Polymath project

The Polymath Project is a collaboration between mathematicians to solve important and difficult math problems by coordinating many mathematicians communicating with each other to find the best way to solve them. The project began in January 2009 on Timothy Gower's blog, where he presented a problem and asked his readers to post partial ideas and partial progress toward a solution. This experiment led to a new answer to a difficult problem, and since then the Polymath project has grown. It describes a specific process of online collaboration to solve a math problem.

origin

In January 2009, Gowers decided to start a social experiment on his blog by choosing an important unsolved math problem and inviting other people to solve it together in the comments section of his blog. Along with the math problem itself, Gowers asked a question that was included in the title of his blog post, “ is massively collaborative mathematics possible? ” That post led to his formation of the Polymath project. The word polymath comes from the Greek and describes a versatile person. According to its word components poly and math , however, it can also be interpreted as "mathematics by many".

Problems solved

Polymath1

The problem originally proposed for this project, now called Polymath1 by the Polymath community, was to find a new combinatorial proof for the density version of the Hales-Jewett theorem . As the project took shape, two threads of discussion emerged. The first one, kept in the comments on Gower's blog, would go ahead with the original goal of finding combinatorial proof. The second, done in the comments of Terence Tao's blog, focused on calculating the boundaries of the density of Hales-Jewett numbers and Moser numbers for low dimensions.

After seven weeks, Gowers announced on his blog that the issue was "likely resolved", although work on Gowers Thread and Taos Thread continued until May 2009, about three months after the initial announcement. In total, over 40 people contributed to the Polymath1 project. Both threads of Polymath1 project were successful, there were two new papers written under the pseudonym DHJ Polymath ,, the initials refer to the problem ( d ensity H ales- J ewett).

Polymath5

This project was set up to solve the Erdős discrepancy problem. It was very active in 2010 and had a brief revival in 2012 but couldn't be resolved in the end. But in September 2015, Terence Tao, one of the participants in Polymath5, was able to solve the problem. A paper proved the averaged form of the Chowla-Elliott conjectures and took advantage of recent advances in analytical number theory on correlations of values of multiplicative functions. Another paper showed how this new finding, combined with some arguments discovered by Polymath5, was enough to give a complete solution to the problem. Polymath5 made a significant contribution to the solution.

Polymath8

The Polymath8 project was proposed to improve the boundaries of small gaps between prime numbers. It has two components: Polymath8a and Polymath8b. Both components of the Polymath8 project were successful, producing two new papers which were published under the pseudonym DHJ Polymath .

Web links

Individual evidence

^ ^A ^b Michael Nielsen: Reinventing discovery: the new era of networked science . Princeton University Press, Princeton NJ 2012, ISBN 978-0-691-14890-8 , pp. 1-3.
↑ Tim Gowers: Is massively collaborative mathematics possible? . In: Gowers' weblog . Retrieved March 30, 2009.
^ T. Gowers, M. Nielsen: Massively collaborative mathematics . In: Nature . 461, No. 7266, 2009, pp. 879-881. bibcode : 2009Natur.461..879G . doi : 10.1038 / 461879a . PMID 19829354 .
^ Tim Gowers: A combinatorial approach to density Hales-Jewett . In: Gower's weblog . February 1, 2009.
↑ Michael Nielsen: The Polymath project: scope of participation . March 20, 2009. Retrieved March 30, 2009.
^ Polymath: Deterministic methods to find primes. arXiv , 2010, accessed June 18, 2017 .
^ Polymath: Density Hales-Jewett and Moser numbers. arXiv , 2010, accessed June 18, 2017 .
^ Polymath: A new proof of the density Hales-Jewett theorem. arXiv , 2009, accessed June 18, 2017 .
^ Polymath8 project .
^ Polymath: New equidistribution estimates of Zhang type . In: Algebra and Number Theory . 2014. doi : 10.2140 / ant.2014.8.2067 .
^ Polymath: Variants of the Selberg sieve, and bounded intervals containing many primes . In: Research in the Mathematical Sciences . 2014. doi : 10.1186 / s40687-014-0012-7 .

[reinventing-1] A ^b Michael Nielsen: Reinventing discovery: the new era of networked science . Princeton University Press, Princeton NJ 2012, ISBN 978-0-691-14890-8 , pp. 1-3.

[2] Tim Gowers: Is massively collaborative mathematics possible? . In: Gowers' weblog . Retrieved March 30, 2009.

[3] T. Gowers, M. Nielsen: Massively collaborative mathematics . In: Nature . 461, No. 7266, 2009, pp. 879-881. bibcode : 2009Natur.461..879G . doi : 10.1038 / 461879a . PMID 19829354 .

[4] Tim Gowers: A combinatorial approach to density Hales-Jewett . In: Gower's weblog . February 1, 2009.

[5] Michael Nielsen: The Polymath project: scope of participation . March 20, 2009. Retrieved March 30, 2009.

[6] Polymath: Deterministic methods to find primes. arXiv , 2010, accessed June 18, 2017 .

[7] Polymath: Density Hales-Jewett and Moser numbers. arXiv , 2010, accessed June 18, 2017 .

[8] Polymath: A new proof of the density Hales-Jewett theorem. arXiv , 2009, accessed June 18, 2017 .

[9] Polymath8 project .

[10] Polymath: New equidistribution estimates of Zhang type . In: Algebra and Number Theory . 2014. doi : 10.2140 / ant.2014.8.2067 .

[11] Polymath: Variants of the Selberg sieve, and bounded intervals containing many primes . In: Research in the Mathematical Sciences . 2014. doi : 10.1186 / s40687-014-0012-7 .