 2009 report] Elsevier reported a profit of 1.1 billion dollars on revenue of 3.2 billion dollars.
** [http://en.wikipedia.org/wiki/Elsevier#Criticism_and_controversies Criticism and controversies of Elsevier] (Wikipedia)
** [http://gizmodo.com/5870241 Elsevier support for the Stop Online Piracy Act (SOPA)] (Gizmodo)
*** [http://en.wikipedia.org/wiki/List_of_organizations_that_support_the_Stop_Online_Piracy_Act List of organizations with official stances on the Stop Online Piracy Act] (Wikipedia)
** [http://www.michaeleisen.org/blog/?p=846 Elsevier support for the Research Works Act (RWA)] (Michael Nielsen)
*** [http://poynder.blogspot.com/2012/01/elsevier-needs-to-get-out-more.html Elsevier needs to get out more] (Richard Poynder)
*** [http://freethoughtblogs.com/pharyngula/2012/01/16/elsevier-evil/ Elsevier = evil] (Phyrangula)
*** [http://www.michaeleisen.org/blog/?p=807 Elsevier-funded NY Congresswoman Carolyn Maloney Wants to Deny Americans Access to Taxpayer Funded Research] (Michael Eisen)
**** [http://www.michaeleisen.org/blog/?p=807#comment-52048 A response by Tom Reller] (Vice President and Head of Global Corporate Relations at Elsevier)
*** Note however that the editorial board of [http://www.thelancet.com/ the Lancet], a very prestigious medical journal published by Elsevier, has [http://www.thelancet.com/journals/lancet/article/PIIS0140-6736(12)60125-1/fulltext come out strongly against the Research Works Act].
*** [http://www.elsevier.com/wps/find/intro.cws_home/elsevierstatement A message to the research community: Elsevier, access, and the Research Works Act], Elsevier, undated as of Feb 6 2012.
** [http://www.whitehouse.gov/sites/default/files/microsites/ostp/scholarly-pubs-%28%23168%29%20Elsevier%20submission.pdf Elsevier submission to the Office of Science and Technology Policy on open access], January 2012.
*** [http://openaccess.kb.se/?p=637 Elsevier tries to block institutional OA mandates], Jan Hagerlid, January 31, 2012.
** [http://www.researchinformation.info/riaut03elsevier.html Why commercial publishers are good for research], Arie Jongejan, CEO Science & Technology, Elsevier, Autumn 2003.
** [http://www.elsevier.com/wps/find/authorsview.authors/preprints Elsevier's policy on authors making their papers available on preprint servers] (Short version: Elsevier allows draft versions of papers to be placed on public servers such as the arXiv, and revised versions of papers to be placed on personal or institutional pages, but final versions of papers are only permitted at the journal site itself.)

* '''Stock analyses of Elsevier and other publishers'''
** [http://www.econ.ucsb.edu/~tedb/Journals/morganstanley.pdf Scientific Publishing: Knowledge is Power], Morgan Stanley, September 20, 2002.
** [http://dl.dropbox.com/u/4398178/Reciprocal%20Space%20Files/001-BR-EndoftheBigDeal-2011.pdf Reed Elsevier: The inevitable crunch point – downgrading to under perform because of growing concerns on Elsevier], Bernstein Research, March 10, 2011.
** [http://dl.dropbox.com/u/4398178/Reciprocal%20Space%20Files/002-BR-ElsevierNegotiations-2011.pdf Reed Elsevier, Bringing down the house – Why Elsevier is vulnerable in its upcoming Big Deal negotiations], Bernstein Research, March 29, 2011.
** [http://dl.dropbox.com/u/4398178/Reciprocal%20Space%20Files/003-BR-ReedCostofKnowledge-2012.pdf Occupy Elsevier], Bernstein Research, February 6, 2012.
** [https://plus.google.com/117663015413546257905/posts/1xRiEyWnipc Noise around boycott against Elsevier offers short term trading opportunity], Exane Paribas, February 7, 2012.
*** [http://cameronneylon.net/blog/a-tale-of-two-analysts/ A tale of two analysts], Cameron Neylon, February 15, 2012.

* '''On open access'''
** [http://en.wikipedia.org/wiki/Open_access Open Access]
** [http://oad.simmons.edu Open Access Directory]
** [http://www.earlham.edu/~peters/fos/overview.htm Open Access Overview] (Peter Suber)

* '''On scholarly journals'''
** [http://www.unc.edu/scholcomdig/whitepapers/panitch-michalak.html The serials crisis] Judith Panitch and Sarah Michalak, A White Paper for the UNC-Chapel Hill Scholarly Communications Convocation, January, 2005.
** [http://www.ams.org/membership/mem-journal-survey AMS Journal Price Survey]
*** [http://www.mathematik.uni-bielefeld.de/~rehmann/BIB/AMS/Publisher.html Math Journal Price Survey], from 2008 data.
** [http://en.wikipedia.org/wiki/Serials_crisis Journal subscription prices have increased far more rapidly than either inflation or spending on research]
** [http://www.mcafee.cc/Journal/Summary.pdf A summary of journal price averages in various disciplines including mathematics as of 2010] (see also [http://www.mcafee.cc/Journal/ the parent site, which contains more detailed information]).
** [http://www.econ.ucsb.edu/~tedb/Journals/BundleContracts.html Big Deal Contract Project] - an analysis of journal bundling contracts, and the attempts by publishers such as Elsevier to prevent them from becoming public.
** [http://oad.simmons.edu/oadwiki/OA_journal_business_models Open access journal business models] (from the Open Access Directory)
** [http://www.mathunion.org/fileadmin/CEIC/bestpractice/bpfinal.pdf Best Current Practices for Journals], endorsed by the International Mathematical Union general assembly, August 16, 2010.
** [http://www.msri.org/attachments/workshops/587/MSRIfinalreport.pdf Mathematics journals: what is valued and what may change], Report of the workshop held at MSRI, Berkeley, California on February 14 – 16 2011.

* '''Miscellaneous links'''
** [http://www.math.umd.edu/research/crisis.html The Crisis in Scientific Publishing] - a collection of links hosted by the University of Maryland.
** [http://www.azimuthproject.org/azimuth/show/Academic+publishing Academic publishing] - a wiki collection of links at the Azimuth project.

== Elsevier mathematics journals ==

This list is taken from [http://www.elsevier.com/wps/find/P11.cws_home/mathjournals here]

* [http://www.elsevier.com/wps/find/journaldescription.cws_home/708310/ Acta Mathematica Scientia]
* [http://www.elsevier.com/locate/yaama Advances in Applied Mathematics]
* [http://www.elsevier.com/locate/advengsoft Advances in Engineering Software]
* [http://www.journals.elsevier.com/advances-in-mathematics/ Advances in Mathematics]
* [http://www.elsevier.com/locate/anihpc Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire]
* [http://www.elsevier.com/locate/apal Annals of Pure & Applied Logic]
* [http://www.elsevier.com/wps/find/journaldescription.cws_home/600714 Annales Scientifiques de l'École Normale Supérieure] (Until 2008)
** This journal is [http://www.math.ens.fr/edition/annales/ now published by the Société mathématique de France].
* [http://www.elsevier.com/locate/arcontrol Annual Reviews in Control]
* [http://www.journals.elsevier.com/applied-and-computational-harmonic-analysis/ Applied & Computional Harmonic Analysis]
** Ingrid Daubechies resigned her position as editor-in-chief in 2012, according to her statement on [http://thecostofknowledge.com the Elsevier boycott site].
* [http://www.elsevier.com/locate/apm Applied Mathematical Modelling]
* [http://www.elsevier.com/locate/amc Applied Mathematics & Computation]
* [http://www.journals.elsevier.com/applied-mathematics-letters/ Applied Mathematics Letters]
** [http://retractionwatch.wordpress.com/2011/06/13/applied-mathematics-letters-posts-apology-for-retracting-intelligent-design-friendly-paper/ Applied Mathematics Letters posts apology for retracting Intelligent Design-friendly paper], Retraction Watch, 13 June 2011.
** [http://www.timeshighereducation.co.uk/story.asp?sectioncode=26&storycode=416514&c=1 Second thoughts result in payout], Paul Jump, Times Higher Education, 16 June 2011.
* [http://www.elsevier.com/locate/apnum Applied Numerical Mathematics]
* [http://www.elsevier.com/locate/artint Artificial Intelligence]
* [http://www.elsevier.com/locate/automatica Automatica]
* [http://www.elsevier.com/locate/btt Biometric Technology Today]
* [http://www.elsevier.com/locate/biosystems Biosystems]
* [http://www.elsevier.com/locate/bulsci Bulletin des Sciences Mathématiques]
* [http://www.journals.elsevier.com/chaos-solitons-and-fractals/ Chaos, Solitons & Fractals]
** There was a significant amount of controversy regarding the quality control at this journal during the tenure of a past editor-in-chief, who stepped down in 2009. Unfortunately, most of the primary reporting on this has been taken down due to ongoing litigation.
** [http://en.wikipedia.org/wiki/Elsevier#Chaos.2C_Solitons_.26_Fractals The Wikipedia section on this issue]
** [http://sbseminar.wordpress.com/2008/11/30/laffaire-el-naschie/ L’affaire El Naschie], Secret Blogging Seminar, November 30, 2008.
** [http://www.ima.umn.edu/~arnold/siam-columns/integrity-under-attack.pdf Integrity under attack: The State of Scholarly Publishing], Douglas Arnold, SIAM news, December 2009.
** [http://www.bbc.co.uk/news/science-environment-15697636 Nature journal libel case begins], Pallab Ghosh, BBC News, November 11, 2011.
* [http://www.elsevier.com/locate/cnsns Communications in Nonlinear Science and Numerical Simulation]
* [http://www.elsevier.com/wps/find/journaldescription.cws_home/600301/description#description Comptes Rendus Mathematique]
* [http://www.elsevier.com/locate/comgeo Computational Geometry]
* [http://www.elsevier.com/locate/csda Computational Statistics & Data Analysis]
* [http://www.elsevier.com/locate/cma Computer Methods in Applied Mechanics and Engineering]
* [http://www.journals.elsevier.com/computers-and-mathematics-with-applications Computers & Mathematics with Applications]
** [http://www.sciencedirect.com/science/article/pii/S0898122109005070 A computer application in mathematics], M. Sivasubramanian, S. Kalimuthu, in Computers and Mathematics with Applications, vol. 59 (2010) pp. 296-297. (This article is discussed in [http://blog.mathunion.org/journals/?no_cache=1&tx_t3blog_pi1%5BblogList%5D%5BshowUid%5D=30&tx_t3blog_pi1%5BblogList%5D%5Byear%5D=2012&tx_t3blog_pi1%5BblogList%5D%5Bmonth%5D=02&tx_t3blog_pi1%5BblogList%5D%5Bday%5D=05&cHash=a2d6424f899302a7ea3b75b9bb591802 this blog post] on the IMU mathematics journal blog, and is also available [http://www.math.hkbu.edu.hk/~ttang/newspaper/funnyarticle11.pdf here].)
** The editorial board [http://about.elsevier.com/pdf/LetterFromEditor.pdf was replaced in 2012].
* [http://www.elsevier.com/locate/conengprac Control Engineering Practice]
* [http://www.elsevier.com/locate/difgeo Differential Geometry and its Applications]
* [http://www.elsevier.com/locate/dam Discrete Applied Mathematics]
* [http://www.elsevier.com/locate/disc Discrete Mathematics]
* [http://www.elsevier.com/locate/disopt Discrete Optimization]
* [http://www.elsevier.com/locate/endm Electronic Notes in Discrete Mathematics]
* [http://www.elsevier.com/locate/entcs Electronic Notes in Theoretical Computer Science]
* [http://www.elsevier.com/locate/enganabound Engineering Analysis with Boundary Elements]
* [http://www.elsevier.com/locate/engappai Engineering Applications of Artificial Intelligence]
* [http://www.elsevier.com/locate/ejc European Journal of Combinatorics]
* [http://www.elsevier.com/locate/ejor European Journal of Operational Research]
* [http://www.elsevier.com/locate/expomath Expositiones Mathematicae]
* [http://www.elsevier.com/locate/ffa Finite Fields and their Applications]
* [http://www.elsevier.com/locate/fss Fuzzy Sets and Systems]
* [http://www.elsevier.com/locate/hm Historia Mathematica]
* [http://www.elsevier.com/locate/indag Indagationes Mathematicae]
* [http://www.elsevier.com/locate/ins Information Sciences]
* [http://www.elsevier.com/locate/ijforecast International Journal of Forecasting]
* [http://www.elsevier.com/locate/nlm International Journal of Non-Linear Mechanics]
* [http://www.elsevier.com/locate/matpur Journal de Mathématiques Pures et Appliquées]
* [http://www.elsevier.com/locate/yjabr Journal of Algebra]
* [http://www.sciencedirect.com/science/journal/01966774 Journal of Algorithms]
** [http://www.cs.colorado.edu/~hal/jalg.html Editorial board resignation], December 13, 2003.
** [http://www.cs.colorado.edu/~hal/chronicle.txt Editorial Board of Scientific Journal Quits, Accusing Elsevier of Price-Gouging], Brock Read, the Chronicle of Higher Education, February 9, 2004.
* [http://www.elsevier.com/locate/jal Journal of Applied Logic]
* [http://www.elsevier.com/locate/jat Journal of Approximation Theory]
* [http://www.elsevier.com/locate/yjcta Journal of Combinatorial Theory, series A]
* [http://www.elsevier.com/locate/yjctb Journal of Combinatorial Theory, series B]
* [http://www.elsevier.com/locate/jco Journal of Complexity]
* [http://www.elsevier.com/locate/cam Journal of Computational & Applied Mathematics]
* [http://www.elsevier.com/locate/jcss Journal of Computer and System Sciences]
* [http://www.elsevier.com/locate/yjdeq Journal of Differential Equations]
* [http://www.elsevier.com/locate/jda Journal of Discrete Algorithms]
* [http://www.elsevier.com/locate/jeconom Journal of Econometrics]
* [http://www.elsevier.com/locate/yjfan Journal of Functional Analysis]
* [http://www.elsevier.com/locate/geomphys Journal of Geometry and Physics]
* [http://www.elsevier.com/locate/jmaa Journal of Mathematical Analysis & Applications]
* [http://www.elsevier.com/locate/jmateco Journal of Mathematical Economics]
* [http://www.elsevier.com/locate/yjmva Journal of Multivariate Analysis]
* [http://www.elsevier.com/locate/jnt Journal of Number Theory]
* [http://www.elsevier.com/locate/jprocont Journal of Process Control]
* [http://www.journals.elsevier.com/journal-of-pure-and-applied-algebra/ Journal of Pure & Applied Algebra]
* [http://www.elsevier.com/locate/jspi Journal of Statistical Planning & Inference]
* [http://www.elsevier.com/locate/fi Journal of the Franklin Institute]
* [http://www.elsevier.com/locate/jkss Journal of the Korean Statistical Society]
* [http://www.elsevier.com/locate/laa Linear Algebra and its Applications]
* [http://www.elsevier.com/locate/mcm Mathematical and Computer Modelling]
* [http://www.elsevier.com/locate/mbs Mathematical Biosciences]
* [http://www.elsevier.com/locate/mss Mathematical Social Science]
* [http://www.elsevier.com/locate/matcom Mathematics and Computers in Simulation]
* [http://www.elsevier.com/locate/neunet Neural Networks]
* [http://www.elsevier.com/locate/na Nonlinear Analysis]
** [http://www.sciencedirect.com/science/article/pii/S0362546X04000409 On the second part of Hilbert's 16th problem], E. Oxenhielm, Nonlinear Analysis 57 (1), April 2004.
*** [http://news.bbc.co.uk/2/hi/science/nature/3243736.stm Historic maths problem 'cracked'] David Whitehouse, BBC, November 27, 2003.
*** [http://tesugen.com/archives/03/12/elin-oxenhielm-update Elin Oxenhielm update], Peter Lindberg, December 3, 2003.
*** [http://www.nature.com/news/2003/031209/full/news031208-4.html Mathematicians dispute proof of century-old problem], John Whitfield, Nature, December 9, 2003.
*** [http://plus.maths.org/content/struggling-sixteen Struggling for sixteen], Rachel Thomas, Plus magazine, December 16, 2003.
*** The paper was eventually [http://www.sciencedirect.com/science/article/pii/S0362546X04000409 withdrawn from the journal by the editors].
** [http://www.sciencedirect.com/science/article/pii/S0362546X0500235X On some contradictory computations in multi-dimensional mathematics], L. Carvalho, Nonlinear Analysis 63 (5-7), November 2005, 725--734. (Claims that the change of variables formula is incorrect.)
*** [http://math.ucr.edu/home/baez/corfield/2006/03/new-bogdanoff-affair_114355412211228579.html A New Bogdanoff Affair?], David Corfield, March 28, 2006.
*** [http://www.sciencedirect.com/science/article/pii/S0362546X06004597 A comment on: ''On some contradictory computations in multi-dimensional mathematics''], E. Capelas de Oliveira, W. Rodrigues, Nonlinear Anal. 67 (7), October 2007, 2316–2320.
*** As of 2012, the original paper of Carvalho has not been retracted from the journal. (However, it is no longer listed as a publication on [http://www.icmc.usp.br/~andcarva/publicac.html Carvalho's web page].)
** [http://blog.mikael.johanssons.org/archive/2006/03/this-is-me-losing-all-faith-in-non-linear-analysis/ This is me losing all faith in Nonlinear Analysis], Mikael Johansson, March 28, 2006.
* [http://www.elsevier.com/locate/nahs Nonlinear Analysis: Hybrid Systems]
* [http://www.elsevier.com/locate/nonrwa Nonlinear Analysis: Real world applications]
* [http://www.elsevier.com/locate/orl Operations Research Letters]
* [http://www.elsevier.com/locate/pr Pattern Recognition]
* [http://www.elsevier.com/locate/physa Physica A: Statistical Mechanics and its Applications]
* [http://www.elsevier.com/locate/physd Physica D: Nonlinear Phenomena]
* [http://www.elsevier.com/locate/simpat Simulation Modelling Practice & Theory]
* [http://www.elsevier.com/locate/stamet Statistical Methodology]
* [http://www.elsevier.com/locate/stapro Statistics and Probability Letters]
* [http://www.elsevier.com/locate/spa Stochastic Processes and their Applications]
* [http://www.elsevier.com/locate/sysconle Systems & Control Letters]
* [http://www.sciencedirect.com/science/journal/00409383 Topology]
** [http://math.ucr.edu/home/baez/topology-letter.pdf Editorial board resignation letter, 10 August 2006]
** [http://www.nysun.com/arts/rebellion-erupts-over-journals-of-academia/42317/ A Rebellion Erupts Over Journals Of Academia], Gary Shapiro, New York Sun, 26 October, 2006.
** [http://www.ams.org/notices/200705/comm-toped-web.pdf Jumping Ship: Topology editorial board resigns], Allyn Jackson, Notices of the American Mathematical Society, May 2007.
** [http://en.wikipedia.org/wiki/Topology_(journal) Wikipedia page on the journal]
** This journal was [http://www.info.sciverse.com/techsupport/journals/jnldiscontinued.htm discontinued in 2012].
* [http://www.journals.elsevier.com/topology-and-its-applications/ Topology & its Applications]
** In 2001, a group of editors of this journal [http://www.uflib.ufl.edu/oa/2009/posters/constitutional-declarationsdeniselgposter2-1.pdf resigned] to form [http://www.msp.warwick.ac.uk/agt/2012/12-01/ Algebraic & Geometric Topology].

== Open Access journals ==

* These lists are taken from the [http://www.doaj.org/ Directory of Open Access Journals] (limited to peer-reviewed journals).
** Perhaps someone could spell out or cut/paste the DOAJ lists below, like the Elsevier list above.

* In [http://www.doaj.org/doaj?func=subject&cpid=58&uiLanguage=en mathematics]

* In [http://www.doaj.org/doaj?func=subject&cpid=59&uiLanguage=en statistics]

* In [http://www.doaj.org/doaj?func=subject&cpid=114&uiLanguage=en computer science], e.g.
** [http://www.jair.org/ Journal of Artificial Intelligence Research]
** [http://www.lmcs-online.org Logical Methods in Computer Science]
** [http://jmlr.csail.mit.edu/ Journal of Machine Learning Research]
** [http://theoryofcomputing.org/ Theory of Computing]
** [http://www.jucs.org/ Journal of Universal Computer Science]
** [http://cjtcs.cs.uchicago.edu/ Chicago Journal of Theoretical Computer Science]

* In [http://www.doaj.org/doaj?func=subject&cpid=49&uiLanguage=en physics], e.g.
** [http://prx.aps.org/ Physical Review X]
** [http://iopscience.iop.org/1367-2630/ The New Journal of Physics]

== Mathematics journal price tables ==

The following tables list the ten most expensive mathematics journals by volume list price (as of 2008), and (for comparison) the ten mathematics journals with the highest impact factor (as of 2000). One should caution that due to complicated (and, in some cases, [http://www.econ.ucsb.edu/~tedb/Journals/BundleContracts.html deliberately obscured]) bundling agreements, the actual price of subscriptions to many journals (including Elsevier journals) may differ somewhat from the official list price. Nevertheless, these tables should convey the rough order of magnitude, at least, of journal costs from publisher to publisher.

Data is drawn from [http://www.mathematik.uni-bielefeld.de/~rehmann/BIB/AMS/Price_per_Volume.html this set of 2007 journal price data] and [http://in-cites.com/research/2001/oct_15_2001-2.html this list of 2000 ISI impact factors]. All prices in US dollars.

=== Top ten mathematics journals by volume list price ===

{|
|Title
|Publisher
|Price/volume
|Price/page
|-
|J. Math. Sci. (New York)
|Springer
|9998
|1.38
|-
|Theoret. Comput. Sci.
|Elsevier
|6551
|1.02
|-
|J. Math. Anal. Appl.
|Academic Press/Elsevier
|6362
|0.36
|-
|J. Algebra
|Academic Press/Elsevier
|5736
|0.51
|-
|Nonlinear Anal.
|Elsevier
|5426
|0.84
|-
|Discrete Math.
|Elsevier
|5269
|1.63
|-
|Appl. Math. Comput.
|Elsevier
|5250
|0.38
|-
|Math. Methods Appl. Sci.
|Wiley/Teubner
|4995
|2.09
|-
|Linear Algebra Appl.
|Elsevier
|4885
|0.94
|-
|Math. Nachr.
|Wiley/VCH Verlag
|4795
|2.58
|}

=== Top ten mathematics journals by impact factor ===

{|
|Title
|Publisher
|Price/volume
|Price/page
|-
|Bull. Amer. Math. Soc.
|American Mathematical Society
|418
|0.64
|-
|Acta Mathematica
|Institut Mittag-Leffler
|392
|0.65
|-
|J. Amer. Math. Soc.
|American Mathematical Society
|287
|0.24
|-
|Comm. Pure Appl. Math.
|Wiley
|3205
|1.74
|-
|Inventiones Mathemat.
|Springer-Verlag
|3232
|1.21
|-
|Annals of Mathematics
|Princeton University Press
|260
|0.13
|-
|Advances in Mathematics
|Elsevier/Academic Press
|3221
|0.41
|-
|Mem. Amer. Math. Soc.
|American Mathematical Society
|N/A
|N/A
|-
|Commun. Contemp. Math.
|World Scientific
|483
|0.51
|-
|Geom. Func. Anal.
|Springer/Birkhauser
|1185
|0.88
|}

== Data from libraries ==

Pricing data from libraries is often hard to come by (for instance, many bundling contracts come with confidentiality agreements). More links in this section would be greatly appreciated.

* [http://www.bibliothek.kit.edu/cms/english/most-expensive-journals%20.php Here is a list of the 10 most expensive journals subscribed to by the Karlsruhe Institute of Technology] as of 2010/2011. 8 of the 10 are published by Elsevier.
* [http://libraries.mit.edu/sites/scholarly/mit-open-access/open-access-at-mit/mit-open-access-policy/publishers-and-the-mit-faculty-open-access-policy/elsevier-fact-sheet/ Elsevier Fact Sheet], MIT libraries. MIT avoids bundling in order to obtain flexibility in its subscriptions, but pays Elsevier almost $2 million/year for its journals.
* [http://www.purdueexponent.org/campus/article_19f1031d-0396-5b21-870a-c7f9f6ca91bc.html According to this news article], Purdue pays Elsevier $2.3 million/year for digital access to its journals, with price increases of approximately 5 percent per year.
* The [http://www.econ.ucsb.edu/~tedb/Journals/BundleContracts.html Bundle Contract Project] seeks to collect bundling contracts from commercial publishers.

Journal publishing reform

2012-01-23T19:39:34Z

Gowers: /* Blog posts */ Added link to Monbiot article

== Pledges, boycotts, and petitions ==

* [http://www.researchwithoutwalls.org/ Research Without Walls]
* [http://www.openaccesspledge.com/ Open Access Pledge]
* http://www-fourier.ujf-grenoble.fr/petitions/index.php?petition=3
* [http://thecostofknowledge.com/ The Cost of Knowledge]
* http://math.berkeley.edu/~kirby/journals.html

== Blog posts ==

* [http://blog.mathunion.org/journals/?no_cache=1&tx_t3blog_pi1%5BblogList%5D%5BshowUid%5D=17&tx_t3blog_pi1%5BblogList%5D%5Byear%5D=2011&tx_t3blog_pi1%5BblogList%5D%5Bmonth%5D=12&tx_t3blog_pi1%5BblogList%5D%5Bday%5D=07&cHash=bb9177d8192db5b5756aca088ea79677 What might be done about high prices of journals?], IMU blog on mathematical journals, July 12 2011.
* [http://www.monbiot.com/2011/08/29/the-lairds-of-learning/ The lairds of learning] Article by George Monbiot, August 29 2011.
* [http://gowers.wordpress.com/2012/01/21/elsevier-my-part-in-its-downfall/ Elsevier - my part in its downfall], Timothy Gowers, January 21, 2012.
* [http://gowers.wordpress.com/2012/01/23/httpthecostofknowledge-com/ The cost of knowledge], Timothy Gowers, January 23 2012.

== Media ==

* [http://classic.the-scientist.com/blog/display/55679/ Elsevier Published 6 Fake Journals], article in ''The Scientist'', May 2009. Summary: Elsevier was paid by unnamed pharmaceutical companies to publish six journals that looked like independent peer-reviewed medical journals, but which were not.
* [http://www.guardian.co.uk/business/2008/may/30/armstrade.weaponstechnology Reed Elsevier makes its final farewell to arms], article in ''The Guardian'', May 2008. Summary: Reed Elsevier was until 2009 organizing arms trade fairs.
* [http://www.reddit.com/r/math/comments/oqirf/one_mathematicians_stance_against_elsevier/ One mathematician's stance against Elsevier], Reddit, January 22 2012.

== Other Information ==

* [http://www.reed-elsevier.com/mediacentre/pressreleases/Documents/2010/Reed%20Elsevier%202009%20Results%20Announcement%2017%20February%202010%20FINAL.pdf Reed Elsevier's 2009 report] Elsevier reported a profit of 1.1 billion dollars on revenue of 3.2 billion dollars
* [http://en.wikipedia.org/wiki/Serials_crisis Journal subscription prices have increased far more rapidly than either inflation or spending on research]

== Elsevier mathematics journals ==

This list is taken from [http://www.elsevier.com/wps/find/P11.cws_home/mathjournals here]

* Acta Mathematica Scientia
* Advances in Applied Mathematics
* Advances in Engineering Software
* Advances in Mathematics
* Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire
* Annals of Pure & Applied Logic
* Annual Reviews in Control
* Applied & Computional Harmonic Analysis
* Applied Mathematical Modelling
* Applied Mathematics & Computation
* Applied Mathematics Letters
* Applied Numerical Mathematics
* Artificial Intelligence
* Automatica
* Biometric Technology Today
* Biosystems
* Bulletin des Sciences Mathématiques
* Chaos, Solitons & Fractals
* Communications in Nonlinear Science and Numerical Simulation
* Comptes Rendus Mathematique
* Computational Geometry
* Computational Statistics & Data Analysis
* Computer Methods in Applied Mechanics and Engineering
* Computers & Mathematics with Applications
* Control Engineering Practice
* Differential Geometry and its Applications
* Discrete Applied Mathematics
* Discrete Mathematics
* Discrete Optimization
* Electronic Notes in Discrete Mathematics
* Electronic Notes in Theoretical Computer Science
* Engineering Analysis with Boundary Elements
* Engineering Applications of Artificial Intelligence
* European Journal of Combinatorics
* European Journal of Operational Research
* Expositiones Mathematicae
* Finite Fields and their Applications
* Fuzzy Sets and Systems
* Historia Mathematica
* Indagationes Mathematicae
* Information Sciences
* International Journal of Forecasting
* International Journal of Non-Linear Mechanics
* Journal de Mathématiques Pures et Appliquées
* Journal of Algebra
* Journal of Algorithms
* Journal of Applied Logic
* Journal of Approximation Theory
* Journal of Combinatorial Theory, series A
* Journal of Combinatorial Theory, series B
* Journal of Complexity
* Journal of Computational & Applied Mathematics
* Journal of Computer and System Sciences
* Journal of Differential Equations
* Journal of Discrete Algorithms
* Journal of Econometrics
* Journal of Functional Analysis
* Journal of Geometry and Physics
* Journal of Mathematical Analysis & Applications
* Journal of Mathematical Economics
* Journal of Multivariate Analysis
* Journal of Number Theory
* Journal of Process Control
* Journal of Pure & Applied Algebra
* Journal of Statistical Planning & Inference
* Journal of the Franklin Institute
* Journal of the Korean Statistical Society
* Linear Algebra and its Applications
* Mathematical and Computer Modelling
* Mathematical Biosciences
* Mathematical Social Science
* Mathematics and Computers in Simulation
* Neural Networks
* Nonlinear Analysis
* Nonlinear Analysis: Hybrid Systems
* Nonlinear Analysis: Real world applications
* Operations Research Letters
* Pattern Recognition
* Physica A: Statistical Mechanics and its Applications
* Physica D: Nonlinear Phenomena
* Simulation Modelling Practice & Theory
* Statistical Methodology
* Statistics and Probability Letters
* Stochastic Processes and their Applications
* Systems & Control Letters
* Topology
* Topology & its Applications

Main Page

2011-02-08T12:42:19Z

Gowers: /* Existing polymath projects */

Main Page

2011-02-08T11:28:19Z

Gowers: Undo destructive spam

BK:Section 3

2011-02-06T23:04:08Z

Gowers: /* The nd-estimate */

Parent page: [[Improving the bounds for Roth's theorem]]

One of the take-away results from Section 3 of the Bateman-Katz paper is Proposition 3.1, an important part of which is in some places referred to as the "nd-estimate". The rough reason for this terminology is that it says that a set <math>A</math> in <math>\mathbb{F}_3^n</math> of density about <math>1/n</math> either has a `good' density increment on a subspace of codimension <math>d</math>, or else the <math>(1/n)</math>-large spectrum of <math>A</math> intersects any <math>d</math>-dimensional subspace in at most about <math>nd</math> points. We shall say later on why this is significant.

==The nd-estimate==

Here is the precise result, stated in slightly different terms to the paper in order to illustrate how it relates to other results. For a subspace <math>V \leq \mathbb{F}_3^n</math> we write
:<math>V^{\perp} = \{ \gamma \in \widehat{\mathbb{F}_3^n} : \gamma(x) = 1 \ \forall x \in V \}</math>
for its annihilator (cf. [[Basic facts about Bohr sets|the section on Bohr sets]]).

:'''Proposition 1''' Let <math>A \subset \mathbb{F}_3^n</math> be a set with density <math>\alpha</math>, and let <math>0 \leq \delta, \eta \leq 1</math> be parameters. Set
:<math>\Delta = \{ \gamma \in \widehat{G} : | \widehat{1_A}(\gamma) | \geq \delta \alpha \} \setminus \{ 0_{\widehat{\mathbb{F}_3^n}} \}</math>.
:Let <math>V \leq \mathbb{F}_3^n</math> be a subspace. Then
:* either <math>A</math> has density at least <math>\alpha(1 + \eta)</math> on <math>V</math>,
:* or <math>|\Delta \cap V^{\perp}| \leq 3\eta \delta^{-2}</math>; in fact <math>\sum_{\gamma \in V^{\perp}} |\widehat{(1_A - \alpha)}(\gamma)|^2 \leq 3\eta \alpha^2</math>.
'''Proof''':
Let us write <math>\mu_V = \frac{|\mathbb{F}_3^n|}{|V|}1_V</math> for the indicator function of <math>V</math> normalized so that <math>\mathbb{E}_x \mu_V(x) = 1</math>. If
:<math>1_A*\mu_V(x) > \alpha(1 + \eta)</math>
for some <math>x \in \mathbb{F}_3^n</math> then we are in the first case, so let us assume that <math>1_A*\mu_V \leq \alpha(1+\eta)</math>. Write <math>f = 1_A - \alpha</math> for the balanced function of <math>A</math>. Then
:<math> | \Delta \cap V^{\perp} | \delta^2 \alpha^2 \leq \sum_{\gamma \in V^{\perp}} |\widehat{f}(\gamma)|^2 = \sum_{\gamma \in \widehat{\mathbb{F}_3^n}} |\widehat{f}(\gamma)|^2 |\widehat{\mu_V}(\gamma)|^2.</math>
By Parseval's identity, this equals
:<math> \mathbb{E}_{x \in \mathbb{F}_3^n} f*\mu_V(x)^2 = \mathbb{E}_{x \in \mathbb{F}_3^n} 1_A*\mu_V(x)^2 - \alpha^2 \leq \alpha^2(2\eta + \eta^2),</math>
which proves the result.

==Comparison with other results about the large spectrum of a set==
The main ingredient in deriving the nd-estimate is Parseval's identity. This identity also has the following useful consequence: letting <math>\Delta</math> be as above, we have
:<math>|\Delta| \delta^2 \alpha^2 \leq \sum_{\gamma \in \widehat{\mathbb{F}_3^n}} |\widehat{1_A}(\gamma)|^2 = \mathbb{E}_x 1_A(x)^2 = \alpha</math>,
whence
:<math>|\Delta| \leq \alpha^{-1} \delta^{-2}</math>,
which should be compared to the bound on <math>| \Delta \cap V^{\perp} |</math> given by the nd-estimate.

There is another useful result about the large spectrum of a set known as Chang's theorem. Informally, this says that the largest size of a linearly independent set in large spectrum <math>\Delta</math> cannot be too large. Unfortunately, with the parameters needed for the Bateman-Katz paper, Chang's theorem reduces to a trivial statement. (Nevertheless, there is [http://arxiv.org/abs/math/0605689 a generalization of Chang's theorem due to Shkredov] that gives a lower bound for the number of additive <math>(2m)</math>-tuples in the large spectrum of a set, which is used in [[BK:Section 4|Section 4]] of the Bateman-Katz paper.)

By contrast, the nd-estimate is something like a statement in the opposite direction: it says that there are quite a lot of linearly independent characters in <math>\Delta</math>, or else there is a density increment. Specifically, if we have picked <math>\gamma_1, \ldots, \gamma_d</math> from <math>\Delta</math>, then
:<math>| \Delta \cap \langle \gamma_1, \ldots, \gamma_d \rangle | \leq 3\eta \delta^{-2}</math>
unless we get a density increment on a (particular) subspace of codimension at most <math>d</math>.
For suitable parameter choices, this says that there are a lot of characters in the large spectrum that are linearly independent of <math>\gamma_1, \ldots, \gamma_d</math>, which is very important in [[BK:Section 5|Section 5]] of the paper.

==Relation to Lemma 2.8 in Sanders's paper==

Basic facts about Bohr sets

2011-02-06T16:56:15Z

Gowers: /* Ways of thinking about Bohr sets */

Parent page: [[Improving the bounds for Roth's theorem]]

==Definition==

===Version for cyclic groups===

Let <math>r_1,\dots,r_k</math> be elements of <math>\mathbb{Z}_N</math> and let δ>0. The Bohr set <math>B(r_1,\dots,r_k;\delta)</math> is the set of all <math>x\in\mathbb{Z}_N</math> such that <math>r_ix</math> lies in the interval <math>[-\delta N,\delta N]</math> for every i=1,2,...,k. If <math>K=\{r_1,\dots,r_k\}</math>, then it is usual to write <math>B(K,\delta)</math> for <math>B(r_1,\dots,r_k;\delta)</math>.

===Version for more general finite Abelian groups===

Let G be a finite Abelian group, let <math>\chi_1,\dots,\chi_k</math> be characters on G and let δ>0. The Bohr set <math>B(\chi_1,\dots,\chi_k;\delta)</math> is the set of all <math>g\in G</math> such that <math>|1-\chi_i(g)|\leq\delta</math> for every i=1,2,...,k.

Note that this definition does not quite coincide with the definition given above in the case <math>G=\mathbb{Z}_N</math>. In practice, the difference is not very important, and sometimes when working with <math>\mathbb{Z}_N</math> it is in any case more convenient to replace the condition given by the inequality <math>|1-\exp(2\pi i r_jx/N)|\leq\delta</math> for each j.

===Version for sets of integers===

Needs to be written ...

===Regularity===

Of considerable importance when it comes to making use of Bohr sets is the notion of regularity, introduced by Bourgain. Here we give the bare definition: below it will be explained why regularity is useful.

The formal definition (as it appears in Sanders's paper) is this. Let K be a set of size d. Then the Bohr set <math>B=B(K,\delta)</math> is C-regular if for every <math>0\leq\eta\leq 1/Cd</math> we have the inequality <math>|B(K,\delta(1+\eta))|\leq(1+Cd\eta)|B(K,\delta)|</math> and also the inequality <math>|B(K,\delta(1-\eta))|\geq(1+Cd\eta)^{-1}|B(K,\delta)|</math>.

The precise numbers here are not too important. What matters is that if you slightly increase the width of a regular Bohr set, then you only slightly increase its size. Another way to think about it is this. Let B' be the "small" Bohr set <math>B(K,\eta)</math>. Then if you choose a random point in B and add to it a random point x' in B', the probability that x+x' also belongs to B is close to 1. An equivalent way of saying this is that the characteristic measure of B is approximately unchanged if you convolve it by the characteristic measure of B'.

==Ways of thinking about Bohr sets==

===Approximate subgroups===

If N is prime, then <math>\mathbb{Z}_N</math> has no non-trivial subgroups. Therefore, if one wishes to translate an argument that works in <math>\mathbb{F}_3^n</math> into one that works in <math>\mathbb{Z}_N</math>, then one must find some kind of analogue for the notion of a subgroup (or subspace) that is not actually a subgroup. Bohr sets are one way of fulfilling this role.

The key property enjoyed by a subgroup is closure: if H is a subgroup of a group G and x,y belong to H, then x+y belongs to H. Although a Bohr set is not closed under addition, a regular Bohr set has a property that can be used as a substitute for closure. Indeed, the property discussed above is exactly the one we use: that if B is a regular Bohr set <math>B(K,\delta)</math> and <math>B'=B(K,\eta)</math> for some suitably small η, then most elements x of B have the property that if you add any element y of B' you obtain another element of B. Thus, B is not closed under addition, but it is "mostly closed" under addition of elements of B'.

===Lattice convex bodies===

===Multidimensional arithmetic progressions===

==Converting <math>\mathbb{F}_3^n</math> concepts into <math>\mathbb{Z}_N</math> concepts==

===Subgroups go to regular Bohr sets===

===Linear maps go to Freiman homomorphisms===

===Linearly independent sets go to dissociated sets===

===Codimension goes to dimension===

===Averaging projections go to convolutions with Bohr measures===

==Localization to a Bohr set==

===Local Fourier analysis===

===A local Bogolyubov lemma===

===A local Chang theorem===

Improving the bounds for Roth's theorem

2011-02-06T11:23:20Z

Gowers: /* Links to more informal discussions of the problem */

This is a wiki for Polymath6, a project that aims to look at recent results of Bateman and Katz and of Sanders, and attempt to combine the ideas that go into them in order to break the log N-barrier in Roth's theorem. I hope that soon there will be expositions of their proofs, as well as of much of the background material needed to understand them. The wiki has only just been started, so has very little material on it so far.

==Background material==

[[Sketch of the Roth/Meshulam argument for cap sets]]

[[Basic facts about Bohr sets]]

[[Sketch of Bourgain's first argument using Bohr sets]]

==The Bateman-Katz argument==

[[Overview]]

[[Section 3: the "nd-estimate"]]

[[Section 4: the large spectrum contains many additive quadruples]]

[[Section 5: the large spectrum of a non-incrementing set is not additively smoothing]]

[[Section 6: the structure of additively non-smoothing sets]]

[[Section 7: the structure of the large spectrum of a non-incrementing cap set]]

[[Section 8: using the structure of the large spectrum to obtain density increments]]

==Sanders's argument==

[[Overview]]

[[The Croot-Sisask lemma]]

[[The Katz-Koester lemma]]

[[Sanders's local version of Chang's theorem]]

==Annotated bibliography==

*Michael Bateman and Nets Katz, [http://arxiv.org/pdf/1101.5851v1 New bounds on cap sets]. The paper that obtains an improvement to the Roth/Meshulam bound for cap sets.

*Tom Sanders, [http://arxiv.org/abs/1011.0104 On Roth's theorem on progressions]. The paper that gets within loglog factors of the 1/logN density barrier in Roth's theorem.

*Ernie Croot and Olof Sisask, [http://arxiv.org/abs/1003.2978 A probabilistic technique for finding almost-periods of convolutions]. The paper that introduced a technique that is central to Sanders's proof.

*Nets Katz and Paul Koester, [http://arxiv.org/abs/0802.4371 On additive doubling and energy], Another paper that introduced a method that Sanders used and that is related to some of the ideas in the Bateman-Katz paper as well.

==Links to more informal discussions of the problem==

*[http://polymathprojects.org/ Blog post by Tom Sanders about the ideas and difficulties involved]

*[http://polymathprojects.files.wordpress.com/2011/02/polymath-3.pdf The way an argument might go], A document written by Nets Katz, summarizing discussions he had with Olof Sisask about the possibilities for combining the Bateman-Katz and Sanders papers.

BK:Section 3

2011-02-06T11:21:15Z

Gowers:

Parent page: [[Improving the bounds for Roth's theorem]]

One of the take-away results from Section 3 of the Bateman-Katz paper is Proposition 3.1, which is in some places referred to as the "nd-estimate". The rough reason for this terminology is that it says that a set <math>A</math> in <math>\mathbb{F}_3^n</math> of density about <math>1/n</math> either has a `good' density increment on a subspace of codimension <math>d</math>, or else the <math>(1/n)</math>-large spectrum of <math>A</math> intersects any <math>d</math>-dimensional subspace in at most about <math>nd</math> points.

Here is the precise result, stated in slightly different terms to the paper in order to illustrate how it relates to other results.

:'''Proposition 1''' Let <math>A</math> be a subset of <math>\mathbb{F}_3^n</math> with density <math>\alpha</math>, and let <math>\delta > 0</math> and <math>0 \leq \eta \leq 1</math> be parameters. Set <math>\Delta = \{ \gamma \in \widehat{G} : | \widehat{1_A}(\gamma) | \geq \delta \alpha \} \setminus \{0\}</math>. Then
# either there is a subspace of <math>\mathbb{F}_3^n</math> of codimension <math>d</math> on which <math>A</math> has density at least <math>\alpha(1 + \eta)</math>
# or <math>|\Delta \cap W| \leq \eta \delta^{-2}</math> for each <math>d</math>-dimensional subspace <math>W \leq \widehat{\mathbb{F}_3^n}</math>.

'''Proof''' Choose a subspace <math>H</math> such that <math>W</math> is the annihilator of <math>H</math>, and let <math>V</math> be a subspace transverse to <math>H</math>. Then for any <math>\gamma\neq0\in W</math>,
:<math>\widehat{1_A}(\gamma)=3^{-n}\sum_{v\in V}(| A\cap(H+v)|-3^{-d}| A|)\gamma(v)</math>
and hence
:<math>\sum_{\gamma\neq0\in W}|\widehat{1_A}(\gamma)|^2=3^{d-2n}\sum_{v\in V}(| A\cap(H+v)|-3^{-d}| A|)^2.</math>
If we let <math>V^+</math> be the subset of <math>V</math> for which each of the squared summands is positive, then either <math>A</math> has the required density increment on a translate of <math>H</math> (which has codimension <math>d</math>), or
:<math>|| A\cap(H+v)|-3^{-d}| A||\ll 3^{-d}| A|\eta.</math>
Hence
:<math>\sum_{v\in V^+}|| A\cap(H+v)|-3^{-d}| A||\ll| A|\eta</math>
and
:<math>\sum_{v\in V^+}|| A\cap(H+v)|-3^{-d}| A||^2\ll 3^{-d}| A|^2\eta^2.</math>
Furthermore, since
:<math>\sum_{v\in V}|| A\cap(H+v)|-3^{-d}| A||=0</math>
defining <math>V^-</math> similarly and combining the trivial estimate
:<math>|| A\cap(H+v)|-3^{-d}| A||\leq3^{-d}| A|</math>
for <math>v\in V^-</math> with the above gives
:<math>\sum_{v\in V^-}|| A\cap(H+v)|-3^{-d}| A||^2\ll3^{-d}| A|^2\eta.</math>
Combining these sum estimates gives
:<math>\sum_{v\in V}|| A\cap(H+v)|-3^{-d}| A||^2\ll3^{-d}| A|^2\eta</math>
and hence
:<math>\sum_{\gamma\neq0\in W}|\widehat{1_A}(\gamma)|^2\ll \alpha^2\eta.</math>
Recalling the definition of <math>\Delta</math>, we have
:<math>|\Delta\cap W|\delta^2\alpha^2\ll\sum_{\gamma\in\Delta\cap W}|\widehat{1_A}(\gamma)|^2\ll\alpha^2\eta.</math>

To be added:
* Statement of size bound on <math>\Delta</math> from Parseval alone
* Statement of Chang's theorem
* Relation to Lemma 2.8 in Sanders's paper

Basic facts about Bohr sets

2011-02-06T11:20:18Z

Gowers:

Parent page: [[Improving the bounds for Roth's theorem]]

==Definition==

===Version for cyclic groups===

Let <math>r_1,\dots,r_k</math> be elements of <math>\mathbb{Z}_N</math> and let δ>0. The Bohr set <math>B(r_1,\dots,r_k;\delta)</math> is the set of all <math>x\in\mathbb{Z}_N</math> such that <math>r_ix</math> lies in the interval <math>[-\delta N,\delta N]</math> for every i=1,2,...,k. If <math>K=\{r_1,\dots,r_k\}</math>, then it is usual to write <math>B(K,\delta)</math> for <math>B(r_1,\dots,r_k;\delta)</math>.

===Version for more general finite Abelian groups===

Let G be a finite Abelian group, let <math>\chi_1,\dots,\chi_k</math> be characters on G and let δ>0. The Bohr set <math>B(\chi_1,\dots,\chi_k;\delta)</math> is the set of all <math>g\in G</math> such that <math>|1-\chi_i(g)|\leq\delta</math> for every i=1,2,...,k.

Note that this definition does not quite coincide with the definition given above in the case <math>G=\mathbb{Z}_N</math>. In practice, the difference is not very important, and sometimes when working with <math>\mathbb{Z}_N</math> it is in any case more convenient to replace the condition given by the inequality <math>|1-\exp(2\pi i r_jx/N)|\leq\delta</math> for each j.

===Version for sets of integers===

Needs to be written ...

===Regularity===

Of considerable importance when it comes to making use of Bohr sets is the notion of regularity, introduced by Bourgain. Here we give the bare definition: below it will be explained why regularity is useful.

The formal definition (as it appears in Sanders's paper) is this. Let K be a set of size d. Then the Bohr set <math>B=B(K,\delta)</math> is C-regular if for every <math>0\leq\eta\leq 1/Cd</math> we have the inequality <math>|B(K,\delta(1+\eta))|\leq(1+Cd\eta)|B(K,\delta)|</math> and also the inequality <math>|B(K,\delta(1-\eta))|\geq(1+Cd\eta)^{-1}|B(K,\delta)|</math>.

The precise numbers here are not too important. What matters is that if you slightly increase the width of a regular Bohr set, then you only slightly increase its size. Another way to think about it is this. Let B' be the "small" Bohr set <math>B(K,\eta)</math>. Then if you choose a random point in B and add to it a random point x' in B', the probability that x+x' also belongs to B is close to 1. An equivalent way of saying this is that the characteristic measure of B is approximately unchanged if you convolve it by the characteristic measure of B'.

==Ways of thinking about Bohr sets==

===Approximate subgroups===

===Lattice convex bodies===

===Multidimensional arithmetic progressions===

==Converting <math>\mathbb{F}_3^n</math> concepts into <math>\mathbb{Z}_N</math> concepts==

===Subgroups go to regular Bohr sets===

===Linear maps go to Freiman homomorphisms===

===Linearly independent sets go to dissociated sets===

===Codimension goes to dimension===

===Averaging projections go to convolutions with Bohr measures===

==Localization to a Bohr set==

===Local Fourier analysis===

===A local Bogolyubov lemma===

===A local Chang theorem===

Basic facts about Bohr sets

2011-02-06T11:16:39Z

Gowers: /* Regularity */

==Definition==

===Version for cyclic groups===

Let <math>r_1,\dots,r_k</math> be elements of <math>\mathbb{Z}_N</math> and let δ>0. The Bohr set <math>B(r_1,\dots,r_k;\delta)</math> is the set of all <math>x\in\mathbb{Z}_N</math> such that <math>r_ix</math> lies in the interval <math>[-\delta N,\delta N]</math> for every i=1,2,...,k. If <math>K=\{r_1,\dots,r_k\}</math>, then it is usual to write <math>B(K,\delta)</math> for <math>B(r_1,\dots,r_k;\delta)</math>.

===Version for more general finite Abelian groups===

Let G be a finite Abelian group, let <math>\chi_1,\dots,\chi_k</math> be characters on G and let δ>0. The Bohr set <math>B(\chi_1,\dots,\chi_k;\delta)</math> is the set of all <math>g\in G</math> such that <math>|1-\chi_i(g)|\leq\delta</math> for every i=1,2,...,k.

Note that this definition does not quite coincide with the definition given above in the case <math>G=\mathbb{Z}_N</math>. In practice, the difference is not very important, and sometimes when working with <math>\mathbb{Z}_N</math> it is in any case more convenient to replace the condition given by the inequality <math>|1-\exp(2\pi i r_jx/N)|\leq\delta</math> for each j.

===Version for sets of integers===

Needs to be written ...

===Regularity===

Of considerable importance when it comes to making use of Bohr sets is the notion of regularity, introduced by Bourgain. Here we give the bare definition: below it will be explained why regularity is useful.

The formal definition (as it appears in Sanders's paper) is this. Let K be a set of size d. Then the Bohr set <math>B=B(K,\delta)</math> is C-regular if for every <math>0\leq\eta\leq 1/Cd</math> we have the inequality <math>|B(K,\delta(1+\eta))|\leq(1+Cd\eta)|B(K,\delta)|</math> and also the inequality <math>|B(K,\delta(1-\eta))|\geq(1+Cd\eta)^{-1}|B(K,\delta)|</math>.

The precise numbers here are not too important. What matters is that if you slightly increase the width of a regular Bohr set, then you only slightly increase its size. Another way to think about it is this. Let B' be the "small" Bohr set <math>B(K,\eta)</math>. Then if you choose a random point in B and add to it a random point x' in B', the probability that x+x' also belongs to B is close to 1. An equivalent way of saying this is that the characteristic measure of B is approximately unchanged if you convolve it by the characteristic measure of B'.

==Ways of thinking about Bohr sets==

===Approximate subgroups===

===Lattice convex bodies===

===Multidimensional arithmetic progressions===

==Converting <math>\mathbb{F}_3^n</math> concepts into <math>\mathbb{Z}_N</math> concepts==

===Subgroups go to regular Bohr sets===

===Linear maps go to Freiman homomorphisms===

===Linearly independent sets go to dissociated sets===

===Codimension goes to dimension===

===Averaging projections go to convolutions with Bohr measures===

==Localization to a Bohr set==

===Local Fourier analysis===

===A local Bogolyubov lemma===

===A local Chang theorem===

Basic facts about Bohr sets

2011-02-06T11:15:52Z

Gowers: /* Definition */

==Definition==

===Version for cyclic groups===

Let <math>r_1,\dots,r_k</math> be elements of <math>\mathbb{Z}_N</math> and let δ>0. The Bohr set <math>B(r_1,\dots,r_k;\delta)</math> is the set of all <math>x\in\mathbb{Z}_N</math> such that <math>r_ix</math> lies in the interval <math>[-\delta N,\delta N]</math> for every i=1,2,...,k. If <math>K=\{r_1,\dots,r_k\}</math>, then it is usual to write <math>B(K,\delta)</math> for <math>B(r_1,\dots,r_k;\delta)</math>.

===Version for more general finite Abelian groups===

Let G be a finite Abelian group, let <math>\chi_1,\dots,\chi_k</math> be characters on G and let δ>0. The Bohr set <math>B(\chi_1,\dots,\chi_k;\delta)</math> is the set of all <math>g\in G</math> such that <math>|1-\chi_i(g)|\leq\delta</math> for every i=1,2,...,k.

Note that this definition does not quite coincide with the definition given above in the case <math>G=\mathbb{Z}_N</math>. In practice, the difference is not very important, and sometimes when working with <math>\mathbb{Z}_N</math> it is in any case more convenient to replace the condition given by the inequality <math>|1-\exp(2\pi i r_jx/N)|\leq\delta</math> for each j.

===Version for sets of integers===

Needs to be written ...

===Regularity===

Of considerable importance when it comes to making use of Bohr sets is the notion of regularity, introduced by Bourgain. Here we give the bare definition: below it will be explained why regularity is useful.

The formal definition (as it appears in Sanders's paper) is this. Let K be a set of size d. Then the Bohr set <math>B=B(K,\delta)</math> is C-regular if for every <math>0\leqη\leq 1/Cd</math> we have the inequality <math>|B(K,\delta(1+\eta))|\leq(1+Cd\eta)|B(K,\delta)|</math> and also the inequality <math>|B(K,\delta(1-\eta))|\geq(1+Cd\eta)^{-1}|B(K,\delta)|</math>.

The precise numbers here are not too important. What matters is that if you slightly increase the width of a regular Bohr set, then you only slightly increase its size. Another way to think about it is this. Let B' be the "small" Bohr set <math>B(K,\eta)</math>. Then if you choose a random point in B and add to it a random point x' in B', the probability that x+x' also belongs to B is close to 1. An equivalent way of saying this is that the characteristic measure of B is approximately unchanged if you convolve it by the characteristic measure of B'.

==Ways of thinking about Bohr sets==

===Approximate subgroups===

===Lattice convex bodies===

===Multidimensional arithmetic progressions===

==Converting <math>\mathbb{F}_3^n</math> concepts into <math>\mathbb{Z}_N</math> concepts==

===Subgroups go to regular Bohr sets===

===Linear maps go to Freiman homomorphisms===

===Linearly independent sets go to dissociated sets===

===Codimension goes to dimension===

===Averaging projections go to convolutions with Bohr measures===

==Localization to a Bohr set==

===Local Fourier analysis===

===A local Bogolyubov lemma===

===A local Chang theorem===

Basic facts about Bohr sets

2011-02-06T09:27:23Z

Gowers:

Improving the bounds for Roth's theorem

2011-02-06T09:15:36Z

Gowers:

This is a wiki for Polymath6, a project that aims to look at recent results of Bateman and Katz and of Sanders, and attempt to combine the ideas that go into them in order to break the log N-barrier in Roth's theorem. I hope that soon there will be expositions of their proofs, as well as of much of the background material needed to understand them. The wiki has only just been started, so has very little material on it so far.

==Background material==

[[Sketch of the Roth/Meshulam argument for cap sets]]

[[Basic facts about Bohr sets]]

[[Sketch of Bourgain's first argument using Bohr sets]]

==The Bateman-Katz argument==

[[Overview]]

[[Section 3: the "nd-estimate"]]

[[Section 4: the large spectrum contains many additive quadruples]]

[[Section 5: the large spectrum of a non-incrementing set is not additively smoothing]]

[[Section 6: the structure of additively non-smoothing sets]]

[[Section 7: the structure of the large spectrum of a non-incrementing cap set]]

[[Section 8: using the structure of the large spectrum to obtain density increments]]

==Sanders's argument==

[[Overview]]

[[The Croot-Sisask lemma]]

[[The Katz-Koester lemma]]

[[Sanders's local version of Chang's theorem]]

==Annotated bibliography==

*Michael Bateman and Nets Katz, [http://arxiv.org/pdf/1101.5851v1 New bounds on cap sets]. The paper that obtains an improvement to the Roth/Meshulam bound for cap sets.

*Tom Sanders, [http://arxiv.org/abs/1011.0104 On Roth's theorem on progressions]. The paper that gets within loglog factors of the 1/logN density barrier in Roth's theorem.

*Ernie Croot and Olof Sisask, [http://arxiv.org/abs/1003.2978 A probabilistic technique for finding almost-periods of convolutions]. The paper that introduced a technique that is central to Sanders's proof.

*Nets Katz and Paul Koester, [http://arxiv.org/abs/0802.4371 On additive doubling and energy], Another paper that introduced a method that Sanders used and that is related to some of the ideas in the Bateman-Katz paper as well.

==Links to more informal discussions of the problem==

*[http://polymathprojects.files.wordpress.com/2011/02/polymath-3.pdf The way an argument might go], A document written by Nets Katz, summarizing discussions he had with Olof Sisask about the possibilities for combining the Bateman-Katz and Sanders papers.

Improving the bounds for Roth's theorem

2011-02-06T09:13:32Z

Gowers:

This is a wiki for Polymath6, a project that aims to look at recent results of Bateman and Katz and of Sanders, and attempt to combine the ideas that go into them in order to break the log N-barrier in Roth's theorem. I hope that soon there will be expositions of their proofs, as well as of much of the background material needed to understand them. The wiki has only just been started, so has very little material on it so far.

==Background material==

[[Sketch of the Roth/Meshulam argument for cap sets]]

[[Basic facts about Bohr sets]]

[[Sketch of Bourgain's first argument using Bohr sets]]

==The Bateman-Katz argument==

[[Overview]]

[[Section 3: the "nd-estimate"]]

[[Section 4: the large spectrum contains many additive quadruples]]

[[Section 5: the large spectrum of a non-incrementing set is not additively smoothing]]

[[Section 6: the structure of additively non-smoothing sets]]

[[Section 7: the structure of the large spectrum of a non-incrementing cap set]]

[[Section 8: using the structure of the large spectrum to obtain density increments]]

==Annotated bibliography==

*Michael Bateman and Nets Katz, [http://arxiv.org/pdf/1101.5851v1 New bounds on cap sets]. The paper that obtains an improvement to the Roth/Meshulam bound for cap sets.

*Tom Sanders, [http://arxiv.org/abs/1011.0104 On Roth's theorem on progressions]. The paper that gets within loglog factors of the 1/logN density barrier in Roth's theorem.

*Ernie Croot and Olof Sisask, [http://arxiv.org/abs/1003.2978 A probabilistic technique for finding almost-periods of convolutions]. The paper that introduced a technique that is central to Sanders's proof.

*Nets Katz and Paul Koester, [http://arxiv.org/abs/0802.4371 On additive doubling and energy], Another paper that introduced a method that Sanders used and that is related to some of the ideas in the Bateman-Katz paper as well.

==Links to more informal discussions of the problem==

*[http://polymathprojects.files.wordpress.com/2011/02/polymath-3.pdf The way an argument might go], A document written by Nets Katz, summarizing discussions he had with Olof Sisask about the possibilities for combining the Bateman-Katz and Sanders papers.

Basic facts about Bohr sets

2011-02-05T19:27:43Z

Gowers: /* Version for sets of integers */

Basic facts about Bohr sets

2011-02-05T19:27:15Z

Gowers: /* Definition */

Basic facts about Bohr sets

2011-02-05T19:26:17Z

Gowers: New page: ==Definition== ===Version for cyclic groups=== Let <math>r_1,\dots,r_k</math> be elements of <math>\mathbb{Z}_N</math> and let δ>0. The Bohr set <math>B(r_1,\dots,r_k;\...

Improving the bounds for Roth's theorem

2011-02-05T19:16:48Z

Gowers: Added a bit more content to page

Improving the bounds for Roth's theorem

2011-02-05T11:53:10Z

Gowers: Added links to Bateman-Katz and Sanders

This is a holding page for a wiki for Polymath6, a project that aims to look at recent results of Bateman and Katz and of Sanders, and attempt to combine the ideas that go into them in order to break the log N-barrier in Roth's theorem. I hope that soon there will be expositions of their proofs, as well as of much of the background material needed to understand them.

==Annotated bibliography==

*Michael Bateman and Nets Katz, [http://arxiv.org/pdf/1101.5851v1 New bounds on cap sets]. The paper that obtains an improvement to the Roth/Meshulam bound for cap sets.

*Tom Sanders, [http://arxiv.org/abs/1011.0104 On Roth's theorem on progressions]. The paper that gets within loglog factors of the 1/logN density barrier in Roth's theorem.

Improving the bounds for Roth's theorem

2011-02-05T11:16:39Z

Gowers: Started page in very preliminary form

Main Page

2011-02-05T11:13:50Z

Gowers: /* Existing polymath projects */ Added Polymath6

Roth's Theorem concerning discrepancy on Arithmetic Progression

2010-07-17T00:07:41Z

Gowers: /* "Representation of the identity proof of \scriptstyle \gg n^{1/8} */

Letting <math>\scriptstyle \mathcal{AP}(N) </math> be the collection of all (not necessarily homogeneous) arithmetic progressions in <math>\{1, 2, ..., N\}</math>, Roth (1964) proved that <math> \scriptstyle \delta(\mathcal{AP}(N),{\mathbf x}) \geq c n^{1/4}</math>, independent of the sequence <math>\scriptstyle {\mathbf x}</math>.

*Roth, K. F., Remark concerning integer sequences. Acta Arith. 9 1964 257--260. MR0168545 (29 #5806)

In 2000, László Lovász gave another proof using semidefinite optimization.

*Lovász, László, Integer sequences and semidefinite programming. Dedicated to Professor Kálmán Gyory on the occasion of his 60th birthday.
Publ. Math. Debrecen 56 (2000), no. 3-4, 475--479. MR1765994 (2001k:11020)

Matoušek and Spencer (1996) have proven that the exponent <math> 1/4 </math> is best possible, although their construction is not constructive.

*Matoušek, Jirí; Spencer, Joel, [http://dx.doi.org/10.1090/S0894-0347-96-00175-0 Discrepancy in arithmetic progressions]. J. Amer. Math. Soc. 9 (1996), no. 1, 195--204. MR1311824 (96c:11089)

== "Representation of the identity'' proof of <math>\scriptstyle \gg n^{1/8}</math> ==
This is an elaboration of the outline in [http://gowers.wordpress.com/2010/03/13/edp12-representing-diagonal-maps/#comment-6764 this post]. A further elaboration that achieves Roth's bound of <math>n^{1/4}</math> can be found [http://gowers.files.wordpress.com/2010/07/rothdiscrepancy2.pdf here].

We break the proof down into 9 easy pieces.

* First, we consider APs modulo <math>n</math> for a large <math>n</math>. At the end, we'll have proven the existence of an AP with diameter smaller than n, so that if it wraps around it does so only once, and so at least half of the discrepancy is on a non-wrap-around AP. Set <math>\omega=e^{2\pi i /n}</math>. Let <math> \scriptstyle {\mathbf x}</math> be a <math> \scriptstyle \pm1</math> column vector (our coloring!), and let <math>\delta</math> be the maximum discrepancy of <math> \scriptstyle {\mathbf x}</math> along any AP. Summations are over all of <math>{\mathbb Z}_n</math> unless noted otherwise, or obviously otherwise.

* Let <math>P_i</math> be the indicator vector of the <math>i</math>-th AP. Suppose that we have some <math>\lambda_{i,j}</math> with

:<math>I = \sum_{i,j} \lambda_{i,j} P_i P_j^T,</math>

where <math>I</math> is the <math> \scriptstyle n\times n</math> identity matrix. Then

:<math>
n={\mathbf x}^T {\mathbf x} = {\mathbf x}^T I {\mathbf x} ={\mathbf x}^T\left(\sum \lambda_{i,j} P_i P_j^T\right) {\mathbf x}
=\sum_{i,j} \lambda ({\mathbf x}^T P_i) (P_j^T {\mathbf x}) \leq \delta^2 \sum |\lambda_{i,j}|.
</math>

So, if <math>\sum |\lambda_{i,j}| = o(n)</math>, necessarily <math>\delta\to\infty</math>. This simplifies the problem considerably: can the identity matrix be written in the form <math>\sum \lambda_{i,j} P_i P_j^T</math> with small <math>\lambda_{i,j}</math>? We no longer need concern ourselves with the vector <math> \scriptstyle {\mathbf x}</math>.

* Set <math>P_{d,a}</math> to be the indicator vector of the AP with length <math>2m+1</math> (with <math>m</math> to be determined later), difference <math>d>1</math>, and center <math>a</math>. Set <math>\omega_r(t)=\omega^{rt}</math>, a column vector whose <math>t</math>-th component is <math>\omega^{rt}</math>. Note that

:<math>I = \frac1n \sum_r \omega_r \overline{\omega_r}^T.</math>

We now proceed to write <math>\omega_r</math> as a sum of <math>P_{d,a}</math>.

* We express a sum in two ways:
:<math>\sum_s P_{d,0}(s) \omega^{r(t-s)} = \omega^{rt} \sum_s P_{d,0}\omega^{-rs}=\omega^{rt} \hat{P}_{d,0}(-r)</math>
and
:<math>\sum_s P_{d,0}(s) \omega^{r(t-s)} = \sum_s P_{d,0}(t-s) \omega^{rs}=\sum_s \omega^{rs}P_{d,s}(t)</math>
Thus,
:<math>\omega_r = \frac{1}{\hat{P}_{d,0}(-r)} \sum_s \omega^{rs} P_{d,s},</math>
the promised sum-of-APs representation of <math>\omega_r</math>, and consequently the promised representation of <math>I</math> as a sum of <math>P_{d,s_1} P_{d,s_2}^T</math>. All that remains is to analyze the coefficients of the representation of <math>I</math>.

* As <math>\hat{P}_{d,0}(-r)=\sum_s P_{d,0}\omega^{-rs}</math>, and <math>P_{d,0}</math> is symmetric about 0, we see that <math>\hat{P}_{d,0}(-r)=\hat{P}_{d,0}(r)</math> is real. Moreover, as it is a geometric series, it is routine to find
:<math>\alpha_r:=\hat{P}_{d,0}(-r)=\frac{\sin\left((2m+1)\pi rd/n\right)}{\sin\left(\pi rd/n\right)}</math>
We will want <math>\alpha_r</math> to be bounded away from 0. To that end for each <math>r</math>, fix now and forever <math>d</math> in <math>[1,\sqrt{n}]</math> with <math>\|rd/n\|\leq n^{-1/2}</math>, where <math>\|\cdot\|</math> means the distance to the nearest integer. This is a classic result of diophantine approximation (Dirichlet's theorem), whose proof is just the pigeonhole principle. Setting <math> \scriptstyle m=\frac15 \sqrt n</math>, we find
:<math>\alpha_r = \frac{\sin\left((2m+1)\pi rd/n\right)}{\sin\left(\pi rd/n\right)} \geq \frac{2\cdot\left((2m+1)rd/n\right)}{\pi rd/n}>m,</math>
and more obviously <math> \scriptstyle \alpha_r\leq 2m+1</math>. In short <math> \scriptstyle \alpha_r</math> has order <math> \scriptstyle \sqrt{n}</math>, to within a constant factor.

*:<math> I = n^{-1} \sum_r \omega_r \overline{\omega_r}^T = n^{-1} \sum_r \alpha_r^{-2}\left(\sum_x \omega^{rx}P_{d,x}\right)\left(\sum_y \omega^{-ry}P_{d,y}^T\right) = \sum_{r,x,y} n^{-1} \alpha_r^{-2} \omega^{r(x-y)} P_{d,x}P_{d,y}^T </math>
It is tempting to try and be done the easy way, but <math> \sum_{r,x,y} \left|n^{-1} \alpha_r^{-2} \omega^{r(x-y)} \right|</math>
is easily recognized as a sum with <math>n^3</math> summands, each of which has size <math>\approx n^{-2}</math>, so that the total is not <math>o(n)</math>. In short, we need to find some cancelation.

* Set <math>R(\Delta)=\{r \colon d=\Delta\}</math>. By a pigeonhole argument, <math> \scriptstyle |R(\Delta)|\leq 2\sqrt{n}</math>. The coefficient of <math>P_{\Delta,x}P_{\Delta,y}^T</math> is <math>\sum_{r\in R(\Delta)} n^{-1}\alpha_r^{-2} \omega^{r(x-y)}.</math>
We need to bound
:<math> \sum_{\Delta=1}^{\sqrt{n}} \sum_{x,y} \left| \sum_{r\in R(\Delta)} n^{-1}\alpha_r^{-2} \omega^{r(x-y)} \right|.</math>

*:<math>
\sum_{x,y} \left| \sum_{r\in R(\Delta)} n^{-1}\alpha_r^{-2} \omega^{r(x-y)} \right|
\leq \left(\sum_{x,y} 1^2 \right)^{1/2} \left( \sum_{x,y} \left| \sum_{r\in R(\Delta)} n^{-1}\alpha_r^{-2} \omega^{r(x-y)} \right|^2\right)^{1/2}</math>
:<math>= n \,\cdot\,\left(\sum_{x,y} \sum_{r_1,r_2} n^{-2} \alpha_{r_1}^{-2} \alpha_{r_2}^{-2} \omega^{(r_1-r_2)(x-y)}\right)^{1/2} = n\,\cdot\, \left( \sum_{r} n^{-2}\alpha_r^{-4} n^2\right)^{1/2}</math>
where the last equality is by noting that <math>\sum_{x,y}\omega^{(r_1-r_2)(x-y)}</math> is either <math>n^2</math> (if <math> \scriptstyle r_1-r_2=0</math>) or 0 (if <math>r_1-r_2\not=0</math>). Since <math>\alpha_r</math> is between <math>m</math> and <math>2m+1</math> (recall <math> \scriptstyle m=\frac15 \sqrt n</math>), we have <math>\alpha_r^{-4} \leq m^{-4} = \frac{5^4}{n^2}</math>. Thus,
:<math> n\,\cdot\, \left( \sum_{r} n^{-2}\alpha_r^{-4} n^2\right)^{1/2} \leq 25 |R(\Delta)|^{1/2}\leq 25\sqrt{2} n^{1/4},</math>
and so
:<math> \sum_{\Delta=1}^{\sqrt{n}} \sum_{x,y} \left| \sum_{r\in R(\Delta)} n^{-1}\alpha_r^{-2} \omega^{r(x-y)} \right|\leq 25\sqrt{2} n^{3/4}.</math>

* Returning to step 2, we have <math>\delta^2 \geq \frac{1}{25\sqrt{2}} n^{1/4}</math>, whence <math>\delta > \frac 17 n^{1/8}</math>.

Obtaining the correct bound in Roth's discrepancy theorem

2010-07-03T16:20:35Z

Gowers: Created page

\documentclass[12pt]{amsart}
\title{Discrepancy theorems and representing diagonal matrices}
\author{D. H. J. Polymath}

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\begin{document}

\maketitle

\section{Introduction}

Let $X$ be a finite set and let $\A$ be a collection of subsets of $X$. For every red/blue colouring $\kappa$ of $X$, the $\A$-\textit{discrepancy} of $\kappa$ is defined to be the maximum over all $A\in\A$ of the difference between the number of red points in $A$ and the number of blue points in $A$.There are many important problems of the following kind: given a set-system $\A$, obtain bounds for the smallest $\A$-discrepancy of any red/blue colouring of the ground set $X$.

One of the best-known results of this kind is due to Roth. It deals with the case where $X$ is the set $\{1,2,\dots,n\}$ and $\A$ is the set of all subsets of $X$ that are arithmetic progressions. The smallest possible discrepancy was shown by Roth to be at least $cn^{1/4}$, and this bound was proved to be tight by Matousek and Spencer.

Later, Lov\'asz gave a different proof of Roth's lower bound using semidefinite programming. The purpose of this paper is to give a third proof, related to Lov\'asz's proof but not quite the same.

To explain the relationship, we need to say a little bit more about the semidefinite programming approach. So let us begin by stating a rather abstract criterion that gives a lower bound for discrepancy. The first step is to reformulate the problem analytically. A simple reformulation is to replace the red/blue colouring by a function $f$ from $X$ to $\{-1,1\}$. Then the quantity we are trying to minimize is
\begin{equation*}
\disc_\A(f)=\max_{A\in\A}|\sum_{x\in A}f(x)|.
\end{equation*}
Once we have reformulated the problem in this way, it is natural to seek a lower bound that is valid for all functions $f$, and not just $\pm 1$-valued functions. Of course, the lower bound will have to depend on $f$, so a natural idea is to try to prove a bound of the form $\disc_\A(f)\geq\|f\|$ for some suitably chosen norm. Since eventually we would like a uniform bound for all $\pm 1$-valued functions, it is also natural if all such functions have the same norm.

It is also natural to try to prove the result by means of some kind of averaging argument, and to use a Euclidean norm for the lower bound. Moreover, one would like to replace the modulus by a modulus squared. With all these thoughts in mind, it is natural to try to find non-negative coefficients $\lambda_A$ and weights $b(x)$ and to seek a bound of the form
\begin{equation*}
\sum_{A\in\A}\lambda_A|\sum_{x\in A}f(x)|^2\geq\sum_{x\in X}b(x)|f(x)|^2.
\end{equation*}
If we have such a bound and $f$ is $\pm 1$-valued, then
\begin{equation*}
\sum_{A\in\A}\lambda_A|\sum_{x\in A}f(x)|^2\geq \sum_{x\in X}b(x),
\end{equation*}
which implies by averaging that $\disc_\A(f)^2$ is at least $\sum_{x\in X}b(x)/\sum_{A\in\A}\lambda_A$.

The basic idea behind the semidefinite programming method is to observe that
\begin{equation*}
Q_\lambda:f\mapsto\sum_{A\in\A}\lambda_A|\sum_{x\in A}f(x)|^2
\end{equation*}
is a positive semidefinite quadratic form on $\R^X$, and that the desired inequality will be true if the quadratic form
\begin{equation*}
Q_{\lambda,b}:f\mapsto\sum_{A\in\A}\lambda_A|\sum_{x\in A}f(x)|^2-\sum_{x\in X}b(x)|f(x)|^2
\end{equation*}
is also positive semidefinite. So for a given choice of coefficients $\lambda_A$ our problem is reduced to a \textit{semidefinite programming problem}, or SDP for short: that is, we would like to maximize the sum $\sum_xb(x)$ subject to the positive semidefiniteness of the quadratic form $Q_{\lambda,b}$. A great deal is known about SDPs. In particular, there are efficient algorithms for solving them, a fact that has many ramifications in extremal combinatorics and theoretical computer science.

It is straightforward to show that if $Q_{\lambda,b}$ is positive semidefinite, then we can extend the discrepancy result to vector-valued functions. More precisely, if each $f(x)$ is a vector in some Euclidean space $H$, then we have the lower bound
\begin{equation*}
\sum_{A\in\A}\lambda_A\|\sum_{x\in A}f(x)\|^2\geq\sum_{x\in X}b(x)\|f(x)\|^2.
\end{equation*}
In particular, it follows that if the $f(x)$ are unit vectors, then $\disc_\A(f)$ (now defined to be the maximum of $\|\sum_{x\in A}f(x)\|$ over all sets $A\in\A$) is again at least the square root of $\sum_{x\in X}b(x)/\sum_{A\in\A}\lambda_A$. Interestingly, the converse is true as well: if $\disc_\A(f)$ is at least $t$ whenever each $f(x)$ is a unit vector in some Hilbert space $H$, then we can find coefficients $\lambda_A$ and $b(x)$ such that $\sum_{x\in X}b(x)/\sum_{A\in\A}\lambda_A=t^2$ and the quadratic form $Q_{\lambda,b}$ is positive semidefinite.

The approach taken in this paper is different, but it is also based on proving an inequality of the form
\begin{equation*}
\sum_{A\in\A}\lambda_A|\sum_{x\in A}f(x)|^2\geq\sum_{x\in X}b(x)|f(x)|^2.
\end{equation*}
This we do as follows. For each set $A\in\A$, let us also write $A$ for its characteristic function. That is, $A(x)=1$ if $x\in A$ and 0 otherwise. If $u,v:X\rightarrow\C$, then we write $u\otimes v$ for the matrix with $xy$ entry equal to $u(x)v(y)$. Suppose we can find coefficients $\lambda_{AB}$ such that $\sum_{A,B\in\A}\lambda_{AB}A\otimes B=D$, where $D$ is a diagonal matrix with $D(x,x)=b(x)$ for every $x\in X$. Then by averaging
\begin{equation*}
\sum_xb(x)|f(x)|^2=\sp{Df,f}=\sum_{A,B\in\A}\lambda_{AB}\sum_{x\in A}f(x)\sum_{y\in B}f(y).
\end{equation*}
Therefore, there exist sets $A,B\in\A$ such that
\begin{equation*}
|\sum_{x\in A}f(x)\sum_{y\in B}f(y)|\geq\frac{\sum_xb(x)}{\sum_{A,B\in\A}|\lambda_{AB}|},
\end{equation*}
from which it follows that $\disc_\A(f)^2\geq\sum_xb(x)/\sum_{A,B\in\A}|\lambda_{AB}|.$

To convert this observation into a proof, one must find an efficient way of representing a diagonal matrix as a linear combination of rank-1 matrices $A\otimes B$, where $A$ and $B$ belong to the set $\A$. In this paper, we shall show how to do so when $X=\{1,2,\dots,n\}$ and $\A$ is the set of all subsets of $X$ that are arithmetic progressions.

We remark that it is possible to show that this approach works and gives a lower bound of $t$ if and only if the following stronger discrepancy-type statement holds. Let $f$ and $g$ be two functions from $X$ to a Euclidean space $H$, and suppose that $\sp{f(x),g(x)}=1$ for every $x\in X$. Then there exist $A,B\in\A$ such that $\sp{\sum_{x\in A}f(x),\sum_{y\in B}g(y)}\geq t^2$. Note also that if $g=f$ then we recover the statement that was equivalent to the success of the SDP approach, so this approach is less likely to work. However, if it works, then it gives a stronger result, and searching for an efficient representation of a diagonal matrix may be easier than proving that a certain matrix is positive semidefinite.

\section{Roth's discrepancy theorem}

Now let us specialize to the case that will interest us in this paper. That is, let $X=\{1,2,\dots,n\}$ and let $\A$ be the set of arithmetic subprogressions of $X$. We shall let $D$ be the identity matrix: that is, we shall take $b(x)=1$ for every $x$. Also, we shall identify $X$ with $\Z_N$.

For each $r\in\Z_N$ let $\omega_r$ be the function $\omega_r(x)=e^{2\pi irx/N}=\omega^{rx}$, where $\omega=e^{2\pi i/N}$. Our starting point is the following very simple lemma. We write $\E_r$ to stand for $N^{-1}\sum_r$.

\begin{lemma}
$I_N=\E_r\omega_r\otimes\overline{\omega_r}$.
\end{lemma}

\begin{proof}
Let us evaluate the right-hand side at $(x,y)$. We obtain
\begin{equation*}
\E_r\omega^{rx}\omega^{-ry}=\E_r\omega^r(x-y)=\d_{xy},
\end{equation*}
which proves the lemma.
\end{proof}

That was not a completely sensible proof: it is straightforward to show that $I_n=\E_ru_r\otimes\overline{u_r}$ for any orthonormal basis $(u_r)$ (with respect to the inner product $\sp{f,g}=\E_xf(x)\overline{g(x)}$).

Next, we show that each function $\omega_r$ can be decomposed as a linear combination of arithmetic progressions with small common difference. For this we need a standard lemma.

\begin{lemma} \label{dirichlet}
Let $0<m\leq N$ and let $\a\in\R$. Then there exists $0<d\leq m$ such that $\|\a d\|\leq m^{-1}$.
\end{lemma}

For each $r$ let us fix a $d$ that satisfies the conclusion of the lemma with $\alpha=r/N$. From the lemma it follows that for every $r$ we can find $0<d\leq m$ such that $|1-\omega^{rd}|\leq 2\pi/m$. Let us now define $P$ to be the interval $[-m/4\pi, m/4\pi]$ (meaning the set of all residues in $\Z_N$ that lie in this interval when they are considered as real numbers). For each $0<d\leq m$ let $P_d$ be the mod-$N$ progression $dP$. Note that the diameter of $P_d$ is at most $m^2/2\pi$: this will be important to us later. Let $\pi_d$ be the characteristic measure of $P_d$. That is, $\pi_d(x)=N/|P_d|$ when $x\in P_d$ and 0 otherwise.

In the next lemma, we define the convolution of two functions $f$ and $g$ by the formula
\begin{equation*}
f*g(x)=\E_{y+z=x}f(y)g(z).
\end{equation*}

\begin{lemma} \label{convapprox}
Suppose that $|1-\omega^{rd}|\leq 2\pi/m$. Then $\omega_r*\pi_d=\lambda_{r,d}\omega_r$ for some real number $\lambda_{r,d}$ that lies between 1/2 and 1.
\end{lemma}

\begin{proof}
Let us evaluate the left-hand side at $x$. We have
\begin{eqnarray*}
\omega_r*\pi_d(x) &=& \E_y\omega^{r(x-y)}\pi_d(y)\\
&=&\omega^{rx}\E_{y\in P_d}\omega^{-ry}.\\
\end{eqnarray*}
Since $P_d$ is symmetric, $\lambda_{r,d}=\E_{y\in P_d}\omega^{-ry}$ is real. Note also that for every $y\in P_d$ we have $y=sd$ for some $s$ of modulus at most $m/4\pi$, from which it follows that $|1-\omega^{-ry}|\leq(m/4\pi)|1-\omega^{-rd}|\leq 1/2$. Therefore, $\lambda_{r,d}\geq 1/2$ as claimed. It is trivial that $\lambda_{r,d}\leq 1$ since $\|\pi_d\|_1=1$.
\end{proof}

Writing $\mu_{r,d}$ for $\lambda_{r,d}^{-1}$, we may rewrite $\omega_r$ as $\mu_{r,d}\omega_r*\pi_d$. Now $\omega_r*\pi_d(x)$ can also be written as $\E_y\omega^{ry}\pi_d(x-y)$. Writing $\pi_{d,y}(x)$ for $\pi_d(x-y)$, we can write this as $\E_y\omega^{ry}\pi_{d,y}(x)$. That is, $\omega_r*\pi_d=\E_y\omega^{ry}\pi_{d,y}$, so $\omega_r=\mu_{r,d}\E_y\omega^{ry}\pi_{d,y}$. Note that $\pi_{d,y}$ is the characteristic measure of the arithmetic progression $P_{d,y}=P_d+y$, so we can also write this as $\mu_{r,d}(N/|P|)\E_y\omega^{ry}P_{d,y}$.

Since, $\omega_r=\mu_{r,d}(N/|P|)\E_y\omega^{ry}P_{d,y}$ for each $r$, and $I_n=\E_r\omega_r\otimes\ol{\omega_r}$, this gives us the decomposition
\begin{equation*}
I_n=\frac{N^2}{|P|^2}\E_r\mu_{r,d}^2\E_{y,z}\omega^{r(y-z)}P_{d,y}\otimes P_{d,z}.
\end{equation*}
Our next task is to show that this decomposition is efficient.

To do this, let us fix $d$ and work out the sum over $y$ and $z$ of the absolute values of the coefficients of $P_{d,y}\otimes P_{d,z}$ in the decomposition. Recall that $d=d(r)$: for each $d$ with $0<d\leq m$ let us write $R(d)$ for the set of $r$ such that $d(r)=d$. Since always choose $d$ such that $\|dr/N\|\leq m^{-1}$, it follows that $|R(d)|\leq 3N/m$ for every $d$.

First we rewrite the decomposition itself as
\begin{equation*}
I_n=\frac{1}{N|P|^2}\sum_r\mu_{r,d(r)}^2\sum_{y,z}\omega^{r(y-z)}P_{d(r),y}\otimes P_{d(r),z}.
\end{equation*}
Now it becomes easier to see that the coefficient of $P_{d,y}\otimes P_{d,z}$ is
\begin{equation*}
\frac{1}{N|P|^2}\sum_{r\in R(d)}\mu_{r,d}^2\omega^{r(y-z)},
\end{equation*}
so the sum in question is
\begin{equation*}
\frac{N}{|P|^2}\E_{y,z}|\sum_{r\in R(d)}\mu_{r,d}^2\omega^{r(y-z)}|,
\end{equation*}

Let $\nu(r)=\mu_{r,d}^2$ if $r\in R(d)$ and $0$ otherwise. Then this expression is equal to
\begin{equation*}
\frac{N^2}{|P|^2}\E_{y,z}|\E_r\nu(r)\omega^{r(y-z)}|=\frac{N^2}{|P|^2}\E_y|\E_r\nu(r)\omega^{ry}|.
\end{equation*}
Now
\begin{eqnarray*}
(\E_y|\E_r\nu(r)\omega^{ry}|)^2 &=& N^{-2}(\sum_y|\E_r\nu(r)\omega^{ry}|)^2\\
&=& N^{-2}\|\hat{\nu}\}_1^2\\
&\leq& N^{-1}\|\hat{\nu}\|_2^2\\
&=& N^{-1}\|\nu\|_2^2\\
&\leq& 4N^{-2}|R(d)|.\\
\end{eqnarray*}

Therefore, since $|P|\geq m/16$ and $|R(d)|\leq 3N/m$, the coefficients have absolute values summing to at most $256(N/m)^2.2N^{-1/2}m^{-1/2}=512N^{3/2}m^{-5/2}$. Since the set of possible $d$ has size $m$, the sum of the absolute values of \textit{all} coefficients is at most $512(N/m)^{3/2}$.

This gives us a discrepancy bound of $2^{-9/2}m^{3/4}N^{-1/4}$ if we take $\A$ to be the set of all arithmetic progressions of the form $P_{d,y}$. However, although these are arithmetic progressions in the $\Z_N$ sense, they do not necessarily become arithmetic progressions when we identify $\Z_N$ with $\{1,2,\dots,N\}$.

This is where the diameter estimate comes in. Since the diameter of $P_d$ is at most $m^2/2\pi$, we know that each $P_{d,y}$ can wrap around at most once, provided that $m\leq\sqrt{N}$. If it wraps around once, then we can split it into two genuine arithmetic progressions, and at least half the discrepancy must occur on one of them. Thus, by taking $m=\sqrt{N}$ we obtain a bound of size $cN^{3/8}N^{-1/4}=cN^{1/8}$.

\section{Improving the bound}

Our next aim is to get from a bound of $cN^{1/8}$ to a bound of $cN^{1/4}$. We begin by giving the basic thought behind the improvement.

In the argument above, we bounded $\|\hat{\nu}\|_1$ above by $N^{1/2}\|\hat{\nu}\|_2$. Now this bound is sharp only if $\hat{\nu}$ is evenly spread throughout $\Z_N$, but that is not the case. Speaking rather roughly, $\nu$ is a bit like the characteristic function of $R(d)$, which is a bit like an arithmetic progression of length $N/m$, which means that $\hat{\nu}$ should be a bit like an arithmetic progression of length $m$, which means that $\|\hat{\nu}\|_1/\|\hat{\nu}\|_2$ should be more like $m^{1/2}$ than $N^{1/2}$. So if we can make these thoughts precise, then it is reasonable to aspire to an improvement by a factor $(m/N)^{1/2}$ to the sum of the coefficients in the decomposition, which would improve the discrepancy bound by a factor of $(N/m)^{1/4}$, taking it from $cm^{3/4}N^{-1/4}$ to $cm^{1/2}$. Encouragingly, this is exactly the Roth bound when $m$ is at its maximum of $c\sqrt{n}$, and it gives us at least some information for all smaller (but non-constant) values of $m$.

A standard trick that will enable us to avoid unwanted logarithmic factors is to work not with characteristic functions of arithmetic progressions but with similar functions that have absolutely summable Fourier coefficients. The following lemma gives us the main technical fact that we need.

\begin{lemma} \label{ell1}
Let $m\leq N/2$ and let $f_{d,m}:\Z_N\rightarrow\C$ be defined by the formula $f_{d,m}(dx)=\max\{1-|x|/m,0\}$ for every $x$ with $|x|\leq N/2$. Then $\|\hat{f}_{d,m}\|_1=1$.
\end{lemma}

\begin{proof}
Let $P$ be the mod-$N$ arithmetic progression $\{d,2d,\dots,md\}$, and also the characteristic function of that arithmetic progression, and similarly for $-P$. Then
\begin{equation*}
P*(-P)(xd)=\E_yP(y)P(y-xd)=N^{-1}|P\cap(P+xd)|=N^{-1}\max\{m-|x|,0\}=N^{-1}mf_{d,m}(dx).
\end{equation*}
We also know that
\begin{equation*}
\|P*(-P)\|_1=\sum_r\hat{P}(r)\ol{\hat{P}(r)}=\|\hat{P}\|_2^2=\|P\|_2^2=N^{-1}m.
\end{equation*}
It follows that $\|\hat{f}_{d,m}\|_1=1,$ as claimed.
\end{proof}

Note that $\hat{f}$ is a non-negative real-valued function, since $\hat{f}(r)=|\hat{P}(r)|^2$ for every $r$. This fact will also be useful to us.

The next lemma is a variant of Lemma \ref{convapprox}.

\begin{lemma} \label{convapprox2}
Let $d,r\in\Z_N$. Then $\omega_r*\pi_d*\pi_d=\mu_{r,d}\omega_r$ for some non-negative real number $\mu_{r,d}$. Moreover, if $|1-\omega^{rd}|\leq 2\pi/m,$ then $1/4\leq\mu_{r,d}\leq 1$.
\end{lemma}

\begin{proof}
The second part of the lemma follows directly from Lemma \ref{convapprox}, applied twice. In general, we know in Lemma \ref{convapprox} that $\lambda_{r,d}$ is real, so the positivity of $\mu_{r,d}$ follows from the fact that $\mu_{r,d}=\lambda_{r,d}^2$.
\end{proof}

The next lemma is a simple consequence of Lemmas \ref{dirichlet} and \ref{convapprox2}. For the next few lemmas, all sums over $d$ will be from $d=1$ to $d=m$.

\begin{lemma}\label{decomposetrig}
Let $s=\lceil N/m\rceil$, and for each $d$ with $0<d\leq m$ and for each $r\in\Z_N$ let $\a_{r,d}=f_{1,2s}(rd)$. Let $\omega_r$ be the function $x\mapsto\omega^{rx}$. Then there is a real number $\lambda_r\geq 1/32$ such that
\begin{equation*}
\lambda_r\omega_r\otimes\ol{\omega_r}=\sum_d\alpha_{r,d}(\omega_r*\pi_d*\pi_d)\otimes(\ol{\omega_r}*\pi_d*\pi_d).
\end{equation*}
\end{lemma}

\begin{proof}
By Lemma \ref{dirichlet} there exists a positive $d\leq m$ such that $\|rd/N\|\leq m^{-1}$. It follows that $f_{1,2s}(rd)=\alpha_{r,d}\geq 1/2$.

For this $d$ we know that $|1-\omega^{rd}|\leq 2\pi/m$, so by Lemma \ref{convapprox2} we can conclude that
\begin{equation*}
\alpha_{r,d}(\omega_r*\pi_d*\pi_d)\otimes(\ol{\omega_r}*\pi_d*\pi_d)
=\alpha_{r,d}\mu_{r,d}^2\omega_r\otimes\ol{\omega_r}
\end{equation*}
for some real constant $\mu_{r,d}\geq 1/4$. For all other $d$, we have the same conclusion, but this time all we can guarantee is that $\alpha_{r,d}\mu_{r,d}^2\geq 0$. Summing over all $d$ and setting $\lambda_r=\sum_d\alpha_{r,d}\mu_{r,d}^2$, we obtain the result stated.
\end{proof}

We are now ready for the main estimate, after which the proof will be more or less finished.

\begin{lemma} \label{mainlemma}
There exist coefficients $\lambda_r$, all at least 1/16, such that the matrix $\E_r\lambda_r\omega_r\otimes\ol{\omega_r}$ can be expressed as a linear combination
\begin{equation*}
\sum_{0<d\leq m}\sum_{x,y}\gamma_{d,x,y}P_{d,x}\otimes P_{d,y}
\end{equation*}
where each $P_{d,x}$ and $P_{d,y}$ is an arithmetic progression mod $N$ of diameter at most $m^2$, and $\sum_{d,x,y}|\gamma_{d,x,y}|\leq N/4m$.
\end{lemma}

\begin{proof}
Lemma \ref{decomposetrig} gives us the decomposition
\begin{eqnarray*}
\E_r\lambda_r\omega_r\otimes\ol{\omega_r}&=&\E_r\sum_d\alpha_{r,d}(\omega_r*\pi_d*\pi_d)\otimes(\ol{\omega_r}*\pi_d*\pi_d)\\
&=&\frac{N}{|P|^2}\sum_r\sum_d\alpha_{r,d}(\omega_r*\pi_d*P_d)\otimes(\ol{\omega_r}*\pi_d*P_d).\\
\end{eqnarray*}
Let us write $Q_d$ for the function $\pi_d*P_d$. Now $\omega_r*Q_d=\E_x\omega^{rx}Q_{d,x}$, where $Q_{d,x}(y)=Q_d(y-x)=Q_d(x-y)$. So we can rewrite our decomposition as
\begin{equation*}
\frac{N}{|P|^2}\sum_r\sum_d\alpha_{r,d}\E_{x,y}\omega^{r(x-y)}Q_{d,x}\otimes Q_{d,y}
=\frac{1}{N|P|^2}\sum_r\sum_d\alpha_{r,d}\sum_{x,y}\omega^{r(x-y)}Q_{d,x}\otimes Q_{d,y}.
\end{equation*}
The coefficient of $Q_{d,x}\otimes Q_{d,y}$ in this decomposition is
\begin{equation*}
\frac{1}{N|P|^2}\sum_r\alpha_{r,d}\omega^{r(x-y)},
\end{equation*}
so the sum of the absolute values of these coefficients is
\begin{eqnarray*}
\frac{1}{N|P|^2}\sum_d\sum_{x,y}|\sum_r\alpha_{r,d}\omega^{r(x-y)}|&=&
\frac{N}{|P|^2}\sum_d\E_{x,y}|\sum_r\alpha_{r,d}\omega^{r(x-y)}|\\
&=&\frac{N}{|P|^2}\sum_d\E_x|\sum_r\alpha_{r,d}\omega^{rx}|\\
&=&\frac{N}{|P|^2}\sum_d\sum_x|\E_r\alpha_{r,d}\omega^{rx}|\\
&=&\frac{N}{|P|^2}\sum_d\|\hat{\alpha}_d\|_1,\\
\end{eqnarray*}
where we define $\alpha_d$ by the formula $\alpha_d(r)=\alpha_{r,d}$.

Now $\alpha_d(r)=f_{1,2s}(dr)=f_{d^{-1},2s}(r)$ for every $r$. Therefore, by Lemma \ref{ell1} we have that $\|\hat{\alpha}_d\|_1=1$ for every $d\leq m$. It follows that the sum of the absolute values of the coefficients is $Nm/|P|^2\leq N/4m$.
\end{proof}

To complete the proof, we first observe that the matrix $\E_r\lambda_r\omega_r\otimes\ol{\omega_r}-I_N/16$ is positive semidefinite. That is for the simple reason that it is equal to $\E_r(\lambda_r-1/16)\omega_r\otimes\ol{\omega_r}$, and we have ensured that each $\lambda_r$ is at least $1/16$. Therefore, by Lemma \ref{mainlemma}, given any function $f:\Z_N\rightarrow\C$, we have some pair $(Q_{d,x},Q_{d,y})$ such that $|\sum_zQ_{d,x}(z)f(z)\sum_wQ_{d,y}(w)\ol{f(w)}|\geq m\|f\|_2^2/4$. (This number $m/4$ is the ratio of the trace $N/16$ of $I_N/16$ to the upper bound $N/4m$ for the sum of the coefficients in the decomposition.) It follows that we can find $x$ such that $|\sum_zQ_{d,x}(z)f(z)|\geq m^{1/2}\|f\|_2/2$. Since $Q_{d,x}$ is an average of characteristic functions of translates of the arithmetic progression $P_d$, it follows that we can find some $x$ such that $|\sum_{z\in P_d+x}f(z)|\geq m^{1/2}\|f\|_2/2$. And finally, since $P_d$ has diameter at most $N$ (assuming that $m\leq c\sqrt{N}$, it follows that we can find an arithmetic progression of length $m$ and common difference at most $m$ on which $f$ has discrepancy at least $m^{1/2}\|f\|_2/4$. In particular, if $f$ is $\pm 1$-valued, then we obtain a lower bound for the AP-discrepancy of $m^{1/2}/4$. Once again, this argument is valid when $m\leq c\sqrt{N}$, so we obtain Roth's bound of $cN^{1/4}$.

\end{document}

Representation of the diagonal

2010-07-03T16:18:33Z

Gowers: /* Remarks */

The following conjecture, if true, would imply the Erdos discrepancy conjecture.

----

For all <math>C > 0</math> there exists a diagonal matrix with trace at least <math>C</math> that can be expressed as <math>\sum_i \lambda_i P_i \otimes Q_i</math>, where <math>\sum_i | \lambda_i | \leq 1</math> and each <math>P_i</math> and <math>Q_i</math> is the characteristic function of a HAP.

----

== Proof of implication ==
Suppose <math>D</math> is a diagonal matrix with entries <math>b_j</math> on the diagonal, with <math>\sum_j b_j</math> unbounded, and <math>D = \sum_i \lambda_i P_i \otimes Q_i</math> where <math>\sum_i | \lambda_i | \leq 1</math> and the <math>P_i</math> and <math>Q_i</math> are HAPs. Suppose <math>x</math> is a <math>\pm 1</math> sequence with finite discrepancy <math>C</math>. Then we can write <math>| \langle x, Dx \rangle |</math> in two ways. On the one hand, <math>| \langle x, Dx \rangle | = | \sum_j b_j x_j^2 | = | \sum_j b_j |</math>, which is unbounded; on the other hand, <math>| \langle x, Dx \rangle | = | \langle x, \sum_i \lambda_i (P_i \otimes Q_i) x \rangle | = | \sum_i \lambda_i \langle x, P_i \rangle \langle x, Q_i \rangle | \leq \sum_i | \lambda_i | | \langle x, P_i \rangle | | \langle x, Q_i \rangle | \leq C^2</math>, a contradiction.

== Remarks ==

Moses pointed out [http://gowers.wordpress.com/2010/03/23/edp13-quick-summary/#comment-6971 here] that we do not actually need to produce a ''diagonal'' matrix <math>D</math> with unbounded trace. It is enough to produce a matrix <math>D</math> such that <math>\sum_i d_{ii} - \sum_{i \neq j} | d_{ij} |</math> is unbounded.

[[Roth's Theorem concerning discrepancy on Arithmetic Progression]] contains a representation-of-diagonal proof in detail.

[[Obtaining the correct bound in Roth's discrepancy theorem|This page]] contains the LaTeX source code for a write-up of a representation-of-diagonal proof that gives the correct bound.

== Possible proof strategies ==

== Heuristic arguments ==

== Numerical results ==
Moses has published some experimental data [http://webspace.princeton.edu/users/moses/EDP/try-lp/ here]. See [http://gowers.wordpress.com/2010/03/07/edp11-the-search-continues/#comment-6668 this comment] (and below it) for an explanation.

Roth's Theorem concerning discrepancy on Arithmetic Progression

2010-07-02T17:34:24Z

Gowers:

Letting <math>\scriptstyle \mathcal{AP}(N) </math> be the collection of all (not necessarily homogeneous) arithmetic progressions in <math>\{1, 2, ..., N\}</math>, Roth (1964) proved that <math> \scriptstyle \delta(\mathcal{AP}(N),{\mathbf x}) \geq c n^{1/4}</math>, independent of the sequence <math>\scriptstyle {\mathbf x}</math>.

*Roth, K. F., Remark concerning integer sequences. Acta Arith. 9 1964 257--260. MR0168545 (29 #5806)

In 2000, László Lovász gave another proof using semidefinite optimization.

*Lovász, László, Integer sequences and semidefinite programming. Dedicated to Professor Kálmán Gyory on the occasion of his 60th birthday.
Publ. Math. Debrecen 56 (2000), no. 3-4, 475--479. MR1765994 (2001k:11020)

Matoušek and Spencer (1996) have proven that the exponent <math> 1/4 </math> is best possible, although their construction is not constructive.

*Matoušek, Jirí; Spencer, Joel, [http://dx.doi.org/10.1090/S0894-0347-96-00175-0 Discrepancy in arithmetic progressions]. J. Amer. Math. Soc. 9 (1996), no. 1, 195--204. MR1311824 (96c:11089)

== "Representation of the identity'' proof of <math>\scriptstyle \gg n^{1/8}</math> ==
This is an elaboration of the outline in [http://gowers.wordpress.com/2010/03/13/edp12-representing-diagonal-maps/#comment-6764 this post]. A further elaboration that achieves Roth's bound of <math>n^{1/4}</math> can be found [http://gowers.files.wordpress.com/2010/07/rothdiscrepancy.pdf here].

We break the proof down into 9 easy pieces.

* First, we consider APs modulo <math>n</math> for a large <math>n</math>. At the end, we'll have proven the existence of an AP with diameter smaller than n, so that if it wraps around it does so only once, and so at least half of the discrepancy is on a non-wrap-around AP. Set <math>\omega=e^{2\pi i /n}</math>. Let <math> \scriptstyle {\mathbf x}</math> be a <math> \scriptstyle \pm1</math> column vector (our coloring!), and let <math>\delta</math> be the maximum discrepancy of <math> \scriptstyle {\mathbf x}</math> along any AP. Summations are over all of <math>{\mathbb Z}_n</math> unless noted otherwise, or obviously otherwise.

* Let <math>P_i</math> be the indicator vector of the <math>i</math>-th AP. Suppose that we have some <math>\lambda_{i,j}</math> with

:<math>I = \sum_{i,j} \lambda_{i,j} P_i P_j^T,</math>

where <math>I</math> is the <math> \scriptstyle n\times n</math> identity matrix. Then

:<math>
n={\mathbf x}^T {\mathbf x} = {\mathbf x}^T I {\mathbf x} ={\mathbf x}^T\left(\sum \lambda_{i,j} P_i P_j^T\right) {\mathbf x}
=\sum_{i,j} \lambda ({\mathbf x}^T P_i) (P_j^T {\mathbf x}) \leq \delta^2 \sum |\lambda_{i,j}|.
</math>

So, if <math>\sum |\lambda_{i,j}| = o(n)</math>, necessarily <math>\delta\to\infty</math>. This simplifies the problem considerably: can the identity matrix be written in the form <math>\sum \lambda_{i,j} P_i P_j^T</math> with small <math>\lambda_{i,j}</math>? We no longer need concern ourselves with the vector <math> \scriptstyle {\mathbf x}</math>.

* Set <math>P_{d,a}</math> to be the indicator vector of the AP with length <math>2m+1</math> (with <math>m</math> to be determined later), difference <math>d>1</math>, and center <math>a</math>. Set <math>\omega_r(t)=\omega^{rt}</math>, a column vector whose <math>t</math>-th component is <math>\omega^{rt}</math>. Note that

:<math>I = \frac1n \sum_r \omega_r \overline{\omega_r}^T.</math>

We now proceed to write <math>\omega_r</math> as a sum of <math>P_{d,a}</math>.

* We express a sum in two ways:
:<math>\sum_s P_{d,0}(s) \omega^{r(t-s)} = \omega^{rt} \sum_s P_{d,0}\omega^{-rs}=\omega^{rt} \hat{P}_{d,0}(-r)</math>
and
:<math>\sum_s P_{d,0}(s) \omega^{r(t-s)} = \sum_s P_{d,0}(t-s) \omega^{rs}=\sum_s \omega^{rs}P_{d,s}(t)</math>
Thus,
:<math>\omega_r = \frac{1}{\hat{P}_{d,0}(-r)} \sum_s \omega^{rs} P_{d,s},</math>
the promised sum-of-APs representation of <math>\omega_r</math>, and consequently the promised representation of <math>I</math> as a sum of <math>P_{d,s_1} P_{d,s_2}^T</math>. All that remains is to analyze the coefficients of the representation of <math>I</math>.

* As <math>\hat{P}_{d,0}(-r)=\sum_s P_{d,0}\omega^{-rs}</math>, and <math>P_{d,0}</math> is symmetric about 0, we see that <math>\hat{P}_{d,0}(-r)=\hat{P}_{d,0}(r)</math> is real. Moreover, as it is a geometric series, it is routine to find
:<math>\alpha_r:=\hat{P}_{d,0}(-r)=\frac{\sin\left((2m+1)\pi rd/n\right)}{\sin\left(\pi rd/n\right)}</math>
We will want <math>\alpha_r</math> to be bounded away from 0. To that end for each <math>r</math>, fix now and forever <math>d</math> in <math>[1,\sqrt{n}]</math> with <math>\|rd/n\|\leq n^{-1/2}</math>, where <math>\|\cdot\|</math> means the distance to the nearest integer. This is a classic result of diophantine approximation (Dirichlet's theorem), whose proof is just the pigeonhole principle. Setting <math> \scriptstyle m=\frac15 \sqrt n</math>, we find
:<math>\alpha_r = \frac{\sin\left((2m+1)\pi rd/n\right)}{\sin\left(\pi rd/n\right)} \geq \frac{2\cdot\left((2m+1)rd/n\right)}{\pi rd/n}>m,</math>
and more obviously <math> \scriptstyle \alpha_r\leq 2m+1</math>. In short <math> \scriptstyle \alpha_r</math> has order <math> \scriptstyle \sqrt{n}</math>, to within a constant factor.

*:<math> I = n^{-1} \sum_r \omega_r \overline{\omega_r}^T = n^{-1} \sum_r \alpha_r^{-2}\left(\sum_x \omega^{rx}P_{d,x}\right)\left(\sum_y \omega^{-ry}P_{d,y}^T\right) = \sum_{r,x,y} n^{-1} \alpha_r^{-2} \omega^{r(x-y)} P_{d,x}P_{d,y}^T </math>
It is tempting to try and be done the easy way, but <math> \sum_{r,x,y} \left|n^{-1} \alpha_r^{-2} \omega^{r(x-y)} \right|</math>
is easily recognized as a sum with <math>n^3</math> summands, each of which has size <math>\approx n^{-2}</math>, so that the total is not <math>o(n)</math>. In short, we need to find some cancelation.

* Set <math>R(\Delta)=\{r \colon d=\Delta\}</math>. By a pigeonhole argument, <math> \scriptstyle |R(\Delta)|\leq 2\sqrt{n}</math>. The coefficient of <math>P_{\Delta,x}P_{\Delta,y}^T</math> is <math>\sum_{r\in R(\Delta)} n^{-1}\alpha_r^{-2} \omega^{r(x-y)}.</math>
We need to bound
:<math> \sum_{\Delta=1}^{\sqrt{n}} \sum_{x,y} \left| \sum_{r\in R(\Delta)} n^{-1}\alpha_r^{-2} \omega^{r(x-y)} \right|.</math>

*:<math>
\sum_{x,y} \left| \sum_{r\in R(\Delta)} n^{-1}\alpha_r^{-2} \omega^{r(x-y)} \right|
\leq \left(\sum_{x,y} 1^2 \right)^{1/2} \left( \sum_{x,y} \left| \sum_{r\in R(\Delta)} n^{-1}\alpha_r^{-2} \omega^{r(x-y)} \right|^2\right)^{1/2}</math>
:<math>= n \,\cdot\,\left(\sum_{x,y} \sum_{r_1,r_2} n^{-2} \alpha_{r_1}^{-2} \alpha_{r_2}^{-2} \omega^{(r_1-r_2)(x-y)}\right)^{1/2} = n\,\cdot\, \left( \sum_{r} n^{-2}\alpha_r^{-4} n^2\right)^{1/2}</math>
where the last equality is by noting that <math>\sum_{x,y}\omega^{(r_1-r_2)(x-y)}</math> is either <math>n^2</math> (if <math> \scriptstyle r_1-r_2=0</math>) or 0 (if <math>r_1-r_2\not=0</math>). Since <math>\alpha_r</math> is between <math>m</math> and <math>2m+1</math> (recall <math> \scriptstyle m=\frac15 \sqrt n</math>), we have <math>\alpha_r^{-4} \leq m^{-4} = \frac{5^4}{n^2}</math>. Thus,
:<math> n\,\cdot\, \left( \sum_{r} n^{-2}\alpha_r^{-4} n^2\right)^{1/2} \leq 25 |R(\Delta)|^{1/2}\leq 25\sqrt{2} n^{1/4},</math>
and so
:<math> \sum_{\Delta=1}^{\sqrt{n}} \sum_{x,y} \left| \sum_{r\in R(\Delta)} n^{-1}\alpha_r^{-2} \omega^{r(x-y)} \right|\leq 25\sqrt{2} n^{3/4}.</math>

* Returning to step 2, we have <math>\delta^2 \geq \frac{1}{25\sqrt{2}} n^{1/4}</math>, whence <math>\delta > \frac 17 n^{1/8}</math>.

Find a good configuration of HAPs

2010-02-07T15:45:14Z

Gowers:

[[The Erdős discrepancy problem|Click here to return to the main Polymath5 page]].

==Introduction==

One of the difficulties of thinking about the Erdős discrepancy problem is that one can get hung up on HAPs with small common differences, when ultimately what should matter is the more typical HAPs, which have large common differences. This is less of a problem when one is looking at multiplicative sequences, since then all one cares about is partial sums. However, the strategy to be described on this page concerns a direct attack on the general problem.

The rough idea is this. Recall that a hypergraph is a collection of subsets of some set X. We borrow graph terminology and call the elements of X verticesand the sets in H edges (or sometimes hyperedges if we want to make it clear that our graph is hyper). If H is a hypergraph with vertex set X and f is a function from X to {-1,1}, then the discrepancy of f is the maximum of <math>|\sum_{x\in A}f(x)|</math> over all edges A of H. The discrepancy of H is the minimum discrepancy of any function <math>f:X\to\{-1,1\}</math>.

The Erdős discrepancy problem is asking us to prove that the discrepancy of the hypergraph whose vertex set is <math>\mathbb{N}</math> and whose edges are all finite HAPs is infinite. One obvious strategy for doing this is to identify within this hypergraph a collection of hypergraphs <math>H_n</math> that have properties that allow us to prove arbitrarily good lower bounds for the discrepancy. What makes this a strategy, rather than a trivial reformulation of the problem (after all, one might suggest that there is no point in taking all HAPs) is that one would be aiming to find subhypergraphs of the HAP hypergraph that lent themselves particularly well to certain kinds of combinatorial arguments.

This point will be much clearer if we discuss an actual example of a subhypergraph that might do the trick. (I shall follow the usual practice, when talking informally about asymptotic arguments, of talking about "a subhypergraph" when strictly speaking what I mean is a sequence of larger and larger subhypergraphs. I shall picture a single subhypergraph that is very large.

==A collection of HAPs that might be useful==

Let us pick three very large integers L, M and N, with N much larger than M and M much larger than L. Let us then take the set of all HAPs of length L that live inside the interval [N,N+M] and have common difference d such that dL is at most o(M). (This o(M) is shorthand for some convenient function we choose later.) I should make clear that what I am calling a HAP here is an arithmetic progression of the form (x,x+d,...,x+(L-1)d) such that d is a factor of x (so that if you continued the progression backwards it would include zero).

One might hope that if L, M and N are sufficiently large, then a general principle along the following lines should hold: almost all numbers behave like average numbers. An example of where this principle does hold is in the number of prime factors. If n is a random number close to N, then not only does n have, on average, roughly log log N prime factors, but the Erdős-Kac theorem tells us that the number of prime factors is approximately normally distributed with mean log log N and standard deviation <math>\sqrt{\log \log N}</math>. Unfortunately, this suggests that the number of factors (as opposed to prime factors) is not concentrated. This could be a problem.

==A toy model of what is going on==

Let f be a function from [N,N+M] to {-1,1}. We would like to obtain a lower bound for the sum

<math>\sum_{x=N}^{N+M}\sum_{d|x}|f(x)+f(x+d)+\dots+f(x+(L-1)d)|^2.</math>

Here, the second sum should be taken to be over all d such that x+Ld also lives in the interval [N,N+M].

Now let us take the attitude that for each d the probability that d is a factor of x is <math>d^{-1}</math>. (That is because we are imagining that x mod d is uniformly distributed.) According to this very simple model (which ignores all sorts of dependences), we ought to be able to get a good iea of the above sum if we replace it by the sum

<math>\sum_{x=N}^{N+M}\sum_dd^{-1}|f(x)+f(x+d)+\dots+f(x+(L-1)d)|^2.</math>

Expanding out the square and interchanging the order of summation, we get

<math>\sum_{1\leq i,j\leq L}\sum_{x=N}^{N+M}\sum_d d^{-1}f(x+id)f(x+jd).</math>

The i=j contribution to this quantity is <math>L\sum_{x=N}^{N+M}\sum_dd^{-1}.</math> For a typical x, we sum over d in an interval [-A,B] with both A and B at least <math>M^{1-\epsilon},</math> so this sum works out at about <math>LM\log M.</math>

If <math>i\ne j,</math> then the pair <math>(x+id,x+jd)</math> can be made to equal some pair <math>(u,v)</math> (by an appropriate choice of x and d) only if j-i is a factor of v-u, and that's sort of an if as well, give or take a few edge effects. The probability of this is <math>|j-i|^{-1}.</math> Also, <math>d=(j-i)^{-1}(v-u),</math> so we can rewrite the inner sum in this case as <math>\sum_{u,v}|v-u|^{-1}f(u)f(v).</math> (This is not supposed to be a rigorous argument.)

What I now hope is that if the partial sums of f remain bounded, then a sum like <math>\sum_{u,v}|v-u|^{-1}f(u)f(v)</math> has to be small, so that in total we find that

<math>\sum_{x=N}^{N+M}\sum_dd^{-1}|f(x)+f(x+d)+\dots+f(x+(L-1)d)|^2\geq LM\log M/2,</math>

from which we can conclude that there exist x and d such that <math>|f(x)+f(x+d)+\dots+f(x+(L-1)d)|^2\geq L,</math> giving us the unboundedness we were looking for.

For this to work we would need to show that it really is the case that the off-diagonal contribution to the sum is small, and, probably more challengingly (unless the first step is plain wrong), that the probabilistic assumptions we made can be justified. A justification would consist in showing that the actual weights (which are 1 if d divides x and 0 otherwise) are sufficiently quasirandom that they approximate, in an appropriate sense, the idealized weights (which are <math>d^{-1}</math>). And we would need to justify the second probabilistic approximation as well.

==Why the above proof idea does not work==

As with many approaches to the Erdős discrepancy problem, this one runs into problems when one looks at what it would say about character-like functions. One of the remarkable features of functions such as <math>\lambda_3</math> (the completely multiplicative function that takes 3 to 1 and m to 1 if m is congruent to 1 mod 3 and -1 if m is congruent to 2 mod 3) is that they have very small drift: for any m<n one has the inequality <math>|\sum_{x=m+1}^n\lambda_3(x)|\leq\log_3(n-m)+1.</math> This implies that they have very small drift along any segment of a homogeneous arithmetic progression (since <math>\lambda_3</math> is completely multiplicative). But the argument above, if it worked, would be giving segments of HAPs of length L along which the drift was <math>\sqrt{L}.</math>

So what, one might ask, is wrong with the probabilistic model? To give a complete answer to this it is necessary to say a bit more about quasirandomness. If G is a graph with vertex set X, then one of the properties we most like it to have, if we want it to imitate a random graph of about the same density, is that if A and B are large subsets of X, then the number of edges of G that go from a point in A to a point in B is roughly the same as it would be for the random graph. More generally, we would say that two graphs G and H are "close" if the number of edges from any large set to any other is roughly the same for G as it is for H. And we can use a very similar definition for weighted graphs, where we replace "number of edges" by "sum of the weights of the edges". We had a graph derived from HAPs and were hoping that it would imitate the weighted graph where the edge from x to y has weight <math>|x-y|^{-1}.</math> (That was not made explicit, but it is pretty much what we were doing.)

Now these two graphs do not in fact imitate each other. For example, a notable and highly relevant difference between the two is that if A is any residue class modulo some prime p and is not the set of multiples of p, then A is an independent set in the HAP graph. (Just to be clear, I join x to y in the HAP graph if y-x divides x and y, which is the same as saying that x and y are consecutive elements of some HAP.) By contrast, in the weighted graph, all residue classes mod p look the same.

==What one might be able to salvage from the wreckage==

What we have here is a certain class of sets -- residue classes modulo small primes -- that do not have approximately the number of edges inside them that would be predicted by the naive probabilistic model above. However, these examples have a very particular structure, so they should spoil the proof only for a very special class of functions. The functions that cause the difficulty are likely to be ones that have significant correlation with residue classes, something that is tailor made to be detected by Fourier analysis.

This strongly suggests that we might be able to prove a result that applies to all functions f that satisfy some Fourier condition. The condition should tell us that f does not correlate with residue classes modulo small primes, so it should tell us something like that <math>\hat{f}(\alpha)</math> is small whenever α is close to a rational with small denominator. Intuitively, these are the functions that "can tell the difference between HAPs and ordinary APs".

So it looks as though there is something to do. I don't know exactly what it is, but I think it should be something like looking at the HAP matrix minus the weight matrix and showing that all its eigenvectors with large eigenvalues are functions with Fourier transforms that are large near some rational with small denominator. With a lemma like that, one might be able to do something.

Find a good configuration of HAPs

2010-02-07T10:15:35Z

Gowers:

Find a good configuration of HAPs

2010-02-07T10:14:02Z

Gowers: /* A collection of HAPs that might be useful */

Find a good configuration of HAPs

2010-02-06T23:42:49Z

Gowers:

Find a good configuration of HAPs

2010-02-06T19:56:27Z

Gowers:

Find a good configuration of HAPs

2010-02-06T19:15:25Z

Gowers: /* A collection of HAPs that might be useful */

Find a good configuration of HAPs

2010-02-06T18:35:42Z

Gowers:

Find a good configuration of HAPs

2010-02-06T18:28:21Z

Gowers:

Click here to return to [[The Erdős discrepancy problem|the main Polymath5 page]].

One of the difficulties of thinking about the Erdős discrepancy problem is that one can get hung up on HAPs with small common differences, when ultimately what should matter is the more typical HAPs, which have large common differences. This is less of a problem when one is looking at multiplicative sequences, since then all one cares about is partial sums. However, the strategy to be described on this page concerns a direct attack on the general problem.

The rough idea is this. Recall that a hypergraph is a collection of subsets of some set X. We borrow graph terminology and call the elements of X verticesand the sets in H edges (or sometimes hyperedges if we want to make it clear that our graph is hyper). If H is a hypergraph with vertex set X and f is a function from X to {-1,1}, then the discrepancy of f is the maximum of <math>|\sum_{x\in A}f(x)|</math> over all edges A of H. The discrepancy of H is the minimum discrepancy of any function <math>f:X\to\{-1,1\}</math>.

The Erdős discrepancy problem is asking us to prove that the discrepancy of the hypergraph whose vertex set is <math>\mathbb{N}</math> and whose edges are all finite HAPs is infinite. One obvious strategy for doing this is to identify within this hypergraph a collection of hypergraphs <math>H_n</math> that have properties that allow us to prove arbitrarily good lower bounds for the discrepancy. What makes this a strategy, rather than a trivial reformulation of the problem (after all, one might suggest that there is no point in taking all HAPs) is that one would be aiming to find subhypergraphs of the HAP hypergraph that lent themselves particularly well to certain kinds of combinatorial arguments.

This point will be much clearer if we discuss an actual example of a subhypergraph that might do the trick. (I shall follow the usual practice, when talking informally about asymptotic arguments, of talking about "a subhypergraph" when strictly speaking what I mean is a sequence of larger and larger subhypergraphs. I shall picture a single subhypergraph that is very large.

Find a good configuration of HAPs

2010-02-06T18:27:56Z

Gowers: Started article

Click here to return to [The Erdős discrepancy problem|the main Polymath5 page].

One of the difficulties of thinking about the Erdős discrepancy problem is that one can get hung up on HAPs with small common differences, when ultimately what should matter is the more typical HAPs, which have large common differences. This is less of a problem when one is looking at multiplicative sequences, since then all one cares about is partial sums. However, the strategy to be described on this page concerns a direct attack on the general problem.

The rough idea is this. Recall that a hypergraph is a collection of subsets of some set X. We borrow graph terminology and call the elements of X verticesand the sets in H edges (or sometimes hyperedges if we want to make it clear that our graph is hyper). If H is a hypergraph with vertex set X and f is a function from X to {-1,1}, then the discrepancy of f is the maximum of <math>|\sum_{x\in A}f(x)|</math> over all edges A of H. The discrepancy of H is the minimum discrepancy of any function <math>f:X\to\{-1,1\}</math>.

The Erdős discrepancy problem is asking us to prove that the discrepancy of the hypergraph whose vertex set is <math>\mathbb{N}</math> and whose edges are all finite HAPs is infinite. One obvious strategy for doing this is to identify within this hypergraph a collection of hypergraphs <math>H_n</math> that have properties that allow us to prove arbitrarily good lower bounds for the discrepancy. What makes this a strategy, rather than a trivial reformulation of the problem (after all, one might suggest that there is no point in taking all HAPs) is that one would be aiming to find subhypergraphs of the HAP hypergraph that lent themselves particularly well to certain kinds of combinatorial arguments.

This point will be much clearer if we discuss an actual example of a subhypergraph that might do the trick. (I shall follow the usual practice, when talking informally about asymptotic arguments, of talking about "a subhypergraph" when strictly speaking what I mean is a sequence of larger and larger subhypergraphs. I shall picture a single subhypergraph that is very large.

The Erdős discrepancy problem

2010-02-06T18:13:53Z

Gowers: /* General proof strategies */ Created link to forthcoming page

If you want to you can [http://michaelnielsen.org/polymath1/index.php?title=Experimental_results jump straight to the main experimental results page].

==Introduction and statement of problem==

Let <math>(x_n)</math> be a <math>\scriptstyle \pm 1</math> sequence and let <math>C</math> be a constant. Must there exist positive integers <math> d,k </math> such that

:<math> \left| \sum_{i=1}^k x_{id} \right| > C </math>?

Known colloquially as "The Erdős discrepancy problem", this question has remained unanswered since the 1930s (Erdős, 1957) and Erdős offered $500 for an answer. It was also asked by Chudakov (1956). It is extremely easy to state, and a very appealing problem, so perhaps Polymath can succeed where individual mathematicians have failed. If so, then, given the notoriety of the problem, it would be a significant coup for the multiply collaborative approach to mathematics. But even if a full solution is not reached, preliminary investigations have already thrown up some interesting ideas which could perhaps be developed into publishable results.

It seems likely that the answer to Erdős's question is yes. If it is, then an easy compactness argument tells us that for every <math>C</math> there exists <math>n</math> such that for every <math>\scriptstyle \pm 1</math> sequence of length <math>n</math> there exist <math>d,k</math> with <math>dk\leq n</math> such that <math> \left| \sum_{i=1}^k x_{id} \right| > C </math>. In view of this, we make some definitions that allow one to talk about the dependence between <math>C</math> and <math>n</math>. For any finite set <math>A</math> of integers, we define the error on <math>A</math> by
:<math> E(A) := \sum_{a\in A} x_a </math>,
and for a set <math>\mathcal{A}</math> of finite sets of integers, we define the discrepancy
:<math> \delta(\mathcal{A},x) := \sup_{A\in \mathcal{A}} |E(A)|. </math>
We can think of the values taken by the sequence <math>(x_n)</math> as a red/blue colouring of the integers that tries to make the number of reds and blues in each <math>\scriptstyle A\in\mathcal{A}</math> as equal as possible. The discrepancy measures the extent to which the sequence fails in this attempt. Taking <math>\scriptstyle \mathcal{HAP}(N)</math> to be the set of homogeneous arithmetic progressions <math>\{d, 2d, 3d, ..., nd\}</math> contained in <math>\{1, 2, ..., N\}</math>, we can restate the question as whether <math>\scriptstyle \delta(\mathcal{HAP}(N),x) \to \infty</math> for every sequence <math>x</math>.

Two related questions have already been solved in the literature. Letting <math>\scriptstyle \mathcal{AP}(N) </math> be the collection of all (not necessarily homogeneous) arithmetic progressions in <math>\{1, 2, ..., N\}</math>, Roth (1964) proved that <math> \scriptstyle \delta(\mathcal{AP}(N),x) \geq c n^{1/4}</math>, independent of the sequence <math>x</math>. Letting <math> \scriptstyle \mathcal{HQAP}(N) </math> be the collection of all homogeneous quasi-arithmetic progressions <math>\scriptstyle\{\lfloor \alpha \rfloor,\lfloor 2\alpha \rfloor,\dots,\lfloor k\alpha \rfloor\}</math> contained in <math>\{1, 2, ..., N\}</math>, Vijay (2008) proved that <math>\scriptstyle \delta(\mathcal{HQAP}(N),x) \geq 0.02 n^{1/6}</math>, independent of the sequence <math>x</math>.

==Some definitions and notational conventions==

A homogeneous arithmetic progression, or HAP, is an arithmetic progression of the form <math> \{d,2d,3d,...,nd\}</math>.

When <math> x</math> is clear from context, we write <math> \delta(N) </math> in place of <math> \delta(\mathcal{HAP}(N),x) </math>.

The discrepancy of a sequence <math>(x_n)</math> is the supremum of <math>|\sum_{n\in P}x_n|</math> over all homogeneous arithmetic progressions P. (Strictly speaking, we should call this something like the HAP-discrepancy, but since we will almost always be talking about HAPs, we adopt the convention that "discrepancy" always means "HAP-discrepancy" unless it is stated otherwise.)
<math>Insert formula here</math>
A sequence <math>(x_n)</math> has discrepancy at most φ(n) if for every natural number N the maximum value of <math>|\sum_{n\in P}x_n|</math> over all homogeneous arithmetic progressions P that are subsets of {1,2,...,N} is at most φ(N).

The EDP is the Erdős discrepancy problem. (This may conceivably be changed if enough people don't like it.)

A sequence <math>(x_n)</math> is completely multiplicative if <math>x_{mn}=x_mx_n</math> for any two positive integers m and n. We shall sometimes abbreviate this to "multiplicative", but the reader should be aware that the word "multiplicative" normally refers to the more general class of sequences such that <math>x_{mn}=x_mx_n</math> whenever m and n are coprime. A completely multiplicative function is determined by the values it takes at primes. The Liouville function λ is the unique completely multiplicative function that takes the value -1 at every prime: if the prime factorization of n is <math>\prod p_i^{a_i}</math> then λ(n) equals <math>(-1)^{\sum a_i}</math>. Another important multiplicative function is <math>\mu_3</math>, the multiplicative function that’s -1 at 3, 1 at numbers that are 1 mod 3 and -1 at numbers that are 2 mod 3. This function has mean-square partial sums which grow logarithmically, [http://gowers.wordpress.com/2010/01/26/edp3-a-very-brief-report-on-where-we-are/#comment-5585 see this calculation].

A HAP-subsequence of a sequence <math>(x_n)</math> is a subsequence of the form <math>x_d,x_{2d},x_{3d},...</math> for some d. If <math>(x_n)</math> is a multiplicative <math>\pm 1</math> sequence, then every HAP-subsequence is equal to either <math>(x_n)</math> or <math>(-x_n)</math>. We shall call a sequence weakly multiplicative if it has only finitely many distinct HAP-subsequences. Let us also call a <math>\pm 1</math> sequence quasi-multiplicative if it is a composition of a completely multiplicative function from <math>\mathbb{N}</math> to an Abelian group G with a function from G to {-1,1} (This definition is too general. See [http://gowers.wordpress.com/2010/01/09/erds-discrepancy-problem-continued/#comment-4843 this and the next comment]). [http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/#comment-4705 It can be shown] that if <math>(x_n)</math> is a weakly multiplicative sequence, then it has an HAP-subsequence that is quasi-multiplicative.

It is convenient to define the maps <math>T_k</math> for <math>k \geq 1</math> by <math>T_k(x)_n = x_{kn}</math>, where <math>x = (x_1, x_2, ...)</math> is a sequence.

==Simple observations==

*To answer the problem negatively, it is sufficient to find a completely multiplicative sequence (that is, a sequence <math>(x_n)</math> such that <math>x_{mn}=x_mx_n</math> for every m,n) such that its partial sums <math>x_1+\dots+x_n</math> are bounded. First mentioned in the proof of the theorem in [http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/ this] post.

*The function that takes n to 1 if the last non-zero digit of n in its ternary representation is 1 and -1 if the last non-zero digit is 2 is completely multiplicative and the partial sum up to n is easily shown to be at most <math>\log_3n +1</math>. Therefore, the rate at which the worst discrepancy grows, as a function of the length of the homogeneous progression, can be as slow as logarithmic. [[Matryoshka_Sequences|More examples of this sort are here.]] [http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/] <s>[http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/#comment-4553 It turns out] that the base can be made significantly higher than 3, so this example is not best possible.</s> [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/#comment-4757 Correction]

*To answer the problem negatively, it is also sufficient to find a completely multiplicative function f from <math>\mathbb{N}</math> to a finite Abelian group G (meaning that f(mn)=f(m)+f(n) for every m,n) and a function h from G to {-1,1} such that for each g in G there exists d with f(d)=g and with the partial sums hf(d)+hf(2d)+...+hf(nd) bounded. In that case, one can set <math>x_n=hf(n)</math>. (Though this observation is simple with the benefit of hindsight, it might not have been made had it not been for the fact that this sort of structure was identified in a long sequence that had been produced experimentally). First mentioned [http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/#comment-4696 here]. Se also [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/ this post] and [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/#comment-4717 this comment].

*[http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/#comment-4705 It can be shown] that if a <math>\pm 1</math> sequence <math>(x_n)</math> starts with 1 and has only finitely many distinct subsequences of the form <math>(x_d,x_{2d},x_{3d},\dots)</math>, then it must have a subsequence that arises in the above way. (This was mentioned just above in the terminology section.)

*The problem for the positive integers is equivalent to the problem for the positive rationals. [http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/#comment-4676](Sketch proof: if you have a function f from the positive integers to {-1,1} that works, then define <math>f_q(x)</math> to be f(q!x) whenever q!x is an integer. Then take a pointwise limit of a subsequence of the functions <math>f_q</math>. [[Limits with better properties|Click here for a more detailed discussion of this construction and what it is good for]].

*Define the [[drift]] of a sequence to be the maximal value of |f(md)+...+f(nd)|. The discrepancy problem is equivalent to showing that the drift is always infinite. It is obvious that it is at least 2 (because |f(2)+f(4)|, |f(2)+f(3)|, |f(3)+f(4)| cannot all be at most 1); one can show that [[drift|it is at least 3]] (which implies as a corollary that the discrepancy is at least 2). One can also show that the [[upper and lower discrepancy]] are each at least 2.

*One can [[topological dynamics formulation|formulate the problem using topological dynamics]].

*Using Fourier analysis, one can [[Fourier reduction|reduce the problem to one about completely multiplicative functions]].

*Here is an [[algorithm for finding multiplicative sequences with bounded discrepancy]].

*Here is a page whose aim is to record a [[human proof that completely multiplicative sequences have discrepancy at least 2]].

*Here is an argument that shows that [[bounded discrepancy multiplicative functions do not correlate with characters]].

* The answer to a [[function field version]] of the problem seems to be negative.

==Experimental evidence==

''Main page: [[Experimental results]]''

A nice feature of the problem is that it lends itself well to investigation on a computer. Although the number of <math>\pm 1</math> sequences grows exponentially, the constraints on these sequences are such that depth-first searches can lead quite quickly to interesting examples. For instance, at the time of writing they have yielded several examples of sequences of length 1124 with discrepancy 2. (This is the current record.) See [[Experimental results|this page]] for more details and further links.

Another sort of evidence is to bound the discrepancy for specific sequences. For example, setting <math>x_1=-x_2=1</math> and <math> x_n=-x_{n/3}</math> or <math>x_n=x_{n-3}</math> according to whether <math>n</math> is a multiple of 3 or not, yields a sequence with

:<math> \delta(N) \leq \log_9(N)+1 </math>

for sufficiently large <math> N </math>. Currently, this is the record-holder for slow growing discrepancy.

The Thue-Morse sequence has discrepancy <math> \delta(N) \gg N^{\log_4(3)} </math>. (See the discussion following [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/#comment-4775 this comment] and the next one for an easy proof of <math>\gg N^{1/2}</math>, and the paper of Newman for the discrepancy along the 3-HAP.)

A random sequence (each <math> x_i </math> chosen independently) has discrepancy at least (asymptotically) <math> \sqrt{2N \log\log N} </math> by the law of the iterated logarithm.

Determining if the discrepancy of [http://en.wikipedia.org/wiki/Liouville_function Liouville's lambda function] is <math> O(n^{1/2+\epsilon})</math> is equivalent to solving the Riemann hypothesis. However, this growth cannot be bounded above by <math>n^{1/2-\epsilon}</math> for any positive ε.

==Interesting subquestions==

Given the length of time that the Erdős discrepancy problem has been open, the chances that it will be solved by Polymath5 are necessarily small. However, there are a number of interesting questions that we do not know the answers to, several of which have arisen naturally from the experimental evidence. Good answers to some of these would certainly constitute publishable results. Here is a partial list -- further additions are very welcome. (When the more theoretical part of the project starts, this section will probably grow substantially and become a separate page.)

*Is there an infinite sequence of discrepancy 2? (Given how long a finite sequence can be, it seems unlikely that we could answer this question just by a clever search of all possibilities on a computer.)

*The long sequences of low discrepancy discovered by computer all have some kind of approximate weak multiplicativity. If we take a hypothetical counterexample <math>(x_n)</math> (which we could even assume has discrepancy 2), can we prove that it, or some other counterexample derived from it by passing to HAP-subsequences and taking pointwise limits, has some kind of interesting multiplicative structure?

*Closely related to the previous question. If <math>(x_n)</math> is a hypothetical counterexample, must it satisfy a compactness property of the following kind: for every positive c there exists M such that if you take any M HAP-subsequences, then there must be two of them, <math>(y_n)</math> and <math>(z_n)</math>, such that <math>\lim\inf N^{-1}\sum_{n=1}^Ny_nz_n\geq 1-c</math>?

*An even weaker question. If <math>(x_n)</math> is a hypothetical counterexample, must it have two HAP-subsequences <math>(y_n)</math> and <math>(z_n)</math> such that the lim inf of <math>N^{-1}\sum_{n=1}^N y_nz_n</math> is greater than 0?

*A similar question, perhaps equivalent to the previous one (this should be fairly easy to check). Given a sequence <math>(x_n)</math> define f(N) to be the average of <math>x_ax_bx_cx_d</math> over all quadruples (a,b,c,d) such that ab=cd and <math>a,b,c,d\leq N</math>. If <math>(x_n)</math> is a counterexample, does that imply that <math>\lim\inf f(N)</math> is greater than 0? [http://thomas1111.wordpress.com/2010/01/15/average-over-quadruples-of-the-first-1124-sequence/ See here for a computation of this average for the first 1124 sequence].

*Is there any completely multiplicative counterexample? (This may turn out to be a very hard question. If so, then answering the previous questions could turn out to be the best we can hope for without making a substantial breakthrough in analytic number theory.)

*Does there exist a <math>\pm 1</math> sequence such that the corresponding discrepancy function grows at a rate that is slower than <math>c\log n</math> for any positive c?

*Does the number of sequences of length n and discrepancy at most C grow exponentially with n or more slowly than exponentially? (Obviously if the conjecture is true then it must be zero for large enough n, but the hope is that this question is a more realistic initial target.)

==General proof strategies==

This section contains links to other pages in which potential approaches to solving the problem are described.

[[First obtain multiplicative structure and then obtain a contradiction]]

[[Find a different parameter, show that it tends to infinity, and show that that implies that the discrepancy tends to infinity]]

[[Prove the result for shifted HAPs instead of HAPs]]

[[Find a good configuration of HAPs]]

==Annotated Bibliography==

*Blog Discussion on Gowers's Weblog
**[http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/ Zeroth Post] (Dec 17 - Jan 6).
**[http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/ First Post] (Jan 6 - Jan 12).
**[http://gowers.wordpress.com/2010/01/09/erds-discrepancy-problem-continued/ Second Post] (Jan 9 - Jan 11).
**[http://gowers.wordpress.com/2010/01/11/the-erds-discrepancy-problem-iii/ Third Post] (Jan 11 - Jan 14).
**[http://gowers.wordpress.com/2010/01/14/the-erds-discrepancy-problem-iv/ Fourth Post] (Jan 14 - 16).
**[http://gowers.wordpress.com/2010/01/16/the-erds-discrepancy-problem-v/ Fifth Post] (Jan 16-19).
**[http://gowers.wordpress.com/2010/01/19/edp1-the-official-start-of-polymath5/ First Theoretical Post] (Jan 19-21)
**[http://gowers.wordpress.com/2010/01/21/edp2-a-few-lessons-from-edp1/ Second Theoretical Post] (Jan 21-26)
**[http://gowers.wordpress.com/2010/01/26/edp3-a-very-brief-report-on-where-we-are/ Third Theoretical Post] (Jan 26 -?)
**[http://gowers.wordpress.com/2010/01/30/edp4-focusing-on-multiplicative-functions/ Fourth Theoretical Post] (Jan 30- Feb 2)
**[http://gowers.wordpress.com/2010/02/02/edp5-another-very-brief-summary/ Fifth Theoretical Post] (Feb 2 - ?)

*Mathias, A. R. D. [http://www.dpmms.cam.ac.uk/~ardm/erdoschu.pdf On a conjecture of Erdős and Čudakov]. Combinatorics, geometry and probability (Cambridge, 1993).

This one page paper establishes that the maximal length of sequence for the case where C=1 is 11, and is the starting point for our experimental studies.

*Tchudakoff, N. G. Theory of the characters of number semigroups. J. Indian Math. Soc. (N.S.) 20 (1956), 11--15. MR0083515 (18,719e)

The Mathias paper states that one of Erdős's problem lists states that this paper "studies related questions". The Math Review for this paper states that it summarizes results from seven other papers that are in Russian. The Math Review leaves the impression that the topic concerns characters of modulus 1.

*Borwein, Peter, and Choi, Stephen. [http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P204.pdf A variant of Liouville's lambda function: some surprizing formulae].

Explicit formulas for the discrepancy of some completely multiplicative functions whose discrepancy is logarithmic. A typical example is: Let <math>\lambda_3(n) = (-1)^{\omega_3(n)}</math> where <math>\omega_3(n)</math> is the number of distinct prime factors congruent to <math>-1 \bmod 3</math> in <math>n</math> (with multiple factors counted multiply). Then the discrepancy of the <math>\lambda_3</math> sequence up to <math>N</math> is exactly the number of 1's in the base three expansion of <math>N</math>. (This turns out not to be so surprising after all, since <math>\lambda_3(n)</math> is precisely the same as the ternary function defined in the second item of the Simple Observations section.)

*Borwein, Peter, Choi, Stephen and Coons, Michael. [http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P225.pdf Completely multiplicative functions taking values in {-1,1}]. The published version of the above paper, which explains the results and proofs more clearly than the preprint, and is more explicit about the relationship with Erdős's question.

*Granville and Soundararajan. [http://arxiv.org/abs/math/0702389 Multiplicative functions in arithmetic progressions]

In this [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/#comment-4729 blog post] Terry Tao wrote: "Granville and Soundararajan have made some study of the discrepancy of bounded multiplicative functions. The situation is remarkably delicate and number-theoretical (and is closely tied with the Granville-Soundararajan theory of pretentious characters)."

*Wirsing, E. Das asymptotische Verhalten von Summen über multiplikative Funktionen. II. (German) [The asymptotic behavior of sums of multiplicative functions. II.] Acta Math. Acad. Sci. Hungar. 18 1967 411--467. MR0223318 (36 #6366) [http://michaelnielsen.org/polymath1/index.php?title=Wirsing_translation (partial) English translation]

*Newman, D. J. [http://www.jstor.org/stable/2036455 On the number of binary digits in a multiple of three]. Proc Amer Math Soc. 21(1969): 719--721.
Proves that the Thue-Morse sequence has discrepancy <math> \gg N^{\log_4(3)}</math>

*Halász, G. [http://gowers.wordpress.com/2010/02/02/edp5-another-very-brief-summary/#comment-5806 On random multiplicative functions]. Hubert Delange colloquium (Orsay, 1982), 74–96, Publ. Math. Orsay, 83-4, Univ. Paris XI, Orsay, 1983.

The discrepancy of a random multiplicative function is close to $\sqrt{N}$.

=== Problem lists on which this problem appears ===

*Erdős, P. and Graham, R. [http://www.math.ucsd.edu/~fan/ron/papers/79_09_combinatorial_number_theory.pdf Old and New Problems and Results in Combinatorial Number Theory: van der Waerden's Theorem and Related Topics], L'Enseignement Math. 25 (1979), 325-344.

Our problem is mentioned at the bottom of page 331, where they indicate knowledge of a coloring with logarithmic discrepancy. On pages 330-1, they review work on the non-homogeneous problem.

*As [http://www.math.niu.edu/~rusin/known-math/93_back/prizes.erd this web page] reveals, the Erdős discrepancy problem was a $500-dollar problem of Erdős, so it is clear that he regarded it as pretty hard.

*P. Erdős. [http://www.renyi.hu/~p_erdos/1957-13.pdf Some unsolved problems], Michigan Math. J. 4 (1957), 291--300 MR20 #5157; Zentralblatt 81,1.

Problem 9 of this paper is ours. Erdős dates the problem to around 1932, and notes what we know about Liouville's function (lower and upper bound).

*Finch, S. [http://algo.inria.fr/csolve/ec.pdf Two-colorings of positive integers]. Dated May 27, 2008.

Summarizes knowledge of discrepancy of two colorings when the discrepancy is restricted to homogeneous progressions, nonhomogeneous progressions, and homogeneous quasi-progressions. Contains bibliography with 17 entries, including most of those above.

=== non-homogeneous AP, quasi-AP, and other related discrepancy papers ===

*Hochberg, Robert. [http://www.springerlink.com/content/q02424284373qw45/ Large Discrepancy In Homogenous Quasi-Arithmetic Progressions]. Combinatorica, Volume 26 (2006), Number 1.

Roth's method for the <math> n^{1/4}</math> lower bound on nonhomogeneous AP discrepancy is adapted to give a lower bound for homogeneous quasi-AP discrepancy. This result is weaker than the Vijay result, but uses a different method.

*Vijay, Sujith. [http://www.combinatorics.org/Volume_15/PDF/v15i1r104.pdf On the discrepancy of quasi-progressions]. Electronic Journal of Combinatorics, R104 of Volume 15(1), 2008.

A quasi-progression is a sequence of the form <math>\lfloor k \alpha \rfloor </math>, with <math>1\leq k \leq K</math> for some K. The main theorem of interest is: If the integers from 0 to n are 2-coloured, there exists a quasi-progression that has discrepancy at least <math> (1/50)n^{1/6}</math>.

* Doerr, Benjamin; Srivastav, Anand; Wehr, Petra. [http://www.combinatorics.org/Volume_11/Abstracts/v11i1r5.html Discrepancy of Cartesian products of arithmetic progressions]. Electron. J. Combin. 11 (2004), no. 1, Research Paper 5, 16 pp. (electronic).

Abstract: We determine the combinatorial discrepancy of the hypergraph H of cartesian
products of d arithmetic progressions in the <math> [N]^d</math> –lattice.
The study of such higher dimensional arithmetic progressions is motivated by a
multi-dimensional version of van derWaerden’s theorem, namely the Gallai-theorem
(1933). We solve the discrepancy problem for d–dimensional arithmetic progressions
by proving <math>disc(H) = \Theta�(N^{d/4})</math> for every fixed positive integer d. This extends the famous
lower bound of <math> \Omega(N^{1/4})</math> of Roth (1964) and the matching upper bound <math> O(N^{1/4})</math>
of Matouˇsek and Spencer (1996) from d = 1 to arbitrary, fixed d. To establish
the lower bound we use harmonic analysis on locally compact abelian groups. For
the upper bound a product coloring arising from the theorem of Matouˇsek and
Spencer is sufficient. We also regard some special cases, e.g., symmetric arithmetic
progressions and infinite arithmetic progressions.

*Cilleruelo, Javier; Hebbinghaus, Nils [http://www.ams.org/mathscinet-getitem?mr=2547932 Discrepancy in generalized arithmetic progressions]. European J. Combin. 30 (2009), no. 7, 1607--1611. MR 2547932

*Valkó, Benedek. [Discrepancy of arithmetic progressions in higher dimensions]. (English summary)
J. Number Theory 92 (2002), no. 1, 117--130. MR1880588 (2003b:11071)

Abstract:
K. F. Roth (1964, Acta. Arith.9, 257–260) proved that the discrepancy of arithmetic progressions contained in [N] is at least <math> cN^{1/4} </math>, and later it was proved that this result is sharp. We consider the d-dimensional version of this problem. We give a lower estimate for the discrepancy of arithmetic progressions on <math> [N]^d </math> and prove that this result is nearly sharp. We use our results to give an upper estimate for the discrepancy of lines on an N×N lattice, and we also give an estimate for the discrepancy of a related random hypergraph.

*Roth, K. F., Remark concerning integer sequences. Acta Arith. 9 1964 257--260. MR0168545 (29 #5806)

Shows that the discrepancy on APs is at least <math>cN^{1/4}</math>.

Find a different parameter, show that it tends to infinity, and show that that implies that the discrepancy tends to infinity

2010-01-28T08:56:16Z

Gowers: Added section on mean square of partials sums

[[The Erdős discrepancy problem|Click here to return to the main Polymath5 page]]

==Introduction==

This is a strategy that could potentially be applied either to the general problem or to the multiplicative case. The latter would probably be easier so I shall mainly discuss that case.

The thought behind it is that it feels somehow as though the best multiplicative examples "ought" to be [[character-like functions|character-like]], even though in fact they are not. But perhaps one could devise a parameter with the following properties.

1. The parameter is as small as possible for character-like sequences.

2. The parameter is unbounded for character-like sequences.

3. The parameter can be bounded in terms of the discrepancy.

If we have properties 1-3, then we have a proof of EDP for multiplicative sequences, since if there were an infinite multiplicative sequence with bounded discrepancy, it would follow from 3 that the new parameter was bounded, which by 1 would imply that the parameter could be bounded for character-like sequences, contradicting 2.

==A proposal for a parameter==

Let <math>x=(x_n)</math> be a <math>\pm 1</math> sequence of length N, and for each n let <math>y_n=x_1+\dots+x_n</math> be the partial sum up to n (with <math>y_0=0</math>. For any subinterval <math>I\subset\{1,2,\dots,N\}</math> let osc(I) denote the difference between the maximum and minimum of the <math>y_n</math> with <math>n\in I</math>. For each r, define the average r-drift</math> δ(r) of the sequence to be the average of osc(I) over all subintervals of <math>\{1,2,\dots,N\}</math> of length r, and finally let the mean oscillation up to m <math>\Delta(m)</math> be the weighted sum <math>(\log m)^{-1}\sum_{r=1}^mr^{-1}\delta(r)</math>.

==Motivation for this particular parameter==

The motivation for a parameter that involves oscillation can be seen in [http://thomas1111.files.wordpress.com/2010/01/seqvchar3better2c.png this diagram], which shows the graphs of the partial sums of two multiplicative sequences. The first is one of the 500 longest possible multiplicative sequences of discrepancy at most 2. (The sequence itself can be found on the page devoted to [multiplicative sequences].) The second is the sequence obtained by sending 3 to -1 and all other primes p to 1 if they are 1 mod 3 and -1 if they are -1 mod 3.

The discrepancy of the second sequence is 3 rather than 2, so in that respect it is a worse sequence. However, its graph oscillates less on all distance scales except the very largest. This suggests that we might try to find a parameter with properties 1-3 by searching for a parameter that is particularly low for the second sequence and other character-like sequences.

Suppose we agree to take some weighted average of the r-drifts. Why should we take this particular one? The idea is that the graphs of the partial sums of the character-like functions have a self-similarity that means that it makes sense to look at them at several different distance scales, each larger than the previous one by a constant factor. We would like to attach equal weight to these distance scales, which suggests an average such as <math>k^{-1}(\delta(2)+\delta(4)+\dots+\delta(2^k))</math>. The particular average chosen is simply a smoother version that does not give any particular significance to one ratio such as 2.

==How might one prove that this parameter has Property 1?==

It is not hard to show that this parameter is unbounded for character-like sequences, and it can trivially be bounded by the discrepancy, so it will be useful only if we can prove that it has Property 1. At the moment it is not even clear what Property 1 means, since there are many different character-like functions, and the parameter takes different values at them. It also appears to be at least locally minimized at character-like sequences, in the sense that it seems difficult to change a character-like sequence at a small number of primes without increasing the parameter. But how could one use it in proofs? At the time of writing this is far from clear, but the parameter has been introduced only very recently, so perhaps it will become clearer.

==Mean square of partial sums==

Let <math>f</math> be a completely multiplicative function (either to {-1,1} or to <math>\mathbb{T}</math>). We are particularly interested in the quantity <math>\max_N|f(1)+\dots+f(N)|</math>. However, estimating a maximum can be hard, and it is often easier to estimate an <math>L_2</math> average instead. This suggests that we might look at the quantity <math>N^{-1}\sum_{n=1}^N|f(1)+\dots+f(n)|^2</math> instead.

Of course, showing that this quantity is unbounded (as <math>N</math> tends to infinity) is a stronger statement than showing that the largest partial sum is unbounded. However, if this stronger statement is true, then it should be easier to prove. And if we test it against the examples we know of completely multiplicative functions, we find that it does appear to be unbounded.

A much stronger reason for being interested in this quantity, and indeed the reason it came up, is that [[Fourier reduction]] has shown that the Erdős discrepancy problem for general <math>\pm 1</math> functions has a positive answer if the mean square partial sum of a completely multiplicative function to <math>\mathbb{T}</math> is bounded below by a function that tends to infinity.

The Erdős discrepancy problem

2010-01-26T12:00:38Z

Gowers: /* Introduction and statement of problem */

If you want to you can [http://michaelnielsen.org/polymath1/index.php?title=Experimental_results jump straight to the main experimental results page].

==Introduction and statement of problem==

Let <math>(x_n)</math> be a <math>\scriptstyle \pm 1</math> sequence and let <math>C</math> be a constant. Must there exist positive integers <math> d,k </math> such that

:<math> \left| \sum_{i=1}^k x_{id} \right| > C </math>?

Known colloquially as "The Erdős discrepancy problem", this question has remained unanswered since the 1930s (Erdős, 1957) and Erdős offered $500 for an answer. It was also asked by Chudakov (1956). It is extremely easy to state, and a very appealing problem, so perhaps Polymath can succeed where individual mathematicians have failed. If so, then, given the notoriety of the problem, it would be a significant coup for the multiply collaborative approach to mathematics. But even if a full solution is not reached, preliminary investigations have already thrown up some interesting ideas which could perhaps be developed into publishable results.

It seems likely that the answer to Erdős's question is yes. If it is, then an easy compactness argument tells us that for every <math>C</math> there exists <math>n</math> such that for every <math>\scriptstyle \pm 1</math> sequence of length <math>n</math> there exist <math>d,k</math> with <math>dk\leq n</math> such that <math> \left| \sum_{i=1}^k x_{id} \right| > C </math>. In view of this, we make some definitions that allow one to talk about the dependence between <math>C</math> and <math>n</math>. For any finite set <math>A</math> of integers, we define the error on <math>A</math> by
:<math> E(A) := \sum_{a\in A} x_a </math>,
and for a set <math>\mathcal{A}</math> of finite sets of integers, we define the discrepancy
:<math> \delta(\mathcal{A},x) := \sup_{A\in \mathcal{A}} |E(A)|. </math>
We can think of the values taken by the sequence <math>(x_n)</math> as a red/blue colouring of the integers that tries to make the number of reds and blues in each <math>\scriptstyle A\in\mathcal{A}</math> as equal as possible. The discrepancy measures the extent to which the sequence fails in this attempt. Taking <math>\scriptstyle \mathcal{HAP}(N)</math> to be the set of homogeneous arithmetic progressions <math>\{d, 2d, 3d, ..., nd\}</math> contained in <math>\{1, 2, ..., N\}</math>, we can restate the question as whether <math>\scriptstyle \delta(\mathcal{HAP}(N),x) \to \infty</math> for every sequence <math>x</math>.

Two related questions have already been solved in the literature. Letting <math>\scriptstyle \mathcal{AP}(N) </math> be the collection of all (not necessarily homogeneous) arithmetic progressions in <math>\{1, 2, ..., N\}</math>, Roth (1964) proved that <math> \scriptstyle \delta(\mathcal{AP}(N),x) \geq c n^{1/4}</math>, independent of the sequence <math>x</math>. Letting <math> \scriptstyle \mathcal{HQAP}(N) </math> be the collection of all homogeneous quasi-arithmetic progressions <math>\scriptstyle\{\lfloor \alpha \rfloor,\lfloor 2\alpha \rfloor,\dots,\lfloor k\alpha \rfloor\}</math> contained in <math>\{1, 2, ..., N\}</math>, Vijay (2008) proved that <math>\scriptstyle \delta(\mathcal{HQAP}(N),x) \geq 0.02 n^{1/6}</math>, independent of the sequence <math>x</math>.

==Some definitions and notational conventions==

A homogeneous arithmetic progression, or HAP, is an arithmetic progression of the form <math> \{d,2d,3d,...,nd\}</math>.

When <math> x</math> is clear from context, we write <math> \delta(N) </math> in place of <math> \delta(\mathcal{HAP}(N),x) </math>.

The discrepancy of a sequence <math>(x_n)</math> is the supremum of <math>|\sum_{n\in P}x_n|</math> over all homogeneous arithmetic progressions P. (Strictly speaking, we should call this something like the HAP-discrepancy, but since we will almost always be talking about HAPs, we adopt the convention that "discrepancy" always means "HAP-discrepancy" unless it is stated otherwise.)
<math>Insert formula here</math>
A sequence <math>(x_n)</math> has discrepancy at most φ(n) if for every natural number N the maximum value of <math>|\sum_{n\in P}x_n|</math> over all homogeneous arithmetic progressions P that are subsets of {1,2,...,N} is at most φ(N).

The EDP is the Erdős discrepancy problem. (This may conceivably be changed if enough people don't like it.)

A sequence <math>(x_n)</math> is completely multiplicative if <math>x_{mn}=x_mx_n</math> for any two positive integers m and n. We shall sometimes abbreviate this to "multiplicative", but the reader should be aware that the word "multiplicative" normally refers to the more general class of sequences such that <math>x_{mn}=x_mx_n</math> whenever m and n are coprime. A completely multiplicative function is determined by the values it takes at primes. The Liouville function λ is the unique completely multiplicative function that takes the value -1 at every prime: if the prime factorization of n is <math>\prod p_i^{a_i}</math> then λ(n) equals <math>(-1)^{\sum a_i}</math>.

A HAP-subsequence of a sequence <math>(x_n)</math> is a subsequence of the form <math>x_d,x_{2d},x_{3d},...</math> for some d. If <math>(x_n)</math> is a multiplicative <math>\pm 1</math> sequence, then every HAP-subsequence is equal to either <math>(x_n)</math> or <math>(-x_n)</math>. We shall call a sequence weakly multiplicative if it has only finitely many distinct HAP-subsequences. Let us also call a <math>\pm 1</math> sequence quasi-multiplicative if it is a composition of a completely multiplicative function from <math>\mathbb{N}</math> to an Abelian group G with a function from G to {-1,1} (This definition is too general. See [http://gowers.wordpress.com/2010/01/09/erds-discrepancy-problem-continued/#comment-4843 this and the next comment]). [http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/#comment-4705 It can be shown] that if <math>(x_n)</math> is a weakly multiplicative sequence, then it has an HAP-subsequence that is quasi-multiplicative.

It is convenient to define the maps <math>T_k</math> for <math>k \geq 1</math> by <math>T_k(x)_n = x_{kn}</math>, where <math>x = (x_1, x_2, ...)</math> is a sequence.

==Simple observations==

*To answer the problem negatively, it is sufficient to find a completely multiplicative sequence (that is, a sequence <math>(x_n)</math> such that <math>x_{mn}=x_mx_n</math> for every m,n) such that its partial sums <math>x_1+\dots+x_n</math> are bounded. First mentioned in the proof of the theorem in [http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/ this] post.

*The function that takes n to 1 if the last non-zero digit of n in its ternary representation is 1 and -1 if the last non-zero digit is 2 is completely multiplicative and the partial sum up to n is easily shown to be at most <math>\log_3n +1</math>. Therefore, the rate at which the worst discrepancy grows, as a function of the length of the homogeneous progression, can be as slow as logarithmic. [http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/] <s>[http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/#comment-4553 It turns out] that the base can be made significantly higher than 3, so this example is not best possible.</s> [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/#comment-4757 Correction]

*To answer the problem negatively, it is also sufficient to find a completely multiplicative function f from <math>\mathbb{N}</math> to a finite Abelian group G (meaning that f(mn)=f(m)+f(n) for every m,n) and a function h from G to {-1,1} such that for each g in G there exists d with f(d)=g and with the partial sums hf(d)+hf(2d)+...+hf(nd) bounded. In that case, one can set <math>x_n=hf(n)</math>. (Though this observation is simple with the benefit of hindsight, it might not have been made had it not been for the fact that this sort of structure was identified in a long sequence that had been produced experimentally). First mentioned [http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/#comment-4696 here]. Se also [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/ this post] and [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/#comment-4717 this comment].

*[http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/#comment-4705 It can be shown] that if a <math>\pm 1</math> sequence <math>(x_n)</math> starts with 1 and has only finitely many distinct subsequences of the form <math>(x_d,x_{2d},x_{3d},\dots)</math>, then it must have a subsequence that arises in the above way. (This was mentioned just above in the terminology section.)

*The problem for the positive integers is equivalent to the problem for the positive rationals. [http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/#comment-4676](Sketch proof: if you have a function f from the positive integers to {-1,1} that works, then define <math>f_q(x)</math> to be f(q!x) whenever q!x is an integer. Then take a pointwise limit of a subsequence of the functions <math>f_q</math>. [[Limits with better properties|Click here for a more detailed discussion of this construction and what it is good for]].

*Define the [[drift]] of a sequence to be the maximal value of |f(md)+...+f(nd)|. The discrepancy problem is equivalent to showing that the drift is always infinite. It is obvious that it is at least 2 (because |f(2)+f(4)|, |f(2)+f(3)|, |f(3)+f(4)| cannot all be at most 1); one can show that [[drift|it is at least 3]] (which implies as a corollary that the discrepancy is at least 2). One can also show that the [[upper and lower discrepancy]] are each at least 2.

*One can [[topological dynamics formulation|formulate the problem using topological dynamics]].

==Experimental evidence==

A nice feature of the problem is that it lends itself well to investigation on a computer. Although the number of <math>\pm 1</math> sequences grows exponentially, the constraints on these sequences are such that depth-first searches can lead quite quickly to interesting examples. For instance, at the time of writing they have yielded several examples of sequences of length 1124 with discrepancy 2. (This is the current record.) See [[Experimental results|this page]] for more details and further links.

Another sort of evidence is to bound the discrepancy for specific sequences. For example, setting <math>x_1=-x_2=1</math> and <math> x_n=-x_{n/3}</math> or <math>x_n=x_{n-3}</math> according to whether <math>n</math> is a multiple of 3 or not, yields a sequence with

:<math> \delta(N) \leq \log_9(N)+1 </math>

for sufficiently large <math> N </math>. Currently, this is the record-holder for slow growing discrepancy.

The Thue-Morse sequence has discrepancy <math> \delta(N) \gg \sqrt{N} </math>. (See the discussion following [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/#comment-4775 this comment] and the next one.)

A random sequence (each <math> x_i </math> chosen independently) has discrepancy at least (asymptotically) <math> \sqrt{2N \log\log N} </math> by the law of the iterated logarithm.

Determining if the discrepancy of [http://en.wikipedia.org/wiki/Liouville_function Liouville's lambda function] is <math> O(n^{1/2+\epsilon})</math> is equivalent to solving the Riemann hypothesis. However, this growth cannot be bounded above by <math>n^{1/2-\epsilon}</math> for any positive ε.

==Interesting subquestions==

Given the length of time that the Erdős discrepancy problem has been open, the chances that it will be solved by Polymath5 are necessarily small. However, there are a number of interesting questions that we do not know the answers to, several of which have arisen naturally from the experimental evidence. Good answers to some of these would certainly constitute publishable results. Here is a partial list -- further additions are very welcome. (When the more theoretical part of the project starts, this section will probably grow substantially and become a separate page.)

*Is there an infinite sequence of discrepancy 2? (Given how long a finite sequence can be, it seems unlikely that we could answer this question just by a clever search of all possibilities on a computer.)

*The long sequences of low discrepancy discovered by computer all have some kind of approximate weak multiplicativity. If we take a hypothetical counterexample <math>(x_n)</math> (which we could even assume has discrepancy 2), can we prove that it, or some other counterexample derived from it by passing to HAP-subsequences and taking pointwise limits, has some kind of interesting multiplicative structure?

*Closely related to the previous question. If <math>(x_n)</math> is a hypothetical counterexample, must it satisfy a compactness property of the following kind: for every positive c there exists M such that if you take any M HAP-subsequences, then there must be two of them, <math>(y_n)</math> and <math>(z_n)</math>, such that <math>\lim\inf N^{-1}\sum_{n=1}^Ny_nz_n\geq 1-c</math>?

*An even weaker question. If <math>(x_n)</math> is a hypothetical counterexample, must it have two HAP-subsequences <math>(y_n)</math> and <math>(z_n)</math> such that the lim inf of <math>N^{-1}\sum_{n=1}^N y_nz_n</math> is greater than 0?

*A similar question, perhaps equivalent to the previous one (this should be fairly easy to check). Given a sequence <math>(x_n)</math> define f(N) to be the average of <math>x_ax_bx_cx_d</math> over all quadruples (a,b,c,d) such that ab=cd and <math>a,b,c,d\leq N</math>. If <math>(x_n)</math> is a counterexample, does that imply that <math>\lim\inf f(N)</math> is greater than 0? [http://thomas1111.wordpress.com/2010/01/15/average-over-quadruples-of-the-first-1124-sequence/ See here for a computation of this average for the first 1124 sequence].

*Is there any completely multiplicative counterexample? (This may turn out to be a very hard question. If so, then answering the previous questions could turn out to be the best we can hope for without making a substantial breakthrough in analytic number theory.)

*Does there exist a <math>\pm 1</math> sequence such that the corresponding discrepancy function grows at a rate that is slower than <math>c\log n</math> for any positive c?

*Does the number of sequences of length n and discrepancy at most C grow exponentially with n or more slowly than exponentially? (Obviously if the conjecture is true then it must be zero for large enough n, but the hope is that this question is a more realistic initial target.)

==General proof strategies==

This section contains links to other pages in which potential approaches to solving the problem are described.

[[First obtain multiplicative structure and then obtain a contradiction]]

[[Find a different parameter, show that it tends to infinity, and show that that implies that the discrepancy tends to infinity]]

[[Prove the result for shifted HAPs instead of HAPs]]

==Annotated Bibliography==

*Blog Discussion on Gowers's Weblog
**[http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/ Zeroth Post] (Dec 17 - Jan 6).
**[http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/ First Post] (Jan 6 - Jan 12).
**[http://gowers.wordpress.com/2010/01/09/erds-discrepancy-problem-continued/ Second Post] (Jan 9 - Jan 11).
**[http://gowers.wordpress.com/2010/01/11/the-erds-discrepancy-problem-iii/ Third Post] (Jan 11 - Jan 14).
**[http://gowers.wordpress.com/2010/01/14/the-erds-discrepancy-problem-iv/ Fourth Post] (Jan 14 - 16).
**[http://gowers.wordpress.com/2010/01/16/the-erds-discrepancy-problem-v/ Fifth Post] (Jan 16-19).
**[http://gowers.wordpress.com/2010/01/19/edp1-the-official-start-of-polymath5/ First Theoretical Post] (Jan 19-21)
**[http://gowers.wordpress.com/2010/01/21/edp2-a-few-lessons-from-edp1/ Second Theoretical Post] (Jan 21-?)

*Mathias, A. R. D. [http://www.dpmms.cam.ac.uk/~ardm/erdoschu.pdf On a conjecture of Erdős and Čudakov]. Combinatorics, geometry and probability (Cambridge, 1993).

This is a short paper establishing the maximal length of sequence for the case where C=1 is 11, and is the starting point for our experimental studies.

*Tchudakoff, N. G. Theory of the characters of number semigroups. J. Indian Math. Soc. (N.S.) 20 (1956), 11--15. MR0083515 (18,719e)

The Mathias paper states that one of Erdős's problem lists states that this paper "studies related questions". The Math Review for this paper states that it summarizes results from seven other papers that are in Russian. The Math Review leaves the impression that the topic concerns characters of modulus 1.

*Borwein, Peter, and Choi, Stephen. [http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P204.pdf A variant of Liouville's lambda function: some surprizing formulae].

Explicit formulas for the discrepancy of some completely multiplicative functions whose discrepancy is logarithmic. A typical example is: Let <math>\lambda_3(n) = (-1)^{\omega_3(n)}</math> where <math>\omega_3(n)</math> is the number of distinct prime factors congruent to <math>-1 \bmod 3</math> in <math>n</math> (with multiple factors counted multiply). Then the discrepancy of the <math>\lambda_3</math> sequence up to <math>N</math> is exactly the number of 1's in the base three expansion of <math>N</math>. (This turns out not to be so surprising after all, since <math>\lambda_3(n)</math> is precisely the same as the ternary function defined in the second item of the Simple Observations section.)

*Borwein, Peter, Choi, Stephen and Coons, Michael. [http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P225.pdf Completely multiplicative functions taking values in {-1,1}]. The published version of the above paper, which explains the results and proofs more clearly than the preprint, and is more explicit about the relationship with Erdős's question.

*Granville and Soundararajan. [http://arxiv.org/abs/math/0702389 Multiplicative functions in arithmetic progressions]

In this [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/#comment-4729 blog post] Terry Tao wrote: "Granville and Soundararajan have made some study of the discrepancy of bounded multiplicative functions. The situation is remarkably delicate and number-theoretical (and is closely tied with the Granville-Soundararajan theory of pretentious characters)."

=== Problem lists on which this problem appears ===

*Erdős, P. and Graham, R. [http://www.math.ucsd.edu/~fan/ron/papers/79_09_combinatorial_number_theory.pdf Old and New Problems and Results in Combinatorial Number Theory: van der Waerden's Theorem and Related Topics], L'Enseignement Math. 25 (1979), 325-344.

Our problem is mentioned at the bottom of page 331, where they indicate knowledge of a coloring with logarithmic discrepancy. On pages 330-1, they review work on the non-homogeneous problem.

*As [http://www.math.niu.edu/~rusin/known-math/93_back/prizes.erd this web page] reveals, the Erdős discrepancy problem was a $500-dollar problem of Erdős, so it is clear that he regarded it as pretty hard.

*P. Erdős. [http://www.renyi.hu/~p_erdos/1957-13.pdf Some unsolved problems], Michigan Math. J. 4 (1957), 291--300 MR20 #5157; Zentralblatt 81,1.

Problem 9 of this paper is ours. Erdős dates the problem to around 1932, and notes what we know about Liouville's function (lower and upper bound).

*Finch, S. [http://algo.inria.fr/csolve/ec.pdf Two-colorings of positive integers]. Dated May 27, 2008.

Summarizes knowledge of discrepancy of two colorings when the discrepancy is restricted to homogeneous progressions, nonhomogeneous progressions, and homogeneous quasi-progressions. Contains bibliography with 17 entries, including most of those above.

=== non-homogeneous AP, quasi-AP, and other related discrepancy papers ===

*Hochberg, Robert. [http://www.springerlink.com/content/q02424284373qw45/ Large Discrepancy In Homogenous Quasi-Arithmetic Progressions]. Combinatorica, Volume 26 (2006), Number 1.

Roth's method for the <math> n^{1/4}</math> lower bound on nonhomogeneous AP discrepancy is adapted to give a lower bound for homogeneous quasi-AP discrepancy. This result is weaker than the Vijay result, but uses a different method.

*Vijay, Sujith. [http://www.combinatorics.org/Volume_15/PDF/v15i1r104.pdf On the discrepancy of quasi-progressions]. Electronic Journal of Combinatorics, R104 of Volume 15(1), 2008.

A quasi-progression is a sequence of the form <math>\lfloor k \alpha \rfloor </math>, with <math>1\leq k \leq K</math> for some K. The main theorem of interest is: If the integers from 0 to n are 2-coloured, there exists a quasi-progression that has discrepancy at least <math> (1/50)n^{1/6}</math>.

* Doerr, Benjamin; Srivastav, Anand; Wehr, Petra. [http://www.combinatorics.org/Volume_11/Abstracts/v11i1r5.html Discrepancy of Cartesian products of arithmetic progressions]. Electron. J. Combin. 11 (2004), no. 1, Research Paper 5, 16 pp. (electronic).

Abstract: We determine the combinatorial discrepancy of the hypergraph H of cartesian
products of d arithmetic progressions in the <math> [N]^d</math> –lattice.
The study of such higher dimensional arithmetic progressions is motivated by a
multi-dimensional version of van derWaerden’s theorem, namely the Gallai-theorem
(1933). We solve the discrepancy problem for d–dimensional arithmetic progressions
by proving <math>disc(H) = \Theta�(N^{d/4})</math> for every fixed positive integer d. This extends the famous
lower bound of <math> \Omega(N^{1/4})</math> of Roth (1964) and the matching upper bound <math> O(N^{1/4})</math>
of Matouˇsek and Spencer (1996) from d = 1 to arbitrary, fixed d. To establish
the lower bound we use harmonic analysis on locally compact abelian groups. For
the upper bound a product coloring arising from the theorem of Matouˇsek and
Spencer is sufficient. We also regard some special cases, e.g., symmetric arithmetic
progressions and infinite arithmetic progressions.

*Cilleruelo, Javier; Hebbinghaus, Nils [http://www.ams.org/mathscinet-getitem?mr=2547932 Discrepancy in generalized arithmetic progressions]. European J. Combin. 30 (2009), no. 7, 1607--1611. MR 2547932

*Valkó, Benedek. [Discrepancy of arithmetic progressions in higher dimensions]. (English summary)
J. Number Theory 92 (2002), no. 1, 117--130. MR1880588 (2003b:11071)

Abstract:
K. F. Roth (1964, Acta. Arith.9, 257–260) proved that the discrepancy of arithmetic progressions contained in [N] is at least <math> cN^{1/4} </math>, and later it was proved that this result is sharp. We consider the d-dimensional version of this problem. We give a lower estimate for the discrepancy of arithmetic progressions on <math> [N]^d </math> and prove that this result is nearly sharp. We use our results to give an upper estimate for the discrepancy of lines on an N×N lattice, and we also give an estimate for the discrepancy of a related random hypergraph.

*Roth, K. F., Remark concerning integer sequences. Acta Arith. 9 1964 257--260. MR0168545 (29 #5806)

Shows that the discrepancy on APs is at least <math>cN^{1/4}</math>.

The Erdős discrepancy problem

2010-01-26T12:00:24Z

Gowers: /* Introduction and statement of problem */

If you want to you can [http://michaelnielsen.org/polymath1/index.php?title=Experimental_results jump straight to the main experimental results page].

==Introduction and statement of problem==

Let <math>(x_n)</math> be a <math>\scriptstyle \pm 1</math> sequence and let <math>C</math> be a constant. Must there exist positive integers <math> d,k </math> such that

:<math> \left| \sum_{i=1}^k x_{id} \right| > C </math>?

Known colloquially as "The Erdős discrepancy problem", this question has remained unanswered since the 1930s (Erdős, 1957) and Erdős offered $500 for an answer. It was also asked by Chudakov (1956). It is extremely easy to state, and a very appealing problem, so perhaps Polymath can succeed where individual mathematicians have failed. If so, then, given the notoriety of the problem, it would be a significant coup for the multiply collaborative approach to mathematics. But even if a full solution is not reached, preliminary investigations have already thrown up some interesting ideas which could perhaps be developed into publishable results.

It seems likely that the answer to Erdős's question is yes. If it is, then an easy compactness argument tells us that for every <math>C</math> there exists <math>n</math> such that for every <math>\scriptstyle \pm 1</math> sequence of length <math>n</math> there exist <math>d,k</math> with <math>dk\leq n</math> such that <math> \left| \sum_{i=1}^k x_{id} \right| > C </math>. In view of this, we make some definitions that allow one to talk about the dependence between <math>C</math> and <math>n</math>. For any finite set <math>A</math> of integers, we define the error on <math>A</math> by
:<math> E(A) := \sum_{a\in A} x_a </math>,
and for a set <math>\mathcal{A}</math> of finite sets of integers, we define the discrepancy
:<math> \delta(\mathcal{A},x) := \sup_{A\in \mathcal{A}} |E(A)|. </math>
We can think of the values taken by the sequence <math>(x_n)</math> as a red/blue colouring of the integers that tries to make the number of reds and blues in each <math>\scriptstyle A\in\mathcal{A}</math> as equal as possible. The discrepancy measures the extent to which the sequence fails in this attempt. Taking <math>\scriptstyle \mathcal{HAP}(N)</math> to be the set of homogeneous arithmetic progressions <math>\{d, 2d, 3d, ..., nd\}</math> contained in <math>\{1, 2, ..., N\}</math>, we can restate the question as whether <math>\scriptstyle \delta(\mathcal{HAP}(N),x) \to \infty</math> for every sequence <math>x</math>.

Two related questions have already been solved in the literature. Letting <math>\scriptstyle \mathcal{AP}(N) </math> be the collection of all (not necessarily homogeneous) arithmetic progressions in <math>\{1, 2, ..., N\}</math>, Roth (1964) proved that <math> \scriptstyle \delta(\mathcal{AP}(N),x) \geq c n^{1/4}</math>, independent of the sequence <math>x</math>. Letting <math> \scriptstyle \mathcal{HQAP}(N) </math> be the collection of all homogeneous quasi-arithmetic progressions <math>\scriptstyle\{\lfloor \alpha \rfloor,\lfloor 2\alpha \rfloor,\dots,\lfloor k\alpha \rfloor\}</math> contained in <math>\{1, 2, ..., N\}</math>, Vijay (2008) proved that <math>\scriptstyle \delta(\mathcal{HQAP}(N),x) \geq 0.02 n^{1/6}</math>, independent of the sequence <math>x</math>.

==Some definitions and notational conventions==

A homogeneous arithmetic progression, or HAP, is an arithmetic progression of the form <math> \{d,2d,3d,...,nd\}</math>.

When <math> x</math> is clear from context, we write <math> \delta(N) </math> in place of <math> \delta(\mathcal{HAP}(N),x) </math>.

The discrepancy of a sequence <math>(x_n)</math> is the supremum of <math>|\sum_{n\in P}x_n|</math> over all homogeneous arithmetic progressions P. (Strictly speaking, we should call this something like the HAP-discrepancy, but since we will almost always be talking about HAPs, we adopt the convention that "discrepancy" always means "HAP-discrepancy" unless it is stated otherwise.)
<math>Insert formula here</math>
A sequence <math>(x_n)</math> has discrepancy at most φ(n) if for every natural number N the maximum value of <math>|\sum_{n\in P}x_n|</math> over all homogeneous arithmetic progressions P that are subsets of {1,2,...,N} is at most φ(N).

The EDP is the Erdős discrepancy problem. (This may conceivably be changed if enough people don't like it.)

A sequence <math>(x_n)</math> is completely multiplicative if <math>x_{mn}=x_mx_n</math> for any two positive integers m and n. We shall sometimes abbreviate this to "multiplicative", but the reader should be aware that the word "multiplicative" normally refers to the more general class of sequences such that <math>x_{mn}=x_mx_n</math> whenever m and n are coprime. A completely multiplicative function is determined by the values it takes at primes. The Liouville function λ is the unique completely multiplicative function that takes the value -1 at every prime: if the prime factorization of n is <math>\prod p_i^{a_i}</math> then λ(n) equals <math>(-1)^{\sum a_i}</math>.

A HAP-subsequence of a sequence <math>(x_n)</math> is a subsequence of the form <math>x_d,x_{2d},x_{3d},...</math> for some d. If <math>(x_n)</math> is a multiplicative <math>\pm 1</math> sequence, then every HAP-subsequence is equal to either <math>(x_n)</math> or <math>(-x_n)</math>. We shall call a sequence weakly multiplicative if it has only finitely many distinct HAP-subsequences. Let us also call a <math>\pm 1</math> sequence quasi-multiplicative if it is a composition of a completely multiplicative function from <math>\mathbb{N}</math> to an Abelian group G with a function from G to {-1,1} (This definition is too general. See [http://gowers.wordpress.com/2010/01/09/erds-discrepancy-problem-continued/#comment-4843 this and the next comment]). [http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/#comment-4705 It can be shown] that if <math>(x_n)</math> is a weakly multiplicative sequence, then it has an HAP-subsequence that is quasi-multiplicative.

It is convenient to define the maps <math>T_k</math> for <math>k \geq 1</math> by <math>T_k(x)_n = x_{kn}</math>, where <math>x = (x_1, x_2, ...)</math> is a sequence.

==Simple observations==

*To answer the problem negatively, it is sufficient to find a completely multiplicative sequence (that is, a sequence <math>(x_n)</math> such that <math>x_{mn}=x_mx_n</math> for every m,n) such that its partial sums <math>x_1+\dots+x_n</math> are bounded. First mentioned in the proof of the theorem in [http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/ this] post.

*The function that takes n to 1 if the last non-zero digit of n in its ternary representation is 1 and -1 if the last non-zero digit is 2 is completely multiplicative and the partial sum up to n is easily shown to be at most <math>\log_3n +1</math>. Therefore, the rate at which the worst discrepancy grows, as a function of the length of the homogeneous progression, can be as slow as logarithmic. [http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/] <s>[http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/#comment-4553 It turns out] that the base can be made significantly higher than 3, so this example is not best possible.</s> [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/#comment-4757 Correction]

*To answer the problem negatively, it is also sufficient to find a completely multiplicative function f from <math>\mathbb{N}</math> to a finite Abelian group G (meaning that f(mn)=f(m)+f(n) for every m,n) and a function h from G to {-1,1} such that for each g in G there exists d with f(d)=g and with the partial sums hf(d)+hf(2d)+...+hf(nd) bounded. In that case, one can set <math>x_n=hf(n)</math>. (Though this observation is simple with the benefit of hindsight, it might not have been made had it not been for the fact that this sort of structure was identified in a long sequence that had been produced experimentally). First mentioned [http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/#comment-4696 here]. Se also [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/ this post] and [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/#comment-4717 this comment].

*[http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/#comment-4705 It can be shown] that if a <math>\pm 1</math> sequence <math>(x_n)</math> starts with 1 and has only finitely many distinct subsequences of the form <math>(x_d,x_{2d},x_{3d},\dots)</math>, then it must have a subsequence that arises in the above way. (This was mentioned just above in the terminology section.)

*The problem for the positive integers is equivalent to the problem for the positive rationals. [http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/#comment-4676](Sketch proof: if you have a function f from the positive integers to {-1,1} that works, then define <math>f_q(x)</math> to be f(q!x) whenever q!x is an integer. Then take a pointwise limit of a subsequence of the functions <math>f_q</math>. [[Limits with better properties|Click here for a more detailed discussion of this construction and what it is good for]].

*Define the [[drift]] of a sequence to be the maximal value of |f(md)+...+f(nd)|. The discrepancy problem is equivalent to showing that the drift is always infinite. It is obvious that it is at least 2 (because |f(2)+f(4)|, |f(2)+f(3)|, |f(3)+f(4)| cannot all be at most 1); one can show that [[drift|it is at least 3]] (which implies as a corollary that the discrepancy is at least 2). One can also show that the [[upper and lower discrepancy]] are each at least 2.

*One can [[topological dynamics formulation|formulate the problem using topological dynamics]].

==Experimental evidence==

A nice feature of the problem is that it lends itself well to investigation on a computer. Although the number of <math>\pm 1</math> sequences grows exponentially, the constraints on these sequences are such that depth-first searches can lead quite quickly to interesting examples. For instance, at the time of writing they have yielded several examples of sequences of length 1124 with discrepancy 2. (This is the current record.) See [[Experimental results|this page]] for more details and further links.

Another sort of evidence is to bound the discrepancy for specific sequences. For example, setting <math>x_1=-x_2=1</math> and <math> x_n=-x_{n/3}</math> or <math>x_n=x_{n-3}</math> according to whether <math>n</math> is a multiple of 3 or not, yields a sequence with

:<math> \delta(N) \leq \log_9(N)+1 </math>

for sufficiently large <math> N </math>. Currently, this is the record-holder for slow growing discrepancy.

The Thue-Morse sequence has discrepancy <math> \delta(N) \gg \sqrt{N} </math>. (See the discussion following [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/#comment-4775 this comment] and the next one.)

A random sequence (each <math> x_i </math> chosen independently) has discrepancy at least (asymptotically) <math> \sqrt{2N \log\log N} </math> by the law of the iterated logarithm.

Determining if the discrepancy of [http://en.wikipedia.org/wiki/Liouville_function Liouville's lambda function] is <math> O(n^{1/2+\epsilon})</math> is equivalent to solving the Riemann hypothesis. However, this growth cannot be bounded above by <math>n^{1/2-\epsilon}</math> for any positive ε.

==Interesting subquestions==

Given the length of time that the Erdős discrepancy problem has been open, the chances that it will be solved by Polymath5 are necessarily small. However, there are a number of interesting questions that we do not know the answers to, several of which have arisen naturally from the experimental evidence. Good answers to some of these would certainly constitute publishable results. Here is a partial list -- further additions are very welcome. (When the more theoretical part of the project starts, this section will probably grow substantially and become a separate page.)

*Is there an infinite sequence of discrepancy 2? (Given how long a finite sequence can be, it seems unlikely that we could answer this question just by a clever search of all possibilities on a computer.)

*The long sequences of low discrepancy discovered by computer all have some kind of approximate weak multiplicativity. If we take a hypothetical counterexample <math>(x_n)</math> (which we could even assume has discrepancy 2), can we prove that it, or some other counterexample derived from it by passing to HAP-subsequences and taking pointwise limits, has some kind of interesting multiplicative structure?

*Closely related to the previous question. If <math>(x_n)</math> is a hypothetical counterexample, must it satisfy a compactness property of the following kind: for every positive c there exists M such that if you take any M HAP-subsequences, then there must be two of them, <math>(y_n)</math> and <math>(z_n)</math>, such that <math>\lim\inf N^{-1}\sum_{n=1}^Ny_nz_n\geq 1-c</math>?

*An even weaker question. If <math>(x_n)</math> is a hypothetical counterexample, must it have two HAP-subsequences <math>(y_n)</math> and <math>(z_n)</math> such that the lim inf of <math>N^{-1}\sum_{n=1}^N y_nz_n</math> is greater than 0?

*A similar question, perhaps equivalent to the previous one (this should be fairly easy to check). Given a sequence <math>(x_n)</math> define f(N) to be the average of <math>x_ax_bx_cx_d</math> over all quadruples (a,b,c,d) such that ab=cd and <math>a,b,c,d\leq N</math>. If <math>(x_n)</math> is a counterexample, does that imply that <math>\lim\inf f(N)</math> is greater than 0? [http://thomas1111.wordpress.com/2010/01/15/average-over-quadruples-of-the-first-1124-sequence/ See here for a computation of this average for the first 1124 sequence].

*Is there any completely multiplicative counterexample? (This may turn out to be a very hard question. If so, then answering the previous questions could turn out to be the best we can hope for without making a substantial breakthrough in analytic number theory.)

*Does there exist a <math>\pm 1</math> sequence such that the corresponding discrepancy function grows at a rate that is slower than <math>c\log n</math> for any positive c?

*Does the number of sequences of length n and discrepancy at most C grow exponentially with n or more slowly than exponentially? (Obviously if the conjecture is true then it must be zero for large enough n, but the hope is that this question is a more realistic initial target.)

==General proof strategies==

This section contains links to other pages in which potential approaches to solving the problem are described.

[[First obtain multiplicative structure and then obtain a contradiction]]

[[Find a different parameter, show that it tends to infinity, and show that that implies that the discrepancy tends to infinity]]

[[Prove the result for shifted HAPs instead of HAPs]]

==Annotated Bibliography==

*Blog Discussion on Gowers's Weblog
**[http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/ Zeroth Post] (Dec 17 - Jan 6).
**[http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/ First Post] (Jan 6 - Jan 12).
**[http://gowers.wordpress.com/2010/01/09/erds-discrepancy-problem-continued/ Second Post] (Jan 9 - Jan 11).
**[http://gowers.wordpress.com/2010/01/11/the-erds-discrepancy-problem-iii/ Third Post] (Jan 11 - Jan 14).
**[http://gowers.wordpress.com/2010/01/14/the-erds-discrepancy-problem-iv/ Fourth Post] (Jan 14 - 16).
**[http://gowers.wordpress.com/2010/01/16/the-erds-discrepancy-problem-v/ Fifth Post] (Jan 16-19).
**[http://gowers.wordpress.com/2010/01/19/edp1-the-official-start-of-polymath5/ First Theoretical Post] (Jan 19-21)
**[http://gowers.wordpress.com/2010/01/21/edp2-a-few-lessons-from-edp1/ Second Theoretical Post] (Jan 21-?)

*Mathias, A. R. D. [http://www.dpmms.cam.ac.uk/~ardm/erdoschu.pdf On a conjecture of Erdős and Čudakov]. Combinatorics, geometry and probability (Cambridge, 1993).

This is a short paper establishing the maximal length of sequence for the case where C=1 is 11, and is the starting point for our experimental studies.

*Tchudakoff, N. G. Theory of the characters of number semigroups. J. Indian Math. Soc. (N.S.) 20 (1956), 11--15. MR0083515 (18,719e)

The Mathias paper states that one of Erdős's problem lists states that this paper "studies related questions". The Math Review for this paper states that it summarizes results from seven other papers that are in Russian. The Math Review leaves the impression that the topic concerns characters of modulus 1.

*Borwein, Peter, and Choi, Stephen. [http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P204.pdf A variant of Liouville's lambda function: some surprizing formulae].

Explicit formulas for the discrepancy of some completely multiplicative functions whose discrepancy is logarithmic. A typical example is: Let <math>\lambda_3(n) = (-1)^{\omega_3(n)}</math> where <math>\omega_3(n)</math> is the number of distinct prime factors congruent to <math>-1 \bmod 3</math> in <math>n</math> (with multiple factors counted multiply). Then the discrepancy of the <math>\lambda_3</math> sequence up to <math>N</math> is exactly the number of 1's in the base three expansion of <math>N</math>. (This turns out not to be so surprising after all, since <math>\lambda_3(n)</math> is precisely the same as the ternary function defined in the second item of the Simple Observations section.)

*Borwein, Peter, Choi, Stephen and Coons, Michael. [http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P225.pdf Completely multiplicative functions taking values in {-1,1}]. The published version of the above paper, which explains the results and proofs more clearly than the preprint, and is more explicit about the relationship with Erdős's question.

*Granville and Soundararajan. [http://arxiv.org/abs/math/0702389 Multiplicative functions in arithmetic progressions]

In this [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/#comment-4729 blog post] Terry Tao wrote: "Granville and Soundararajan have made some study of the discrepancy of bounded multiplicative functions. The situation is remarkably delicate and number-theoretical (and is closely tied with the Granville-Soundararajan theory of pretentious characters)."

=== Problem lists on which this problem appears ===

*Erdős, P. and Graham, R. [http://www.math.ucsd.edu/~fan/ron/papers/79_09_combinatorial_number_theory.pdf Old and New Problems and Results in Combinatorial Number Theory: van der Waerden's Theorem and Related Topics], L'Enseignement Math. 25 (1979), 325-344.

Our problem is mentioned at the bottom of page 331, where they indicate knowledge of a coloring with logarithmic discrepancy. On pages 330-1, they review work on the non-homogeneous problem.

*As [http://www.math.niu.edu/~rusin/known-math/93_back/prizes.erd this web page] reveals, the Erdős discrepancy problem was a $500-dollar problem of Erdős, so it is clear that he regarded it as pretty hard.

*P. Erdős. [http://www.renyi.hu/~p_erdos/1957-13.pdf Some unsolved problems], Michigan Math. J. 4 (1957), 291--300 MR20 #5157; Zentralblatt 81,1.

Problem 9 of this paper is ours. Erdős dates the problem to around 1932, and notes what we know about Liouville's function (lower and upper bound).

*Finch, S. [http://algo.inria.fr/csolve/ec.pdf Two-colorings of positive integers]. Dated May 27, 2008.

Summarizes knowledge of discrepancy of two colorings when the discrepancy is restricted to homogeneous progressions, nonhomogeneous progressions, and homogeneous quasi-progressions. Contains bibliography with 17 entries, including most of those above.

=== non-homogeneous AP, quasi-AP, and other related discrepancy papers ===

*Hochberg, Robert. [http://www.springerlink.com/content/q02424284373qw45/ Large Discrepancy In Homogenous Quasi-Arithmetic Progressions]. Combinatorica, Volume 26 (2006), Number 1.

Roth's method for the <math> n^{1/4}</math> lower bound on nonhomogeneous AP discrepancy is adapted to give a lower bound for homogeneous quasi-AP discrepancy. This result is weaker than the Vijay result, but uses a different method.

*Vijay, Sujith. [http://www.combinatorics.org/Volume_15/PDF/v15i1r104.pdf On the discrepancy of quasi-progressions]. Electronic Journal of Combinatorics, R104 of Volume 15(1), 2008.

A quasi-progression is a sequence of the form <math>\lfloor k \alpha \rfloor </math>, with <math>1\leq k \leq K</math> for some K. The main theorem of interest is: If the integers from 0 to n are 2-coloured, there exists a quasi-progression that has discrepancy at least <math> (1/50)n^{1/6}</math>.

* Doerr, Benjamin; Srivastav, Anand; Wehr, Petra. [http://www.combinatorics.org/Volume_11/Abstracts/v11i1r5.html Discrepancy of Cartesian products of arithmetic progressions]. Electron. J. Combin. 11 (2004), no. 1, Research Paper 5, 16 pp. (electronic).

Abstract: We determine the combinatorial discrepancy of the hypergraph H of cartesian
products of d arithmetic progressions in the <math> [N]^d</math> –lattice.
The study of such higher dimensional arithmetic progressions is motivated by a
multi-dimensional version of van derWaerden’s theorem, namely the Gallai-theorem
(1933). We solve the discrepancy problem for d–dimensional arithmetic progressions
by proving <math>disc(H) = \Theta�(N^{d/4})</math> for every fixed positive integer d. This extends the famous
lower bound of <math> \Omega(N^{1/4})</math> of Roth (1964) and the matching upper bound <math> O(N^{1/4})</math>
of Matouˇsek and Spencer (1996) from d = 1 to arbitrary, fixed d. To establish
the lower bound we use harmonic analysis on locally compact abelian groups. For
the upper bound a product coloring arising from the theorem of Matouˇsek and
Spencer is sufficient. We also regard some special cases, e.g., symmetric arithmetic
progressions and infinite arithmetic progressions.

*Cilleruelo, Javier; Hebbinghaus, Nils [http://www.ams.org/mathscinet-getitem?mr=2547932 Discrepancy in generalized arithmetic progressions]. European J. Combin. 30 (2009), no. 7, 1607--1611. MR 2547932

*Valkó, Benedek. [Discrepancy of arithmetic progressions in higher dimensions]. (English summary)
J. Number Theory 92 (2002), no. 1, 117--130. MR1880588 (2003b:11071)

Abstract:
K. F. Roth (1964, Acta. Arith.9, 257–260) proved that the discrepancy of arithmetic progressions contained in [N] is at least <math> cN^{1/4} </math>, and later it was proved that this result is sharp. We consider the d-dimensional version of this problem. We give a lower estimate for the discrepancy of arithmetic progressions on <math> [N]^d </math> and prove that this result is nearly sharp. We use our results to give an upper estimate for the discrepancy of lines on an N×N lattice, and we also give an estimate for the discrepancy of a related random hypergraph.

*Roth, K. F., Remark concerning integer sequences. Acta Arith. 9 1964 257--260. MR0168545 (29 #5806)

Shows that the discrepancy on APs is at least <math>cN^{1/4}</math>.

The Erdős discrepancy problem

2010-01-26T11:59:10Z

Gowers: /* Introduction and statement of problem */ Made a few changes. In particular, turned the question round for consistency about what counts as a "positive" answer.

If you want to you can [http://michaelnielsen.org/polymath1/index.php?title=Experimental_results jump straight to the main experimental results page].

==Introduction and statement of problem==

Let <math>(x_n)</math> be a <math>\scriptstyle \pm 1</math> sequence and let <math>C</math> be a constant. Must there exist positive integers <math> d,k </math> such that

:<math> \left| \sum_{i=1}^k x_{id} \right| > C </math>?

Known colloquially as "The Erdős discrepancy problem", this question has remained unanswered since the 1930s (Erdős, 1957) and Erdős offered $500 for an answer. It was also asked by Chudakov (1956). It is extremely easy to state, and a very appealing problem, so perhaps Polymath can succeed where individual mathematicians have failed. If so, then, given the notoriety of the problem, it would be a significant coup for the multiply collaborative approach to mathematics. But even if a full solution is not reached, preliminary investigations have already thrown up some interesting ideas which could perhaps be developed into publishable results.

It seems likely that the answer to Erdős's question is yes. If it is, then an easy compactness argument tells us that for every <math>C</math> there exists <math>n</math> such that for every <math>\scriptstyle \pm 1</math> sequence of length <math>n</math> there exist <math>d,k</math> with <math>dk\leq n</math> such that <math> \left| \sum_{i=1}^k x_{id} \right| > C </math>. In view of this, we make some definitions that allow one to talk about the dependence between <math>C</math> and <math>n</math>. For any finite set <math>A</math> of integers, we define the error on <math>A</math> by
:<math> E(A) := \sum_{a\in A} x_a </math>,
and for a set <math>\mathcal{A}</math> of finite sets of integers, we define the discrepancy
:<math> \delta(\mathcal{A},x) := \sup_{A\in \mathcal{A}} |E(A)|. </math>
We can think of the values taken by the sequence <math>(x_n)</math> as a red/blue colouring of the integers that tries to make the number of reds and blues in each <math>\scriptstyle A\in\mathcal{A}</math> as equal as possible. The discrepancy measures the extent to which the sequence fails in this attempt. Taking <math>\scriptstyle \mathcal{HAP}(N)</math> to be the set of homogeneous arithmetic progressions <math>\{d, 2d, 3d, ..., nd\}</math> contained in <math>\{1, 2, ..., N\}</math>, we can restate the question as whether <math>\scriptstyle \delta(\mathcal{HAP}(N),x) \to \infty</math> for every sequence <math>x</math>.

Two related questions have already been solved in the literature. Letting <math>\scriptstyle \mathcal{AP}(N) </math> be the collection of all (not necessarily homogeneous) arithmetic progressions in <math>\{1, 2, ..., N\}</math>, Roth (1964) proved that <math> \scriptstyle \delta(\mathcal{AP}(N),x) \geq c n^{1/4}</math>, independent of the sequence <math>x</math>. Letting <math> \scriptstyle \mathcal{HQAP}(N) </math> be the collection of all homogeneous quasi-arithmetic progressions <math>\scriptstyle\{\lfloor \alpha \rfloor,\lfloor 2\alpha \rfloor,\dots,\lfloor k\alpha \rfloor\}</math> contained in <math>\{1, 2, ..., N\}</math>, Vijay (2008) proved that <math>\scriptstyle \delta(\mathcal{HQAP}(N),x) \geq 0.02 n^{1/6}</math>, independent of the sequence <math>x</math>.

==Some definitions and notational conventions==

A homogeneous arithmetic progression, or HAP, is an arithmetic progression of the form <math> \{d,2d,3d,...,nd\}</math>.

When <math> x</math> is clear from context, we write <math> \delta(N) </math> in place of <math> \delta(\mathcal{HAP}(N),x) </math>.

The discrepancy of a sequence <math>(x_n)</math> is the supremum of <math>|\sum_{n\in P}x_n|</math> over all homogeneous arithmetic progressions P. (Strictly speaking, we should call this something like the HAP-discrepancy, but since we will almost always be talking about HAPs, we adopt the convention that "discrepancy" always means "HAP-discrepancy" unless it is stated otherwise.)
<math>Insert formula here</math>
A sequence <math>(x_n)</math> has discrepancy at most φ(n) if for every natural number N the maximum value of <math>|\sum_{n\in P}x_n|</math> over all homogeneous arithmetic progressions P that are subsets of {1,2,...,N} is at most φ(N).

The EDP is the Erdős discrepancy problem. (This may conceivably be changed if enough people don't like it.)

A sequence <math>(x_n)</math> is completely multiplicative if <math>x_{mn}=x_mx_n</math> for any two positive integers m and n. We shall sometimes abbreviate this to "multiplicative", but the reader should be aware that the word "multiplicative" normally refers to the more general class of sequences such that <math>x_{mn}=x_mx_n</math> whenever m and n are coprime. A completely multiplicative function is determined by the values it takes at primes. The Liouville function λ is the unique completely multiplicative function that takes the value -1 at every prime: if the prime factorization of n is <math>\prod p_i^{a_i}</math> then λ(n) equals <math>(-1)^{\sum a_i}</math>.

A HAP-subsequence of a sequence <math>(x_n)</math> is a subsequence of the form <math>x_d,x_{2d},x_{3d},...</math> for some d. If <math>(x_n)</math> is a multiplicative <math>\pm 1</math> sequence, then every HAP-subsequence is equal to either <math>(x_n)</math> or <math>(-x_n)</math>. We shall call a sequence weakly multiplicative if it has only finitely many distinct HAP-subsequences. Let us also call a <math>\pm 1</math> sequence quasi-multiplicative if it is a composition of a completely multiplicative function from <math>\mathbb{N}</math> to an Abelian group G with a function from G to {-1,1} (This definition is too general. See [http://gowers.wordpress.com/2010/01/09/erds-discrepancy-problem-continued/#comment-4843 this and the next comment]). [http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/#comment-4705 It can be shown] that if <math>(x_n)</math> is a weakly multiplicative sequence, then it has an HAP-subsequence that is quasi-multiplicative.

It is convenient to define the maps <math>T_k</math> for <math>k \geq 1</math> by <math>T_k(x)_n = x_{kn}</math>, where <math>x = (x_1, x_2, ...)</math> is a sequence.

==Simple observations==

*To answer the problem negatively, it is sufficient to find a completely multiplicative sequence (that is, a sequence <math>(x_n)</math> such that <math>x_{mn}=x_mx_n</math> for every m,n) such that its partial sums <math>x_1+\dots+x_n</math> are bounded. First mentioned in the proof of the theorem in [http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/ this] post.

*The function that takes n to 1 if the last non-zero digit of n in its ternary representation is 1 and -1 if the last non-zero digit is 2 is completely multiplicative and the partial sum up to n is easily shown to be at most <math>\log_3n +1</math>. Therefore, the rate at which the worst discrepancy grows, as a function of the length of the homogeneous progression, can be as slow as logarithmic. [http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/] <s>[http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/#comment-4553 It turns out] that the base can be made significantly higher than 3, so this example is not best possible.</s> [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/#comment-4757 Correction]

*To answer the problem negatively, it is also sufficient to find a completely multiplicative function f from <math>\mathbb{N}</math> to a finite Abelian group G (meaning that f(mn)=f(m)+f(n) for every m,n) and a function h from G to {-1,1} such that for each g in G there exists d with f(d)=g and with the partial sums hf(d)+hf(2d)+...+hf(nd) bounded. In that case, one can set <math>x_n=hf(n)</math>. (Though this observation is simple with the benefit of hindsight, it might not have been made had it not been for the fact that this sort of structure was identified in a long sequence that had been produced experimentally). First mentioned [http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/#comment-4696 here]. Se also [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/ this post] and [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/#comment-4717 this comment].

*[http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/#comment-4705 It can be shown] that if a <math>\pm 1</math> sequence <math>(x_n)</math> starts with 1 and has only finitely many distinct subsequences of the form <math>(x_d,x_{2d},x_{3d},\dots)</math>, then it must have a subsequence that arises in the above way. (This was mentioned just above in the terminology section.)

*The problem for the positive integers is equivalent to the problem for the positive rationals. [http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/#comment-4676](Sketch proof: if you have a function f from the positive integers to {-1,1} that works, then define <math>f_q(x)</math> to be f(q!x) whenever q!x is an integer. Then take a pointwise limit of a subsequence of the functions <math>f_q</math>. [[Limits with better properties|Click here for a more detailed discussion of this construction and what it is good for]].

*Define the [[drift]] of a sequence to be the maximal value of |f(md)+...+f(nd)|. The discrepancy problem is equivalent to showing that the drift is always infinite. It is obvious that it is at least 2 (because |f(2)+f(4)|, |f(2)+f(3)|, |f(3)+f(4)| cannot all be at most 1); one can show that [[drift|it is at least 3]] (which implies as a corollary that the discrepancy is at least 2). One can also show that the [[upper and lower discrepancy]] are each at least 2.

*One can [[topological dynamics formulation|formulate the problem using topological dynamics]].

==Experimental evidence==

A nice feature of the problem is that it lends itself well to investigation on a computer. Although the number of <math>\pm 1</math> sequences grows exponentially, the constraints on these sequences are such that depth-first searches can lead quite quickly to interesting examples. For instance, at the time of writing they have yielded several examples of sequences of length 1124 with discrepancy 2. (This is the current record.) See [[Experimental results|this page]] for more details and further links.

Another sort of evidence is to bound the discrepancy for specific sequences. For example, setting <math>x_1=-x_2=1</math> and <math> x_n=-x_{n/3}</math> or <math>x_n=x_{n-3}</math> according to whether <math>n</math> is a multiple of 3 or not, yields a sequence with

:<math> \delta(N) \leq \log_9(N)+1 </math>

for sufficiently large <math> N </math>. Currently, this is the record-holder for slow growing discrepancy.

The Thue-Morse sequence has discrepancy <math> \delta(N) \gg \sqrt{N} </math>. (See the discussion following [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/#comment-4775 this comment] and the next one.)

A random sequence (each <math> x_i </math> chosen independently) has discrepancy at least (asymptotically) <math> \sqrt{2N \log\log N} </math> by the law of the iterated logarithm.

Determining if the discrepancy of [http://en.wikipedia.org/wiki/Liouville_function Liouville's lambda function] is <math> O(n^{1/2+\epsilon})</math> is equivalent to solving the Riemann hypothesis. However, this growth cannot be bounded above by <math>n^{1/2-\epsilon}</math> for any positive ε.

==Interesting subquestions==

Given the length of time that the Erdős discrepancy problem has been open, the chances that it will be solved by Polymath5 are necessarily small. However, there are a number of interesting questions that we do not know the answers to, several of which have arisen naturally from the experimental evidence. Good answers to some of these would certainly constitute publishable results. Here is a partial list -- further additions are very welcome. (When the more theoretical part of the project starts, this section will probably grow substantially and become a separate page.)

*Is there an infinite sequence of discrepancy 2? (Given how long a finite sequence can be, it seems unlikely that we could answer this question just by a clever search of all possibilities on a computer.)

*The long sequences of low discrepancy discovered by computer all have some kind of approximate weak multiplicativity. If we take a hypothetical counterexample <math>(x_n)</math> (which we could even assume has discrepancy 2), can we prove that it, or some other counterexample derived from it by passing to HAP-subsequences and taking pointwise limits, has some kind of interesting multiplicative structure?

*Closely related to the previous question. If <math>(x_n)</math> is a hypothetical counterexample, must it satisfy a compactness property of the following kind: for every positive c there exists M such that if you take any M HAP-subsequences, then there must be two of them, <math>(y_n)</math> and <math>(z_n)</math>, such that <math>\lim\inf N^{-1}\sum_{n=1}^Ny_nz_n\geq 1-c</math>?

*An even weaker question. If <math>(x_n)</math> is a hypothetical counterexample, must it have two HAP-subsequences <math>(y_n)</math> and <math>(z_n)</math> such that the lim inf of <math>N^{-1}\sum_{n=1}^N y_nz_n</math> is greater than 0?

*A similar question, perhaps equivalent to the previous one (this should be fairly easy to check). Given a sequence <math>(x_n)</math> define f(N) to be the average of <math>x_ax_bx_cx_d</math> over all quadruples (a,b,c,d) such that ab=cd and <math>a,b,c,d\leq N</math>. If <math>(x_n)</math> is a counterexample, does that imply that <math>\lim\inf f(N)</math> is greater than 0? [http://thomas1111.wordpress.com/2010/01/15/average-over-quadruples-of-the-first-1124-sequence/ See here for a computation of this average for the first 1124 sequence].

*Is there any completely multiplicative counterexample? (This may turn out to be a very hard question. If so, then answering the previous questions could turn out to be the best we can hope for without making a substantial breakthrough in analytic number theory.)

*Does there exist a <math>\pm 1</math> sequence such that the corresponding discrepancy function grows at a rate that is slower than <math>c\log n</math> for any positive c?

*Does the number of sequences of length n and discrepancy at most C grow exponentially with n or more slowly than exponentially? (Obviously if the conjecture is true then it must be zero for large enough n, but the hope is that this question is a more realistic initial target.)

==General proof strategies==

This section contains links to other pages in which potential approaches to solving the problem are described.

[[First obtain multiplicative structure and then obtain a contradiction]]

[[Find a different parameter, show that it tends to infinity, and show that that implies that the discrepancy tends to infinity]]

[[Prove the result for shifted HAPs instead of HAPs]]

==Annotated Bibliography==

*Blog Discussion on Gowers's Weblog
**[http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/ Zeroth Post] (Dec 17 - Jan 6).
**[http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/ First Post] (Jan 6 - Jan 12).
**[http://gowers.wordpress.com/2010/01/09/erds-discrepancy-problem-continued/ Second Post] (Jan 9 - Jan 11).
**[http://gowers.wordpress.com/2010/01/11/the-erds-discrepancy-problem-iii/ Third Post] (Jan 11 - Jan 14).
**[http://gowers.wordpress.com/2010/01/14/the-erds-discrepancy-problem-iv/ Fourth Post] (Jan 14 - 16).
**[http://gowers.wordpress.com/2010/01/16/the-erds-discrepancy-problem-v/ Fifth Post] (Jan 16-19).
**[http://gowers.wordpress.com/2010/01/19/edp1-the-official-start-of-polymath5/ First Theoretical Post] (Jan 19-21)
**[http://gowers.wordpress.com/2010/01/21/edp2-a-few-lessons-from-edp1/ Second Theoretical Post] (Jan 21-?)

*Mathias, A. R. D. [http://www.dpmms.cam.ac.uk/~ardm/erdoschu.pdf On a conjecture of Erdős and Čudakov]. Combinatorics, geometry and probability (Cambridge, 1993).

This is a short paper establishing the maximal length of sequence for the case where C=1 is 11, and is the starting point for our experimental studies.

*Tchudakoff, N. G. Theory of the characters of number semigroups. J. Indian Math. Soc. (N.S.) 20 (1956), 11--15. MR0083515 (18,719e)

The Mathias paper states that one of Erdős's problem lists states that this paper "studies related questions". The Math Review for this paper states that it summarizes results from seven other papers that are in Russian. The Math Review leaves the impression that the topic concerns characters of modulus 1.

*Borwein, Peter, and Choi, Stephen. [http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P204.pdf A variant of Liouville's lambda function: some surprizing formulae].

Explicit formulas for the discrepancy of some completely multiplicative functions whose discrepancy is logarithmic. A typical example is: Let <math>\lambda_3(n) = (-1)^{\omega_3(n)}</math> where <math>\omega_3(n)</math> is the number of distinct prime factors congruent to <math>-1 \bmod 3</math> in <math>n</math> (with multiple factors counted multiply). Then the discrepancy of the <math>\lambda_3</math> sequence up to <math>N</math> is exactly the number of 1's in the base three expansion of <math>N</math>. (This turns out not to be so surprising after all, since <math>\lambda_3(n)</math> is precisely the same as the ternary function defined in the second item of the Simple Observations section.)

*Borwein, Peter, Choi, Stephen and Coons, Michael. [http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P225.pdf Completely multiplicative functions taking values in {-1,1}]. The published version of the above paper, which explains the results and proofs more clearly than the preprint, and is more explicit about the relationship with Erdős's question.

*Granville and Soundararajan. [http://arxiv.org/abs/math/0702389 Multiplicative functions in arithmetic progressions]

In this [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/#comment-4729 blog post] Terry Tao wrote: "Granville and Soundararajan have made some study of the discrepancy of bounded multiplicative functions. The situation is remarkably delicate and number-theoretical (and is closely tied with the Granville-Soundararajan theory of pretentious characters)."

=== Problem lists on which this problem appears ===

*Erdős, P. and Graham, R. [http://www.math.ucsd.edu/~fan/ron/papers/79_09_combinatorial_number_theory.pdf Old and New Problems and Results in Combinatorial Number Theory: van der Waerden's Theorem and Related Topics], L'Enseignement Math. 25 (1979), 325-344.

Our problem is mentioned at the bottom of page 331, where they indicate knowledge of a coloring with logarithmic discrepancy. On pages 330-1, they review work on the non-homogeneous problem.

*As [http://www.math.niu.edu/~rusin/known-math/93_back/prizes.erd this web page] reveals, the Erdős discrepancy problem was a $500-dollar problem of Erdős, so it is clear that he regarded it as pretty hard.

*P. Erdős. [http://www.renyi.hu/~p_erdos/1957-13.pdf Some unsolved problems], Michigan Math. J. 4 (1957), 291--300 MR20 #5157; Zentralblatt 81,1.

Problem 9 of this paper is ours. Erdős dates the problem to around 1932, and notes what we know about Liouville's function (lower and upper bound).

*Finch, S. [http://algo.inria.fr/csolve/ec.pdf Two-colorings of positive integers]. Dated May 27, 2008.

Summarizes knowledge of discrepancy of two colorings when the discrepancy is restricted to homogeneous progressions, nonhomogeneous progressions, and homogeneous quasi-progressions. Contains bibliography with 17 entries, including most of those above.

=== non-homogeneous AP, quasi-AP, and other related discrepancy papers ===

*Hochberg, Robert. [http://www.springerlink.com/content/q02424284373qw45/ Large Discrepancy In Homogenous Quasi-Arithmetic Progressions]. Combinatorica, Volume 26 (2006), Number 1.

Roth's method for the <math> n^{1/4}</math> lower bound on nonhomogeneous AP discrepancy is adapted to give a lower bound for homogeneous quasi-AP discrepancy. This result is weaker than the Vijay result, but uses a different method.

*Vijay, Sujith. [http://www.combinatorics.org/Volume_15/PDF/v15i1r104.pdf On the discrepancy of quasi-progressions]. Electronic Journal of Combinatorics, R104 of Volume 15(1), 2008.

A quasi-progression is a sequence of the form <math>\lfloor k \alpha \rfloor </math>, with <math>1\leq k \leq K</math> for some K. The main theorem of interest is: If the integers from 0 to n are 2-coloured, there exists a quasi-progression that has discrepancy at least <math> (1/50)n^{1/6}</math>.

* Doerr, Benjamin; Srivastav, Anand; Wehr, Petra. [http://www.combinatorics.org/Volume_11/Abstracts/v11i1r5.html Discrepancy of Cartesian products of arithmetic progressions]. Electron. J. Combin. 11 (2004), no. 1, Research Paper 5, 16 pp. (electronic).

Abstract: We determine the combinatorial discrepancy of the hypergraph H of cartesian
products of d arithmetic progressions in the <math> [N]^d</math> –lattice.
The study of such higher dimensional arithmetic progressions is motivated by a
multi-dimensional version of van derWaerden’s theorem, namely the Gallai-theorem
(1933). We solve the discrepancy problem for d–dimensional arithmetic progressions
by proving <math>disc(H) = \Theta�(N^{d/4})</math> for every fixed positive integer d. This extends the famous
lower bound of <math> \Omega(N^{1/4})</math> of Roth (1964) and the matching upper bound <math> O(N^{1/4})</math>
of Matouˇsek and Spencer (1996) from d = 1 to arbitrary, fixed d. To establish
the lower bound we use harmonic analysis on locally compact abelian groups. For
the upper bound a product coloring arising from the theorem of Matouˇsek and
Spencer is sufficient. We also regard some special cases, e.g., symmetric arithmetic
progressions and infinite arithmetic progressions.

*Cilleruelo, Javier; Hebbinghaus, Nils [http://www.ams.org/mathscinet-getitem?mr=2547932 Discrepancy in generalized arithmetic progressions]. European J. Combin. 30 (2009), no. 7, 1607--1611. MR 2547932

*Valkó, Benedek. [Discrepancy of arithmetic progressions in higher dimensions]. (English summary)
J. Number Theory 92 (2002), no. 1, 117--130. MR1880588 (2003b:11071)

Abstract:
K. F. Roth (1964, Acta. Arith.9, 257–260) proved that the discrepancy of arithmetic progressions contained in [N] is at least <math> cN^{1/4} </math>, and later it was proved that this result is sharp. We consider the d-dimensional version of this problem. We give a lower estimate for the discrepancy of arithmetic progressions on <math> [N]^d </math> and prove that this result is nearly sharp. We use our results to give an upper estimate for the discrepancy of lines on an N×N lattice, and we also give an estimate for the discrepancy of a related random hypergraph.

*Roth, K. F., Remark concerning integer sequences. Acta Arith. 9 1964 257--260. MR0168545 (29 #5806)

Shows that the discrepancy on APs is at least <math>cN^{1/4}</math>.

Character-like functions

2010-01-24T21:46:46Z

Gowers:

[[The Erdős discrepancy problem|Click here to return to the main Polymath5 page]]

Borwein and Choi define a chararacter-like function to be a function <math>\lambda_p</math> determined by the following properties: it is completely multiplicative, p maps to 1, all other primes map to 1 if they are quadratic residues mod p and -1 otherwise. This function agrees with the Legendre character except at multiples of p (where the Legendre character equals zero).

One can get better bounds in the Erdős discrepancy problem by sending p to -1 instead -- indeed, the best construction we know that works for all n is this modification in the case p=3.

From a theoretical point of view, it may be better to define a generalized character-like function to be any completely multiplicative function with the following properties: there exists p such that the value at any non-multiple n of p is <math>\lambda_p(n)</math>; the sequence <math>(x_{pn})_{n=1}^\infty</math> is a generalized character-like function. In other words, instead of going up by a factor of p every time, one goes up by different primes at each stage.

In general, the larger the primes are, the worse the discrepancy of the sequence will be. (It is not hard to show that the discrepancy of the Legendre character itself is around <math>\sqrt{p}</math>.) Therefore, it may be possible to devise a measure of how character-like a function is that is better when the primes used are smaller. So far we do not have such a measure.