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* [[imo 2009 q6|Mini-polymath1]]: Solving Problem 6 of the 2009 International Mathematical Olympiad.  Initiated July 20, 2009; five proofs obtained so far.
 
* [[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.   
 
* [[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.
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* [[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.
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* [[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.
 
* [[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.
 
* [[Improving the bounds for Roth's theorem|Polymath6]]: Improving the bounds for Roth's theorem. Proposed Feb 5, 2011.
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* [[imo 2012|Mini-polymath4]]: Solving a problem from the 2012 International Mathematical Olympiad.  Proposed, Jun 3, 2012; launched, July 12 2012.
 
* [[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.
 
* [[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.
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* [[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.
 
* [[Discretized Borel Determinacy and P=NP|Polymath9]]: exploring Borel determinacy-based methods for giving complexity bounds.  Proposed, Oct 24, 2013; launched, Nov 3, 2013.
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* [[The Erdos-Rado sunflower lemma|Polymath10]]: improving the bounds for the Erdos-Rado sunflower lemma.  Launched, Nov 2, 2015.
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* [[Frankl's union-closed conjecture|Polymath11]]: proving Frankl's union-closed conjecture. Proposed Jan 21, 2016; launched Jan 29, 2016.  Concluded, Jan 17, 2017.
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* [[Rota's conjecture|Polymath12]]: proving Rota's conjecture.  Proposed Feb 28, 2017.
  
 
== Polymath-like projects ==
 
== 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.
 
* 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.
 
* A wiki page clearinghouse for the [[Deolalikar P vs NP paper]].  Launched Aug 10, 2010.
* <del>[http://researchtrends.wikia.com/wiki/Main_Page Math Research Trends Wiki] "research in the middle"</del> This project is recommended to be discontinued in favor of <b>[http://portonmath.wordpress.com/2013/03/23/collaborative-research/ collaborative research at PlanetMath]</b>.
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* <del>[http://researchtrends.wikia.com/wiki/Main_Page Math Research Trends Wiki] "research in the middle"</del> This project is recommended to be discontinued in favor of <b>[https://conference.portonvictor.org/wiki/Research_in_the_middle Research in the middle project] at [https://conference.portonvictor.org Virtual scientific conference]</b>.
 
* The page for the [[ABC conjecture]] contains links and information about Mochizuki's claimed proof of this conjecture.
 
* The page for the [[ABC conjecture]] contains links and information about Mochizuki's claimed proof of this conjecture.
  

Latest revision as of 14:49, 11 April 2017

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

Many polymath projects will be proposed, planned, and run at This Blog.

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

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

Existing polymath projects

  • Polymath1: New proofs and bounds for the density Hales-Jewett theorem. Initiated Feb 1, 2009; research results have now been published.
  • Polymath2: Must an “explicitly defined” Banach space contain [math]c_0[/math] or [math]l_p[/math]? Initiated Feb 17, 2009; attempts to relaunch via wiki, June 9 2010.
  • 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; launched, September 30, 2010.
  • Polymath4: A deterministic way to find primes. Proposed July 27, 2009; launched Aug 9, 2009. Research results have now been published.
  • Polymath5: The Erdős discrepancy problem. Proposed Jan 10, 2010; launched Jan 19, 2010. Activity ceased by the end of 2012, but results from the project were used to solve the problem in 2015.
  • Mini-polymath2: Solving Problem 5 the 2010 International Mathematical Olympiad. Proposed Jun 12, 2010; launched and solved, Jul 8 2010.
  • Polymath6: Improving the bounds for Roth's theorem. Proposed Feb 5, 2011.
  • Mini-polymath3: Solving a problem from the 2011 International Mathematical Olympiad. Proposed Jun 9, 2011; launched and solved, Jul 19, 2011.
  • Mini-polymath4: Solving a problem from the 2012 International Mathematical Olympiad. Proposed, Jun 3, 2012; launched, July 12 2012.
  • Polymath7: Establishing the Hot Spots conjecture for acute-angled triangles. Proposed, May 31st, 2012; launched, Jun 8, 2012.
  • Polymath8: Improving the bounds for small gaps between primes. Proposed, June 4, 2013; launched, June 4, 2013. Research results have now been published.
  • Polymath9: exploring Borel determinacy-based methods for giving complexity bounds. Proposed, Oct 24, 2013; launched, Nov 3, 2013.
  • Polymath10: improving the bounds for the Erdos-Rado sunflower lemma. Launched, Nov 2, 2015.
  • Polymath11: proving Frankl's union-closed conjecture. Proposed Jan 21, 2016; launched Jan 29, 2016. Concluded, Jan 17, 2017.
  • Polymath12: proving Rota's conjecture. Proposed Feb 28, 2017.

Polymath-like projects

Proposed polymath projects

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

Additional links are very welcome.

Other links

Note on anonymous editing

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

Note on image uploads

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