Polymath Wiki - User contributions [en]

Other proposed projects

2020-03-27T15:20:29Z

VictorPorton: The transition from quantity to quality formalized

This page is a repository for any polymath proposals which are not fleshed out enough to have their own separate posts for the proposal. Contributions are welcome.

== The transition from quantity to quality ==

The transition from quantity to quality (probably, first formulated by the philosopher Hegel) is a well known philosophical concept. Can we formalize it?

I propose a formalization:

For an ordinary differential equation, it is when the problem of a property of a differential equation (we can for simplicity assume that it has exactly one solution for a given initial value problem) that it takes a positive value for a given point ''x'' is undecidable.

I will explain this more intuitively: The value of the solution at a given point ''x'' is quantity. If it is above zero is quality. The transition from quantity to quality may be undecidable. (Really? May it be? If yes, for which kinds of differential equations?)

The issues I propose for the polymath project:

* Further generalize my definition of transition from quantity to quality (e.g. for partial differential equations).

* Research properties of such transitions.

In principle, further development of mathematics may discover whether Marx's (or is it Hegel's) concept that e.g. biology is undecidable based only on chemistry, etc. (however, this would be extremely hard to prove and even formalize). But this shows that my research proposal may have great perspectives for further development and applications to natural sciences.

== Inherent math vs human inventions such as chess ==

We feel that group theory is a beautiful mathematical theory, but rules of chess are not but are an invention of people.

I propose to consider which formally described systems count as mathematics and which are simple human inventions.

One approach would be to assign a rate (probably a real number) for different systems of how much "natural" they are. For example chess would have low naturality rate and group theory high one.

No good idea how to approach this issue. But Polymath Project is specifically for such problems which are difficult to approach by a single person.

One idea is to consider of "how much" (whatever this may mean) problems or situations are reduced to a given formalistic, how much general it is, whatever this may mean.

== Beating the trivial subset sum algorithm ==

This problem was proposed by Ernie Croot, though he would not have the time to run a project based on this problem.

It is a problem that is easy to state, probably will succumb to elementary methods, and probably could be solved if enough people contributed ideas. Here goes: consider the usual subset sum (or is it knapsack?) problem where you are given a list of positive integers N_1, …, N_k, and a target number T, and you must decide whether there is some subset of N_1, …, N_k that sums to T. The problem is to beat the “trivial algorithm”, which I shall describe presently.

The first thing to realize is that there is a subset sum equal to T iff there is one equal to S-T, where S=N_1 + … + N_k. Furthermore, subsets of size t summing to T correspond uniquely to subsets of size k-t summing to S-T. In this way, you only need to consider subsets of size at most k/2 (and check whether they sum of T or S-T) to solve the problem. But now you can use the usual “collision technique” to reduce the problem to subsets of size at most k/4, by forming a table of all subsets of at most this size, along with their sum of elements, until you find a disjoint pair of subsets that sums to either T or S-T. The running time of this procedure should be comparable to (k choose k/4) = c^(k+o(k)), for a certain constant c that is easy to work out. This is what I mean by the “trivial algorithm”. Now, the problem is find an algorithm — any at all — that runs in time at most d^k, where d < c. To my knowledge no such algorithm is know to exist!

note: Stasys Jukna has worked on lower bounds wrt dynamic programming algorithms running on the Knapsack problem which the Subset Sum is a special case. see sec 3.2 of this ECCC paper, [http://eccc.hpi-web.de/report/2012/041/#revision1 Limitations of Incremental Dynamic Programming] [[User:Vzn|Vzn]] 17:50, 28 December 2012 (UTC)

== Coupling determinantal processes ==

Any n-dimensional subspace V of a Euclidean space <math>{\Bbb R}^N</math> gives rise to a random subset A_V of {1,...,N}, with the probability that <math>A_V = \{i_1,\ldots,i_k\}</math> being the square of the magnitude of the projection of <math>e_{i_1} \wedge \ldots \wedge e_{i_n}</math> to V. This is known as the determinantal process associated to V.

If V is a subspace of W, it is known that one can couple <math>A_V</math> to <math>A_W</math> in such a way that the former set is a subset of the latter, but no "natural" way of doing this is known. One problem in this project would be to find such a natural way.

A related problem: if V, W are orthogonal, is it always possible to couple <math>A_V, A_W, A_{V+W}</math> together in such a way that <math>A_{V + W} = A_V \cup A_W</math>?

These questions are raised in page 38 of [http://uk.arxiv.org/PS_cache/math/pdf/0204/0204325v4.pdf this paper of Lyons], and also discussed at [http://terrytao.wordpress.com/2009/08/23/determinantal-processes/ this blog post].

== Stable commutator length in the free group ==

Let G be the free group on two generators, and let [G,G] be the commutator subgroup. Given any g in [G,G], the commutator length cl(g) is the least number of commutators needed to express g, and the stable commutator length scl(g) is the lim of cl(g^n)/n.

It is known that scl(g) >= 1/2 for any non-trivial g. Find a combinatorial proof of this fact.

It is conjectured that { scl(g): g in [G,G] } has an isolated point at 1/2. Prove this.

Reference: scl, Danny Calegari

== Quantum cellular automata ==

The proposal is tackling [http://mathoverflow.net/questions/78707/are-all-quantum-cellular-automata-invertible-representable these 2 questions].

== Yang-Mills existence and mass gap ==

Quite recently, [http://pro.osu.edu/profiles/dynin.1/ Alexander Dynin], a mathematician at Ohio State University with a reputable CV, proposed a solution of the Millennium prize problem on Yang-Mills existence and mass gap (see [http://arxiv.org/abs/1110.4682 here] and [http://arxiv.org/abs/0903.4727 here]). I have discussed this in my blog (see [http://marcofrasca.wordpress.com/2011/11/07/a-millenium-problem-issue/ here]) but I am a physicist and I cannot be sure about the correctness of all the mathematical arguments by the author. Of course, I am involved in this line of research as a physicist and, in our area, significant progress seems to have been made (e.g., besides my works, see Alexander (Sasha) Migdal's papers [http://arxiv.org/abs/1109.1623 here] and refs. therein and [http://marcofrasca.wordpress.com/2011/11/28/yang-mills-mass-gap-scenario-further-confirmations/ my blog entry]). So, it would be of paramount importance to have such a question addressed by the community of mathematicians at large, much in the same way as happened last year with "N vs. NP" question for [http://michaelnielsen.org/polymath1/index.php?title=Deolalikar_P_vs_NP_paper Deolalikar's paper], in order to fix the avenues to pursue for the community of theoretical physicists.--[[User:Mfrasca|Marco Frasca]] 09:30, 30 November 2011 (UTC)

== 2012 is the 100th anniversary of Landau's problems ==

I am suggesting a "Just For Grins" attack on Oppermann's Conjecture that, once proved, makes proofs of Legendre's Conjecture, Brocard's Conjecture, and Andrica's Conjecture slam dunks. Also, there is an outside chance that the twin-primes conjecture could be proved (requires Brocard's Conjecture).

http://en.wikipedia.org/wiki/Landau_problems

User: Rudy Toody

== Jun Fukuyama NP vs P/Poly proof ==

Jun Fukuyama, PhD announced a proof for NP vs P/Poly in July 2012 but the theoretical computer science and mathematics communities have not engaged with it much so far. this page [[Jun Fukuyama's P≠NP Paper]] has more info on his background, the proof, discussion, etc —[[User:Vzn|Vzn]] 17:34, 28 December 2012 (UTC)

== Outline for a NP vs P/Poly proof ==

[http://vzn1.wordpress.com/2012/12/08/outline-for-a-np-vsppoly-proof-based-on-monotone-circuits-hypergraphs-and-factoring/ outline/overview for a NP vs P/Poly proof] based on monotone circuits, hypergraphs, factoring, and slice functions was posted to a blog 12/8/2012. the author is not claiming a proof but presents a general/novel high-level outline/overview based on many years of research. the author is active online and has [http://cstheory.stackexchange.com/users/7884/vzn 2.7K rep] on the [http://cstheory.stackexchange.com/ theoretical computer science stack exchange] and has posted a peer-reviewed fragment of the outline there, [http://cstheory.stackexchange.com/questions/13967/factoring-cartesian-bitwise-join-of-bit-vectors "cartesian bitwise join of bit vectors"], and also on [http://mathoverflow.net/questions/108655/hypergraph-cartesian-join-operation-over-same-vertex-set mathoverflow] where there is a distant link to research on [http://www.cs.cmu.edu/~katayanagi/2009/knuth_abstract.html ZDDs] by Knuth. —[[User:Vzn|Vzn]] 18:11, 28 December 2012 (UTC)

== Collatz conjecture via computational analysis ==

Also by the same author, [http://vzn1.wordpress.com/code/collatz-conjecture-experiments/ Collatz conjecture experiments] has computational/algorithmic experiments to analyze the Collatz conjecture. in May 2013 some early/preliminary yet remarkable analysis (somewhat related to techniques described) was obtained that seems to be the basis for an inductive proof. the code is not yet included on that page and the proof will require a sort of "reverse engineering" of the code result. the current page has code to analyze the problem via FSM transducers. a new approach that does not require the transducer was devised and it reveals a striking fractal-like, apparent hidden, yet highly regular order/pattern of traversal of all integers. the new approach is based on a simple graph ordering of the computational verification sequence. —[[User:Vzn|Vzn]] 17:03, 24 May 2013 (UTC)

Main Page

2017-04-11T22:49:45Z

VictorPorton: /* Polymath-like projects */ removed yet broken links\

{{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. Concluded, Jan 17, 2017.
* [[Rota's conjecture|Polymath12]]: proving Rota's conjecture. Proposed Feb 28, 2017.

== Polymath-like 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 [https://conference.portonvictor.org/wiki/Research_in_the_middle Research in the middle project] at [https://conference.portonvictor.org Virtual scientific conference].
* 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

Main Page

2017-04-11T22:48:25Z

VictorPorton: /* Polymath-like projects */ removed a broken link

{{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. Concluded, Jan 17, 2017.
* [[Rota's conjecture|Polymath12]]: proving Rota's conjecture. Proposed Feb 28, 2017.

== 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
* 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 [https://conference.portonvictor.org/wiki/Research_in_the_middle Research in the middle project] at [https://conference.portonvictor.org Virtual scientific conference].
* 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

Main Page

2017-04-11T18:13:53Z

VictorPorton: /* Polymath-like 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. Concluded, Jan 17, 2017.
* [[Rota's conjecture|Polymath12]]: proving Rota's conjecture. Proposed Feb 28, 2017.

== 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 [https://conference.portonvictor.org/wiki/Research_in_the_middle Research in the middle project] at [https://conference.portonvictor.org Virtual scientific conference].
* 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

Other proposed projects

2015-08-22T20:49:07Z

VictorPorton: Is chess mathematics?

This page is a repository for any polymath proposals which are not fleshed out enough to have their own separate posts for the proposal. Contributions are welcome.

== Inherent math vs human inventions such as chess ==

We feel that group theory is a beautiful mathematical theory, but rules of chess are not but are an invention of people.

I propose to consider which formally described systems count as mathematics and which are simple human inventions.

One approach would be to assign a rate (probably a real number) for different systems of how much "natural" they are. For example chess would have low naturality rate and group theory high one.

No good idea how to approach this issue. But Polymath Project is specifically for such problems which are difficult to approach by a single person.

One idea is to consider of "how much" (whatever this may mean) problems or situations are reduced to a given formalistic, how much general it is, whatever this may mean.

== Beating the trivial subset sum algorithm ==

This problem was proposed by Ernie Croot, though he would not have the time to run a project based on this problem.

It is a problem that is easy to state, probably will succumb to elementary methods, and probably could be solved if enough people contributed ideas. Here goes: consider the usual subset sum (or is it knapsack?) problem where you are given a list of positive integers N_1, …, N_k, and a target number T, and you must decide whether there is some subset of N_1, …, N_k that sums to T. The problem is to beat the “trivial algorithm”, which I shall describe presently.

The first thing to realize is that there is a subset sum equal to T iff there is one equal to S-T, where S=N_1 + … + N_k. Furthermore, subsets of size t summing to T correspond uniquely to subsets of size k-t summing to S-T. In this way, you only need to consider subsets of size at most k/2 (and check whether they sum of T or S-T) to solve the problem. But now you can use the usual “collision technique” to reduce the problem to subsets of size at most k/4, by forming a table of all subsets of at most this size, along with their sum of elements, until you find a disjoint pair of subsets that sums to either T or S-T. The running time of this procedure should be comparable to (k choose k/4) = c^(k+o(k)), for a certain constant c that is easy to work out. This is what I mean by the “trivial algorithm”. Now, the problem is find an algorithm — any at all — that runs in time at most d^k, where d < c. To my knowledge no such algorithm is know to exist!

note: Stasys Jukna has worked on lower bounds wrt dynamic programming algorithms running on the Knapsack problem which the Subset Sum is a special case. see sec 3.2 of this ECCC paper, [http://eccc.hpi-web.de/report/2012/041/#revision1 Limitations of Incremental Dynamic Programming] [[User:Vzn|Vzn]] 17:50, 28 December 2012 (UTC)

== Coupling determinantal processes ==

Any n-dimensional subspace V of a Euclidean space <math>{\Bbb R}^N</math> gives rise to a random subset A_V of {1,...,N}, with the probability that <math>A_V = \{i_1,\ldots,i_k\}</math> being the square of the magnitude of the projection of <math>e_{i_1} \wedge \ldots \wedge e_{i_n}</math> to V. This is known as the determinantal process associated to V.

If V is a subspace of W, it is known that one can couple <math>A_V</math> to <math>A_W</math> in such a way that the former set is a subset of the latter, but no "natural" way of doing this is known. One problem in this project would be to find such a natural way.

A related problem: if V, W are orthogonal, is it always possible to couple <math>A_V, A_W, A_{V+W}</math> together in such a way that <math>A_{V + W} = A_V \cup A_W</math>?

These questions are raised in page 38 of [http://uk.arxiv.org/PS_cache/math/pdf/0204/0204325v4.pdf this paper of Lyons], and also discussed at [http://terrytao.wordpress.com/2009/08/23/determinantal-processes/ this blog post].

== Stable commutator length in the free group ==

Let G be the free group on two generators, and let [G,G] be the commutator subgroup. Given any g in [G,G], the commutator length cl(g) is the least number of commutators needed to express g, and the stable commutator length scl(g) is the lim of cl(g^n)/n.

It is known that scl(g) >= 1/2 for any non-trivial g. Find a combinatorial proof of this fact.

It is conjectured that { scl(g): g in [G,G] } has an isolated point at 1/2. Prove this.

Reference: scl, Danny Calegari

== Quantum cellular automata ==

The proposal is tackling [http://mathoverflow.net/questions/78707/are-all-quantum-cellular-automata-invertible-representable these 2 questions].

== Yang-Mills existence and mass gap ==

Quite recently, [http://pro.osu.edu/profiles/dynin.1/ Alexander Dynin], a mathematician at Ohio State University with a reputable CV, proposed a solution of the Millennium prize problem on Yang-Mills existence and mass gap (see [http://arxiv.org/abs/1110.4682 here] and [http://arxiv.org/abs/0903.4727 here]). I have discussed this in my blog (see [http://marcofrasca.wordpress.com/2011/11/07/a-millenium-problem-issue/ here]) but I am a physicist and I cannot be sure about the correctness of all the mathematical arguments by the author. Of course, I am involved in this line of research as a physicist and, in our area, significant progress seems to have been made (e.g., besides my works, see Alexander (Sasha) Migdal's papers [http://arxiv.org/abs/1109.1623 here] and refs. therein and [http://marcofrasca.wordpress.com/2011/11/28/yang-mills-mass-gap-scenario-further-confirmations/ my blog entry]). So, it would be of paramount importance to have such a question addressed by the community of mathematicians at large, much in the same way as happened last year with "N vs. NP" question for [http://michaelnielsen.org/polymath1/index.php?title=Deolalikar_P_vs_NP_paper Deolalikar's paper], in order to fix the avenues to pursue for the community of theoretical physicists.--[[User:Mfrasca|Marco Frasca]] 09:30, 30 November 2011 (UTC)

== 2012 is the 100th anniversary of Landau's problems ==

I am suggesting a "Just For Grins" attack on Oppermann's Conjecture that, once proved, makes proofs of Legendre's Conjecture, Brocard's Conjecture, and Andrica's Conjecture slam dunks. Also, there is an outside chance that the twin-primes conjecture could be proved (requires Brocard's Conjecture).

http://en.wikipedia.org/wiki/Landau_problems

User: Rudy Toody

== Jun Fukuyama NP vs P/Poly proof ==

Jun Fukuyama, PhD announced a proof for NP vs P/Poly in July 2012 but the theoretical computer science and mathematics communities have not engaged with it much so far. this page [[Jun Fukuyama's P≠NP Paper]] has more info on his background, the proof, discussion, etc —[[User:Vzn|Vzn]] 17:34, 28 December 2012 (UTC)

== Outline for a NP vs P/Poly proof ==

[http://vzn1.wordpress.com/2012/12/08/outline-for-a-np-vsppoly-proof-based-on-monotone-circuits-hypergraphs-and-factoring/ outline/overview for a NP vs P/Poly proof] based on monotone circuits, hypergraphs, factoring, and slice functions was posted to a blog 12/8/2012. the author is not claiming a proof but presents a general/novel high-level outline/overview based on many years of research. the author is active online and has [http://cstheory.stackexchange.com/users/7884/vzn 2.7K rep] on the [http://cstheory.stackexchange.com/ theoretical computer science stack exchange] and has posted a peer-reviewed fragment of the outline there, [http://cstheory.stackexchange.com/questions/13967/factoring-cartesian-bitwise-join-of-bit-vectors "cartesian bitwise join of bit vectors"], and also on [http://mathoverflow.net/questions/108655/hypergraph-cartesian-join-operation-over-same-vertex-set mathoverflow] where there is a distant link to research on [http://www.cs.cmu.edu/~katayanagi/2009/knuth_abstract.html ZDDs] by Knuth. —[[User:Vzn|Vzn]] 18:11, 28 December 2012 (UTC)

== Collatz conjecture via computational analysis ==

Also by the same author, [http://vzn1.wordpress.com/code/collatz-conjecture-experiments/ Collatz conjecture experiments] has computational/algorithmic experiments to analyze the Collatz conjecture. in May 2013 some early/preliminary yet remarkable analysis (somewhat related to techniques described) was obtained that seems to be the basis for an inductive proof. the code is not yet included on that page and the proof will require a sort of "reverse engineering" of the code result. the current page has code to analyze the problem via FSM transducers. a new approach that does not require the transducer was devised and it reveals a striking fractal-like, apparent hidden, yet highly regular order/pattern of traversal of all integers. the new approach is based on a simple graph ordering of the computational verification sequence. —[[User:Vzn|Vzn]] 17:03, 24 May 2013 (UTC)

Main Page

2013-11-25T20:11:39Z

VictorPorton: /* Polymath-like 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 been accepted for publication.
* [[The Erdős discrepancy problem|Polymath5]]: The Erdős discrepancy problem. Proposed Jan 10, 2010; launched Jan 19, 2010.
* [[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.
* [[Discretized Borel Determinacy and P=NP|Polymath9]]: exploring Borel determinacy-based methods for giving complexity bounds. Proposed, Oct 24, 2013; launched, Nov 3, 2013.

== 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://www.princeton.edu/~mbarany/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.
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

Main Page

2013-11-25T18:45:18Z

VictorPorton: /* Polymath-like 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 been accepted for publication.
* [[The Erdős discrepancy problem|Polymath5]]: The Erdős discrepancy problem. Proposed Jan 10, 2010; launched Jan 19, 2010.
* [[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.
* [[Discretized Borel Determinacy and P=NP|Polymath9]]: exploring Borel determinacy-based methods for giving complexity bounds. Proposed, Oct 24, 2013; launched, Nov 3, 2013.

== Polymath-like projects ==

* [http://portonmath.tiddlyspace.com/ "Theory of singularities" research attempt] and [http://portonmath.tiddlyspace.com/ attempt to prove that certain categories are cartesian closed] (click it the top menu to choose one these two projects) 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://www.princeton.edu/~mbarany/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.
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

Main Page

2013-11-15T22:17:59Z

VictorPorton: /* Polymath-like 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 been accepted for publication.
* [[The Erdős discrepancy problem|Polymath5]]: The Erdős discrepancy problem. Proposed Jan 10, 2010; launched Jan 19, 2010.
* [[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.

== Polymath-like projects ==

* [http://portonmath.tiddlyspace.com/ "Theory of singularities" research attempt] 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://www.princeton.edu/~mbarany/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.
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

Main Page

2013-11-09T23:10:43Z

VictorPorton: /* Polymath-like projects */ "Theory of singularities" link

{{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 been accepted for publication.
* [[The Erdős discrepancy problem|Polymath5]]: The Erdős discrepancy problem. Proposed Jan 10, 2010; launched Jan 19, 2010.
* [[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.

== Polymath-like projects ==

* [http://portonmath.tiddlyspace.com/ TiddleSpace] which contains "Theory of singularities" research attempt.
* [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://www.princeton.edu/~mbarany/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.
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

Other proposed projects

2013-07-29T16:25:51Z

VictorPorton: /* Equality of several differences of filters */ Removed as a mostly solved problem

This page is a repository for any polymath proposals which are not fleshed out enough to have their own separate posts for the proposal. Contributions are welcome.

== Beating the trivial subset sum algorithm ==

This problem was proposed by Ernie Croot, though he would not have the time to run a project based on this problem.

It is a problem that is easy to state, probably will succumb to elementary methods, and probably could be solved if enough people contributed ideas. Here goes: consider the usual subset sum (or is it knapsack?) problem where you are given a list of positive integers N_1, …, N_k, and a target number T, and you must decide whether there is some subset of N_1, …, N_k that sums to T. The problem is to beat the “trivial algorithm”, which I shall describe presently.

The first thing to realize is that there is a subset sum equal to T iff there is one equal to S-T, where S=N_1 + … + N_k. Furthermore, subsets of size t summing to T correspond uniquely to subsets of size k-t summing to S-T. In this way, you only need to consider subsets of size at most k/2 (and check whether they sum of T or S-T) to solve the problem. But now you can use the usual “collision technique” to reduce the problem to subsets of size at most k/4, by forming a table of all subsets of at most this size, along with their sum of elements, until you find a disjoint pair of subsets that sums to either T or S-T. The running time of this procedure should be comparable to (k choose k/4) = c^(k+o(k)), for a certain constant c that is easy to work out. This is what I mean by the “trivial algorithm”. Now, the problem is find an algorithm — any at all — that runs in time at most d^k, where d < c. To my knowledge no such algorithm is know to exist!

note: Stasys Jukna has worked on lower bounds wrt dynamic programming algorithms running on the Knapsack problem which the Subset Sum is a special case. see sec 3.2 of this ECCC paper, [http://eccc.hpi-web.de/report/2012/041/#revision1 Limitations of Incremental Dynamic Programming] [[User:Vzn|Vzn]] 17:50, 28 December 2012 (UTC)

== Coupling determinantal processes ==

Any n-dimensional subspace V of a Euclidean space <math>{\Bbb R}^N</math> gives rise to a random subset A_V of {1,...,N}, with the probability that <math>A_V = \{i_1,\ldots,i_k\}</math> being the square of the magnitude of the projection of <math>e_{i_1} \wedge \ldots \wedge e_{i_n}</math> to V. This is known as the determinantal process associated to V.

If V is a subspace of W, it is known that one can couple <math>A_V</math> to <math>A_W</math> in such a way that the former set is a subset of the latter, but no "natural" way of doing this is known. One problem in this project would be to find such a natural way.

A related problem: if V, W are orthogonal, is it always possible to couple <math>A_V, A_W, A_{V+W}</math> together in such a way that <math>A_{V + W} = A_V \cup A_W</math>?

These questions are raised in page 38 of [http://uk.arxiv.org/PS_cache/math/pdf/0204/0204325v4.pdf this paper of Lyons], and also discussed at [http://terrytao.wordpress.com/2009/08/23/determinantal-processes/ this blog post].

== Stable commutator length in the free group ==

Let G be the free group on two generators, and let [G,G] be the commutator subgroup. Given any g in [G,G], the commutator length cl(g) is the least number of commutators needed to express g, and the stable commutator length scl(g) is the lim of cl(g^n)/n.

It is known that scl(g) >= 1/2 for any non-trivial g. Find a combinatorial proof of this fact.

It is conjectured that { scl(g): g in [G,G] } has an isolated point at 1/2. Prove this.

Reference: scl, Danny Calegari

== Quantum cellular automata ==

The proposal is tackling [http://mathoverflow.net/questions/78707/are-all-quantum-cellular-automata-invertible-representable these 2 questions].

== Yang-Mills existence and mass gap ==

Quite recently, [http://pro.osu.edu/profiles/dynin.1/ Alexander Dynin], a mathematician at Ohio State University with a reputable CV, proposed a solution of the Millennium prize problem on Yang-Mills existence and mass gap (see [http://arxiv.org/abs/1110.4682 here] and [http://arxiv.org/abs/0903.4727 here]). I have discussed this in my blog (see [http://marcofrasca.wordpress.com/2011/11/07/a-millenium-problem-issue/ here]) but I am a physicist and I cannot be sure about the correctness of all the mathematical arguments by the author. Of course, I am involved in this line of research as a physicist and, in our area, significant progress seems to have been made (e.g., besides my works, see Alexander (Sasha) Migdal's papers [http://arxiv.org/abs/1109.1623 here] and refs. therein and [http://marcofrasca.wordpress.com/2011/11/28/yang-mills-mass-gap-scenario-further-confirmations/ my blog entry]). So, it would be of paramount importance to have such a question addressed by the community of mathematicians at large, much in the same way as happened last year with "N vs. NP" question for [http://michaelnielsen.org/polymath1/index.php?title=Deolalikar_P_vs_NP_paper Deolalikar's paper], in order to fix the avenues to pursue for the community of theoretical physicists.--[[User:Mfrasca|Marco Frasca]] 09:30, 30 November 2011 (UTC)

== 2012 is the 100th anniversary of Landau's problems ==

I am suggesting a "Just For Grins" attack on Oppermann's Conjecture that, once proved, makes proofs of Legendre's Conjecture, Brocard's Conjecture, and Andrica's Conjecture slam dunks. Also, there is an outside chance that the twin-primes conjecture could be proved (requires Brocard's Conjecture).

http://en.wikipedia.org/wiki/Landau_problems

User: Rudy Toody

== Jun Fukuyama NP vs P/Poly proof ==

Jun Fukuyama, PhD announced a proof for NP vs P/Poly in July 2012 but the theoretical computer science and mathematics communities have not engaged with it much so far. this page [[Jun Fukuyama's P≠NP Paper]] has more info on his background, the proof, discussion, etc —[[User:Vzn|Vzn]] 17:34, 28 December 2012 (UTC)

== Outline for a NP vs P/Poly proof ==

[http://vzn1.wordpress.com/2012/12/08/outline-for-a-np-vsppoly-proof-based-on-monotone-circuits-hypergraphs-and-factoring/ outline/overview for a NP vs P/Poly proof] based on monotone circuits, hypergraphs, factoring, and slice functions was posted to a blog 12/8/2012. the author is not claiming a proof but presents a general/novel high-level outline/overview based on many years of research. the author is active online and has [http://cstheory.stackexchange.com/users/7884/vzn 2.7K rep] on the [http://cstheory.stackexchange.com/ theoretical computer science stack exchange] and has posted a peer-reviewed fragment of the outline there, [http://cstheory.stackexchange.com/questions/13967/factoring-cartesian-bitwise-join-of-bit-vectors "cartesian bitwise join of bit vectors"], and also on [http://mathoverflow.net/questions/108655/hypergraph-cartesian-join-operation-over-same-vertex-set mathoverflow] where there is a distant link to research on [http://www.cs.cmu.edu/~katayanagi/2009/knuth_abstract.html ZDDs] by Knuth. —[[User:Vzn|Vzn]] 18:11, 28 December 2012 (UTC)

== Collatz conjecture via computational analysis ==

Also by the same author, [http://vzn1.wordpress.com/code/collatz-conjecture-experiments/ Collatz conjecture experiments] has computational/algorithmic experiments to analyze the Collatz conjecture. in May 2013 some early/preliminary yet remarkable analysis (somewhat related to techniques described) was obtained that seems to be the basis for an inductive proof. the code is not yet included on that page and the proof will require a sort of "reverse engineering" of the code result. the current page has code to analyze the problem via FSM transducers. a new approach that does not require the transducer was devised and it reveals a striking fractal-like, apparent hidden, yet highly regular order/pattern of traversal of all integers. the new approach is based on a simple graph ordering of the computational verification sequence. —[[User:Vzn|Vzn]] 17:03, 24 May 2013 (UTC)

Other proposed projects

2013-07-28T15:27:25Z

VictorPorton: /* Equality of several differences of filters */

Talk:Logo

2013-07-27T21:47:29Z

VictorPorton:

Please leave comments here, identifying your favourite, or favourites.

==New Proposal for simple logo==

I made some new proposals for the polymath logo. I tried to create something simple, symbolic, that looks nice at small and large scale and in color or black and white. You can see some variations on the same "theme" here: https://github.com/mseri/polymath-logos#variation-on-a-theme

The Inkscape svg source is available on the same website if you want to play/experiment with them. And a pdf containing all the logos to check how do they look printed is available there too: https://github.com/mseri/polymath-logos/blob/master/polymath-logos.pdf

--[[User:Mseri|mseri]] 11:39, 5 June 2013 (UTC)

== Simple Logo ==

Here is a simple proposal: https://picasaweb.google.com/lh/photo/Ns8fhSWnpeh0Hdm6rgum5g?feat=directlink

== Opinion ==

I particularly like the first logo to use the "Sigma" idea. It's simple and direct, but the Sigma conveys an interesting double message. I would perhaps like something a bit brighter, though.

--[[User:WikiSysop|WikiSysop]] 16:18, 10 May 2011 (UTC)

How about something simple, involving mathematical characters? For example: http://tinyurl.com/3arb6wy
I just whipped this up in word so it's more of an idea that someone with photoshop skills may wish to take further

--[[User:Aindriu|Aindriu]] 22:29, 11 May 2011 (UTC)

I like this new suggestion from Russell: http://ixitol.com/PolyMath2.jpg. Not sure the black background works, but the bright and varied colours are great. It suggests variation, but with an ultimate cohesiveness.
--[[User:WikiSysop|WikiSysop]] 18:46, 13 May 2011 (UTC)

Maybe combine the bright colours of http://ixitol.com/PolyMath2.jpg with the "Sigma" idea from http://cl.ly/3Y23180A1U2j3I0M2C1K.png?
--[[User:WikiSysop|WikiSysop]] 18:48, 13 May 2011 (UTC)

Re "Maybe combine..."; That could work... perhaps send out a hi-rez 'sigma' image, to whomever is interested, for trying out various color schemes.
-- [[User:Russell|Russell]]

I like Russell's latest design a lot: http://ixitol.com/PolyMath4.jpg. It's a simple, clean design, that still conveys the idea of many contributions.
--[[User:WikiSysop|WikiSysop]] 10:53, 14 May 2011 (UTC)

Author of "simple sigma" logo here. Sorry - didn't notice the discussion on here. I'll post a link to a vector version of the simple sigma logo and a brighter version in a bit.
--[[User:IgorKofman|IgorKofman]]

@IgorKofman - great, look forward to seeing it.
--[[User:WikiSysop|WikiSysop]] 14:14, 20 May 2011 (UTC)

I propose going with http://ixitol.com/PolyMath4.jpg. I'll wait a couple of days more for objections / alternate suggestions, and if none are made, I'll make that the logo.
--[[User:WikiSysop|WikiSysop]] 19:14, 24 May 2011 (UTC)

I'm also not wild about any of them, but I find it hard to say why. I think the best explanation I can think of is that they are insufficiently compact — they look more like words than logos. Maybe one could make a logo just out of a <math>\pi</math> and a <math>\mu</math>. -- [[User:Gowers|Gowers]]

@gowers – The \pi-\mu idea sounds like it might work well, if anyone’s willing to put something together. My favourite at present is http://ixitol.com/PolyMath4.jpg – do you strongly dislike the suggestion?
--[[User:WikiSysop|WikiSysop]] 17:32, 25 May 2011 (UTC)

Here's a few variations on the simple sigma idea and the illustrator file:
http://emberapp.com/igorkofman/images/adobe-illustrator-cs5
http://www.cl.ly/2i1L1N170U2s4528341d
--[[User:IgorKofman|IgorKofman]]

I did a trial of http://ixitol.com/PolyMath4.jpg. While I like the logo, I think it has two problems: (1) It's too small; and (2) the background isn't transparent. It'd be nice to fix these problems. Note that point (1) is connected to Tim Gowers' point, above. This problem also afflicts IgorKofman's suggested logos, and several of the other logos.
--[[User:WikiSysop|WikiSysop]] 11:50, 29 May 2011 (UTC)

Here's something a bit more compact: http://f.cl.ly/items/1F2n1l0G333R2g1r0w12/polymath7.png
Or even: http://f.cl.ly/items/2i2P3j3v371i0P053b2A/polymath6.png / http://f.cl.ly/items/1f1s021E0k2U1A0H1d1F/polymath8.png
--[[User:IgorKofman|IgorKofman]]

I really like those, IgorKofman, especially polymath6.png. --[[User:Adeel|Adeel]] 16:28, 26 July 2011 (UTC)

:Me too, they're great. I think that either the font of the word "POLYMATH" or the small sigma symbol should be changed so that the sigma in place of the M doesn't stand out too much. Currently, the sigma is noticeably thinner than the other letters, and it has serifs, while the other letters don't. [[User:JohnJamesSmith0|JohnJamesSmith0]] 23:10, 13 August 2011 (UTC)

Talk:Logo

2013-07-27T21:47:06Z

VictorPorton: /* My opinion */ removed my opinion on older logos, because some new logos appeared

Other proposed projects

2013-07-27T20:47:03Z

VictorPorton: /* Equality of several differences of filters */ literature references

Other proposed projects

2013-07-27T20:19:13Z

VictorPorton: /* Equality of several differences of filters */

Other proposed projects

2013-07-27T20:18:01Z

VictorPorton: /* Equality of several differences of filters */

Other proposed projects

2013-07-27T20:13:42Z

VictorPorton: Added conjecture about equality of several differences of filters

Main Page

2013-04-30T01:36:24Z

VictorPorton: /* Polymath-like 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]].

Jan 17, 2013: The creation of new accounts is temporarily suspended, due to spam. Please email mn@michaelnielsen.org if you'd like an account set up.

== 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 been accepted for publication.
* [[The Erdős discrepancy problem|Polymath5]]: The Erdős discrepancy problem. Proposed Jan 10, 2010; launched Jan 19, 2010.
* [[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.

== Polymath-like projects ==

* [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://www.princeton.edu/~mbarany/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.
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

Main Page

2013-03-23T19:27:03Z

VictorPorton: /* Polymath-like projects */ collaborative research at PlanetMath

{{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]].

Jan 17, 2013: The creation of new accounts is temporarily suspended, due to spam. Please email mn@michaelnielsen.org if you'd like an account set up.

== 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 been accepted for publication.
* [[The Erdős discrepancy problem|Polymath5]]: The Erdős discrepancy problem. Proposed Jan 10, 2010; launched Jan 19, 2010.
* [[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.

== Polymath-like 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://www.princeton.edu/~mbarany/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.
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

Main Page

2012-07-30T20:50:11Z

VictorPorton: /* Polymath-like projects */ Added link to Math Research Trends Wiki

{{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]].

== 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 been accepted for publication.
* [[The Erdős discrepancy problem|Polymath5]]: The Erdős discrepancy problem. Proposed Jan 10, 2010; launched Jan 19, 2010.
* [[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.

== Polymath-like 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 [[Deolalikar P vs NP paper]]. Launched Aug 10, 2010.
* [http://researchtrends.wikia.com/wiki/Main_Page Math Research Trends Wiki] "research in the middle"

== 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://www.princeton.edu/~mbarany/cv.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.
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.

Main Page

2012-05-29T19:20:34Z

VictorPorton: Reverse a SPAM link This Blog() back

{{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]].

== Existing polymath projects ==

* [[Polymath1]]: New proofs and bounds for the density Hales-Jewett theorem. Initiated Feb 1, 2009; research results have now been submitted for publication.
* [[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 been submitted for publication.
* [[The Erdős discrepancy problem|Polymath5]]. The Erdős discrepancy problem. Proposed Jan 10, 2010; launched Jan 19, 2010.
* [[imo 2010|Mini-polymath2]]: Solving Problem 5 the 2010 International Mathematical Olympiad. Proposed Jun 12, 2010; launched Jul 8, 2010; 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, 2010.

== Polymath-like 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 [[Deolalikar P vs NP paper]]. Launched Aug 10, 2010.

== Proposed polymath projects ==

* [http://gilkalai.wordpress.com/2009/03/25/an-open-discussion-and-polls-around-roths-theorem/ see also]. 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://en.wordpress.com/tag/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://www.princeton.edu/~mbarany/cv.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.
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.

Main Page

2012-05-29T19:19:56Z

VictorPorton: Reverse a SPAM link This Blog() back

{{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]].

== Existing polymath projects ==

* [[Polymath1]]: New proofs and bounds for the density Hales-Jewett theorem. Initiated Feb 1, 2009; research results have now been submitted for publication.
* [[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 been submitted for publication.
* [[The Erdős discrepancy problem|Polymath5]]. The Erdős discrepancy problem. Proposed Jan 10, 2010; launched Jan 19, 2010.
* [[imo 2010|Mini-polymath2]]: Solving Problem 5 the 2010 International Mathematical Olympiad. Proposed Jun 12, 2010; launched Jul 8, 2010; 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, 2010.

== Polymath-like 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 [[Deolalikar P vs NP paper]]. Launched Aug 10, 2010.

== Proposed polymath projects ==

* [http://gilkalai.wordpress.com/2009/03/25/an-open-discussion-and-polls-around-roths-theorem/ see also]. 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://en.wordpress.com/tag/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://www.thaibet-sbobet.com 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://www.princeton.edu/~mbarany/cv.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.
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.

Main Page

2012-05-29T19:17:33Z

VictorPorton: Reverse a SPAM link This Blog() back

{{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]].

== Existing polymath projects ==

* [[Polymath1]]: New proofs and bounds for the density Hales-Jewett theorem. Initiated Feb 1, 2009; research results have now been submitted for publication.
* [[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 been submitted for publication.
* [[The Erdős discrepancy problem|Polymath5]]. The Erdős discrepancy problem. Proposed Jan 10, 2010; launched Jan 19, 2010.
* [[imo 2010|Mini-polymath2]]: Solving Problem 5 the 2010 International Mathematical Olympiad. Proposed Jun 12, 2010; launched Jul 8, 2010; 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, 2010.

== Polymath-like 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 [[Deolalikar P vs NP paper]]. Launched Aug 10, 2010.

== Proposed polymath projects ==

* [http://www.th-m88.com see also]. 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://en.wordpress.com/tag/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://www.thaibet-sbobet.com 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://www.princeton.edu/~mbarany/cv.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.
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.

Other proposed projects

2012-04-03T23:02:00Z

VictorPorton: Removed the section /* Filters on posets and generalizations */

Talk:Logo

2011-04-28T18:51:25Z

VictorPorton: I don’t like any logo of the suggested

Please leave comments here, identifying your favourite, or favourites.

==My opinion==

I don’t like any logo of the suggested.

This is not as bad as the rest:
http://dl.dropbox.com/u/126293/polymath-v1.png
[[User:VictorPorton|VictorPorton]] 18:51, 28 April 2011 (UTC)

Main Page

2009-10-24T21:45:27Z

VictorPorton: /* Discussions about polymath */ Added "Collaborative math research – a real example" link

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].

== Existing polymath projects ==

* [[Polymath1]]: New proofs and bounds for the density Hales-Jewett theorem. Initiated Feb 1, 2009; now in the process of writing up the results.
* [http://gowers.wordpress.com/2009/02/17/must-an-explicitly-defined-banach-space-contain-c_0-or-ell_p/ Polymath2]: Must an “explicitly defined” Banach space contain c_0 or ell_p? Initiated Feb 17, 2009; largely inactive at present
* [[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.
* [[finding primes|Polymath4]]: A deterministic way to find primes. Proposed July 27, 2009; launched Aug 9, 2009. Ongoing.

== 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.

A (partial) list of proposed projects can be found [http://en.wordpress.com/tag/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

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.

Other proposed projects

2009-08-30T17:20:52Z

VictorPorton: /* Filters on posets and generalizations */ Added ref to a conjecture

Other proposed projects

2009-08-29T19:09:10Z

VictorPorton: /* Filters on posets and generalizations */ Updated to refer to wikidot.com

Other proposed projects

2009-08-29T15:02:56Z

VictorPorton: /* Filters on posets and generalizations */ Suspended due misfeautures of a wiki

Other proposed projects

2009-08-28T22:11:49Z

VictorPorton: /* Filters on posets and generalizations */ Corrected link to the new wiki

Other proposed projects

2009-08-27T20:45:53Z

VictorPorton: Added proposal to write "Filters on posets and generalizations"