Difference between revisions of "Main Page"
(→Proof strategies) 
m (→Existing polymath projects) 

(291 intermediate revisions by 59 users not shown)  
Line 1:  Line 1:  
−  +  {{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/ismassivelycollaborativemathematicspossible/ 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  +  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 HalesJewett theorem. Initiated Feb 1, 2009; research results have now been published.  
+  * [[Definable Banach SpacesPolymath2]]: 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 q6Minipolymath1]]: Solving Problem 6 of the 2009 International Mathematical Olympiad. Initiated July 20, 2009; five proofs obtained so far.  
+  * [[The polynomial Hirsch conjecturePolymath3]]. The polynomial Hirsch conjecture. Proposed July 17, 2009; launched, September 30, 2010.  
+  * [[finding primesPolymath4]]: A deterministic way to find primes. Proposed July 27, 2009; launched Aug 9, 2009. Research results have now been published.  
+  * [[The Erdős discrepancy problemPolymath5]]: 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 2010Minipolymath2]]: Solving Problem 5 the 2010 International Mathematical Olympiad. Proposed Jun 12, 2010; launched and solved, Jul 8 2010.  
+  * [[Improving the bounds for Roth's theoremPolymath6]]: Improving the bounds for Roth's theorem. Proposed Feb 5, 2011.  
+  * [[imo 2011Minipolymath3]]: Solving a problem from the 2011 International Mathematical Olympiad. Proposed Jun 9, 2011; launched and solved, Jul 19, 2011.  
+  * [[imo 2012Minipolymath4]]: Solving a problem from the 2012 International Mathematical Olympiad. Proposed, Jun 3, 2012; launched, July 12 2012.  
+  * [[The hot spots conjecturePolymath7]]: Establishing the Hot Spots conjecture for acuteangled triangles. Proposed, May 31st, 2012; launched, Jun 8, 2012.  
+  * [[Bounded gaps between primesPolymath8]]: 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=NPPolymath9]]: exploring Borel determinacybased methods for giving complexity bounds. Proposed, Oct 24, 2013; launched, Nov 3, 2013.  
+  * [[The ErdosRado sunflower lemmaPolymath10]]: improving the bounds for the ErdosRado sunflower lemma. Launched, Nov 2, 2015.  
+  * [[Frankl's unionclosed conjecturePolymath11]]: proving Frankl's unionclosed conjecture. Proposed Jan 21, 2016; launched Jan 29, 2016. Concluded, Jan 17, 2017.  
+  * [[Rota's conjecturePolymath12]]: proving Rota's conjecture. Proposed Feb 28, 2017.  
+  * [[Intransitive dicePolymath13]]: Intransitive dice. Proposed Apr 28, 2017.  
+  * [[linear normPolymath14]]: Classifying homogeneous norms on groups. Initiated Dec 16, 2017; solved Dec 21, 2017. Research results have now been published.  
+  * [[De_BruijnNewman constantPolymath15]]: Upper bounding the de BruinNewman constant. Proposed, Jan 24 2018; launched Jan 27 2018.  
+  * [[HadwigerNelson problemPolymath16]]: Simplifying the lower bound proof for the HadwigerNelson problem. Proposed, Apr 10, 2018; launched, Apr 14, 2018.  
−  ==  +  == Polymathlike projects == 
−  *  +  * Scott Aaronson's "philomath project": "[http://scottaaronson.com/blog/?p=453 Sensitivity vs. Block sensitivity]" (see also [http://mathoverflow.net/questions/31482/thesensitivityof2coloringsoftheddimensionalintegerlattice 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 <b>[https://conference.portonvictor.org/wiki/Research_in_the_middle Research in the middle project] at [https://conference.portonvictor.org Virtual scientific conference]</b>. 
−  *  +  * 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/anopendiscussionandpollsaroundrothstheorem/ The cap set problem]. Proposed March 25, 2009 (see also these [http://gilkalai.wordpress.com/2009/05/11/aroundthecapsetproblemb/ two] [http://gilkalai.wordpress.com/2009/05/18/thecapsetproblemandfranklrodltheoremc/ followup] posts).  
+  * [[Boshernitzan’s problem]]. Proposed July 27, 2009.  
+  * [http://gowers.wordpress.com/2009/09/16/possiblefuturepolymathprojects/ Possible future polymath projects]. Discussion opened September 16, 2009.  
+  * [http://rjlipton.wordpress.com/2011/05/12/apossiblepolymathproject/ 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/polymathproposals/ 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 projectshere]].  
−  +  == Discussions about polymath ==  
−  ==  +  * [http://gowers.wordpress.com/2009/01/27/ismassivelycollaborativemathematicspossible/ Is massively collaborative mathematics possible?] Tim Gowers, January 27, 2009. 
+  * [http://lucatrevisan.wordpress.com/2009/02/01/apeopleshistoryofmathematics/ 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/yetanothermath20proposal.html Yet another math 2.0 proposal] Lieven le Bruyn, February 11, 2009.  
+  * [http://gowers.wordpress.com/2009/03/10/polymath1andopencollaborativemathematics/ 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/canpolymathbescaledup/ Can polymath be scaled up?] Tim Gowers, March 24, 2009.  
+  * [http://whatisresearch.wordpress.com/2009/03/24/concludingnotesonthepolymathprojectandachallenge/ Concluding notes on the polymath project  and a challenge] Vilpulniak, March 24, 2009.  
+  * [http://michaelnielsen.org/blog/onscalingupthepolymathproject/ On scaling up the polymath project] Michael Nielsen, March 25, 2009.  
+  * [http://numberwarrior.wordpress.com/2009/03/25/agentleintroductiontothepolymathproject/ 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/imo2009q6minipolymathprojectimpressionsreflectionsanalysis/ IMO 2009 Q6 as minipolymath project: impressions, reflections, analysis] Terence Tao, July 22, 2009.  
+  * [http://polymathprojects.org/2009/07/27/selectingthenextpolymathproject/ Selecting the next polymath project] Terence Tao, July 27, 2009.  
+  * [http://blog.jonudell.net/2009/07/31/polymathequalsuserinnovatio/ 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/collaborativemathematicsetc/ 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/collaborativeresearchoffilters/ Collaborative math research – a real example] Victor Porton, October 24, 2009  
+  * [http://whatisresearch.wordpress.com/2009/10/26/polymathagain/ Polymath again] Vipulniak, October 26, 2009  
+  * [http://www.kennislink.nl/publicaties/wiskundemetzijnallen 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/massivelycollaborativemathematicslessonsfrompolymath1/ Massively Collaborative Mathematics: lessons from polymath1], Hypios, Jan 13 2010  
+  * [http://ths1104.wordpress.com/2010/02/13/openreflexionssurfonddepolymaths/ Open réflexions sur fond de Polymaths] (French), ths1104, Feb 13 2010  
+  * [http://www.javiertordable.com/blog/2010/02/25/collaborativemathematicsfutureofscience Collaborative Mathematics and The Future of Science] Javier Tordable, February 26 2010  
+  * [http://www.scientificamerican.com/article.cfm?id=problemsolvedtictactoeblog Problem Solved, LOL: A Complex TicTacToe Puzzle Falls Thanks to Blog Comments] Davide Castelvecchi, Scientific American, March 17 2010  
+  * [http://www.thebigquestions.com/2010/04/08/bloggingtictactoeandthefutureofmath/ 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/mg21028113.900howtobuildtheglobalmathematicsbrain.html How to build the global mathematics brain], Jacob Aron, New Scientist, 4 May 2011.  
+  * [http://www.newscientist.com/article/mg21028112.900mathematicsbecomesmoresociable.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/willcrowdsourcingrevolutionizescholarship 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/parallellines1.14759?WT.ec_id=NATURE20140227 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/generalpolymathrules/ 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  
−  +  
−  +  
−  +  
−  +  
−  +  
−  +  
−  +  
−  +  
−  +  
−  + 
Latest revision as of 11:10, 27 November 2018
This is the wiki for polymath projects  massively collaborative online mathematical projects. The idea of such projects originated in Tim Gowers' blog post Is massively collaborative mathematics possible?
Many polymath projects will be proposed, planned, and run at 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 HalesJewett theorem. Initiated Feb 1, 2009; research results have now been published.
 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.
 Minipolymath1: Solving Problem 6 of the 2009 International Mathematical Olympiad. Initiated July 20, 2009; five proofs obtained so far.
 Polymath3. The polynomial Hirsch conjecture. Proposed July 17, 2009; launched, September 30, 2010.
 Polymath4: A deterministic way to find primes. Proposed July 27, 2009; launched Aug 9, 2009. Research results have now been published.
 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.
 Minipolymath2: Solving Problem 5 the 2010 International Mathematical Olympiad. Proposed Jun 12, 2010; launched and solved, Jul 8 2010.
 Polymath6: Improving the bounds for Roth's theorem. Proposed Feb 5, 2011.
 Minipolymath3: Solving a problem from the 2011 International Mathematical Olympiad. Proposed Jun 9, 2011; launched and solved, Jul 19, 2011.
 Minipolymath4: Solving a problem from the 2012 International Mathematical Olympiad. Proposed, Jun 3, 2012; launched, July 12 2012.
 Polymath7: Establishing the Hot Spots conjecture for acuteangled triangles. Proposed, May 31st, 2012; launched, Jun 8, 2012.
 Polymath8: Improving the bounds for small gaps between primes. Proposed, June 4, 2013; launched, June 4, 2013. Research results have now been published.
 Polymath9: exploring Borel determinacybased methods for giving complexity bounds. Proposed, Oct 24, 2013; launched, Nov 3, 2013.
 Polymath10: improving the bounds for the ErdosRado sunflower lemma. Launched, Nov 2, 2015.
 Polymath11: proving Frankl's unionclosed conjecture. Proposed Jan 21, 2016; launched Jan 29, 2016. Concluded, Jan 17, 2017.
 Polymath12: proving Rota's conjecture. Proposed Feb 28, 2017.
 Polymath13: Intransitive dice. Proposed Apr 28, 2017.
 Polymath14: Classifying homogeneous norms on groups. Initiated Dec 16, 2017; solved Dec 21, 2017. Research results have now been published.
 Polymath15: Upper bounding the de BruinNewman constant. Proposed, Jan 24 2018; launched Jan 27 2018.
 Polymath16: Simplifying the lower bound proof for the HadwigerNelson problem. Proposed, Apr 10, 2018; launched, Apr 14, 2018.
Polymathlike projects
 Scott Aaronson's "philomath project": "Sensitivity vs. Block sensitivity" (see also this Math Overflow question). Launched Jul 13, 2010.
 A wiki page clearinghouse for the Deolalikar P vs NP paper. Launched Aug 10, 2010.

Math Research Trends Wiki "research in the middle"This project is recommended to be discontinued in favor of Research in the middle project at Virtual scientific conference.  The page for the ABC conjecture contains links and information about Mochizuki's claimed proof of this conjecture.
Proposed polymath projects
 The cap set problem. Proposed March 25, 2009 (see also these two followup posts).
 Boshernitzan’s problem. Proposed July 27, 2009.
 Possible future polymath projects. Discussion opened September 16, 2009.
 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 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 here.
Discussions about polymath
 Is massively collaborative mathematics possible? Tim Gowers, January 27, 2009.
 A people's history of mathematics Luca Trevisan, February 1, 2009.
 The polymath project Michael Nielsen, February 3, 2009.
 Yet another math 2.0 proposal Lieven le Bruyn, February 11, 2009.
 Polymath1 and open collaborative mathematics Tim Gowers, March 10, 2009.
 Polymath Edmund Harriss, March 14, 2009.
 Massive open collaboration in mathematics declared a success Slashdot, March 18, 2009.
 How changing the technology of collaboration can change the nature of collaboration Michael Nielsen, March 18, 2009.
 The polymath project: scope of participation Michael Nielsen, March 20, 2009.
 Can polymath be scaled up? Tim Gowers, March 24, 2009.
 Concluding notes on the polymath project  and a challenge Vilpulniak, March 24, 2009.
 On scaling up the polymath project Michael Nielsen, March 25, 2009.
 A gentle introduction to the polymath project Jason Dyer, March 25, 2009.
 Tim Gowers and the polymaths Ian Douglas (the Telegraph), April 29, 2009
 IMO 2009 Q6 as minipolymath project: impressions, reflections, analysis Terence Tao, July 22, 2009.
 Selecting the next polymath project Terence Tao, July 27, 2009.
 Polymath equals user innovation Jon Udell, July 31, 2009.
 An overview of the polymath project Christina Pikas, August 1, 2009
 Collaborative mathematics etc. Vipulniak, August 9, 2009
 Massively collaborative mathematics Tim Gowers, Michael Nielsen, Nature, October 15, 2009
 Collaborative math research – a real example Victor Porton, October 24, 2009
 Polymath again Vipulniak, October 26, 2009
 Wiskunde met zijn allen (Dutch), Alex van den Brandhof, Kennislink, November 12, 2009
 Mathematics by collaboration, Julie Rehmeyer, ScienceNews, December 8, 2009
 Massively Collaborative Mathematics, Jordan Ellenberg, The Ninth Annual Year in Ideas, New York Times, 2009.
 Massively Collaborative Mathematics: lessons from polymath1, Hypios, Jan 13 2010
 Open réflexions sur fond de Polymaths (French), ths1104, Feb 13 2010
 Collaborative Mathematics and The Future of Science Javier Tordable, February 26 2010
 Problem Solved, LOL: A Complex TicTacToe Puzzle Falls Thanks to Blog Comments Davide Castelvecchi, Scientific American, March 17 2010
 Blogging, Tic Tac Toe, and the Future of Math Steve Landsburg, The Big Questions, April 4 2010
 Massively Collaborative Mathematics Julie Rehmeyer, SIAM News, Volume 43(3), April 2010 (to appear)
 `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.
 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.
 How to build the global mathematics brain, Jacob Aron, New Scientist, 4 May 2011.
 Mathematics becomes more sociable, New Scientist, 5 May 2011.
 Mathematical Advances: Lone or Massively Collaborative Endeavors? from IAS Institute Letter for fall 2010 based on a discussion organized by IAS fall 2010.
 Will ‘Crowdsourcing’ Revolutionize Scholarship? An article in UConn Today by Jeremy Teitelbaum, Fall 2010.
 The New Einsteins Will Be Scientists Who Share The Wall street journal, October 2011.
 Parallel lines, editorial, Nature 506, 407–408 (27 February 2014).
Additional links are very welcome.
Other links
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