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This is the wiki for polymath projects - massively collaborative online mathematical projects. The idea of such projects originated in Tim Gowers' blog post Is massively collaborative mathematics possible?

Many polymath projects will be proposed, planned, and run at this blog.

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.
• Polymath2: Must an “explicitly defined” Banach space contain [math]\displaystyle{ c_0 }[/math] or [math]\displaystyle{ l_p }[/math]? Initiated Feb 17, 2009; attempts to relaunch via wiki.
• Mini-polymath1: Solving Problem 6 of the 2009 International Mathematical Olympiad. Initiated July 20, 2009; five proofs obtained so far.
• Polymath3. The polynomial Hirsch conjecture. Proposed July 17, 2009.
• Polymath4: A deterministic way to find primes. Proposed July 27, 2009; launched Aug 9, 2009.
• Polymath5. The Erdős discrepancy problem. Proposed Jan 10, 2010; launched Jan 19, 2010.
• Mini-polymath2: Solving a problem from the 2010 International Mathematical Olympiad. Proposed Jun 12, 2010; launched Jul 8, 2010; solved, Jul 8 2010.

Polymath-like projects

• Scott Aaronson's [philomath project]: "Sensitivity vs. Block sensitivity" (see also [this Math Overflow question]). Launched Jul 13, 2010.

Proposed polymath projects

• The cap set problem. Proposed March 25, 2009 (see also these two followup posts).
• Boshernitzan’s problem. Proposed July 27, 2009.
• Possible future polymath projects. Discussion opened September 16, 2009.

A (partial) list of proposed projects can be found here.

If you have a tentative proposal for a polymath project, you can either make a post on it on your own blog, or place it here.

Discussions about polymath

• Is massively collaborative mathematics possible? Tim Gowers, January 27, 2009.
• A people's history of mathematics Luca Trevisan, February 1, 2009.
• The polymath project Michael Nielsen, February 3, 2009.
• Yet another math 2.0 proposal Lieven le Bruyn, February 11, 2009.
• Polymath1 and open collaborative mathematics Tim Gowers, March 10, 2009.
• Polymath Edmund Harriss, March 14, 2009.
• Massive open collaboration in mathematics declared a success Slashdot, March 18, 2009.
• How changing the technology of collaboration can change the nature of collaboration Michael Nielsen, March 18, 2009.
• The polymath project: scope of participation Michael Nielsen, March 20, 2009.
• Can polymath be scaled up? Tim Gowers, March 24, 2009.
• Concluding notes on the polymath project - and a challenge Vilpulniak, March 24, 2009.
• On scaling up the polymath project Michael Nielsen, March 25, 2009.
• A gentle introduction to the polymath project Jason Dyer, March 25, 2009.
• Tim Gowers and the polymaths Ian Douglas (the Telegraph), April 29, 2009
• IMO 2009 Q6 as mini-polymath project: impressions, reflections, analysis Terence Tao, July 22, 2009.
• Selecting the next polymath project Terence Tao, July 27, 2009.
• Polymath equals user innovation Jon Udell, July 31, 2009.
• An overview of the polymath project Christina Pikas, August 1, 2009
• Collaborative mathematics etc. Vipulniak, August 9, 2009
• Massively collaborative mathematics Tim Gowers, Michael Nielsen, Nature, October 15, 2009
• Collaborative math research – a real example Victor Porton, October 24, 2009
• Polymath again Vipulniak, October 26, 2009
• Wiskunde met zijn allen (Dutch), Alex van den Brandhof, Kennislink, November 12, 2009
• Mathematics by collaboration, Julie Rehmeyer, ScienceNews, December 8, 2009
• Massively Collaborative Mathematics, Jordan Ellenberg, The Ninth Annual Year in Ideas, New York Times, 2009.
• Massively Collaborative Mathematics: lessons from polymath1, Hypios, Jan 13 2010
• Open réflexions sur fond de Polymaths (French), ths1104, Feb 13 2010
• Collaborative Mathematics and The Future of Science Javier Tordable, February 26 2010
• Problem Solved, LOL: A Complex Tic-Tac-Toe Puzzle Falls Thanks to Blog Comments Davide Castelvecchi, Scientific American, March 17 2010
• Blogging, Tic Tac Toe, and the Future of Math Steve Landsburg, The Big Questions, April 4 2010
• Massively Collaborative Mathematics Julie Rehmeyer, SIAM News, Volume 43(3), April 2010 (to appear)
• `But this is blog maths and we're free to make up conventions as we go along': Polymath1 and the Modalities of `Massively Collaborative Mathematics.' Michael Barany, Proceedings of the 6th International Symposium on Wikis and Open Collaboration, Gdansk, Poland, 2010.

Additional links are very welcome.

Other links

• The polymath blog
• General polymath rules

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