91:. This project is built upon the same idea of the Polymath project that massive collaboration in mathematics is possible and possibly quite fruitful. However, this is specifically aimed at only high school and college students with a goal of creating "a specific opportunity for the upcoming generation of math and science researchers." The problems are original research and unsolved problems in mathematics. All high school and college students from around the world with advanced background of mathematics are encouraged to participate. Older participants are welcomed to participate as mentors and encouraged not to post solutions to the problems. The first Crowdmath project began on March 1, 2016.
159:, one of the participants of Polymath5, solved the problem in a pair of papers. One paper proved an averaged form of the Chowla and Elliott conjectures, making use of recent advances in analytic number theory concerning correlations of values of multiplicative functions. The other paper showed how this new result, combined with some arguments discovered by Polymath5, were enough to give a complete solution to the problem. Thus, Polymath5 ended up making a significant contribution to the solution.
123:
After seven weeks, Gowers announced on his blog that the problem was "probably solved", though work would continue on both Gowers's thread and Tao's thread well into May 2009, some three months after the initial announcement. In total over 40 people contributed to the
Polymath1 project. Both threads
108:. As the project took form, two main threads of discourse emerged. The first thread, which was carried out in the comments of Gowers's blog, would continue with the original goal of finding a combinatorial proof. The second thread, which was carried out in the comments of
46:'s blog when he posted a problem and asked his readers to post partial ideas and partial progress toward a solution. This experiment resulted in a new answer to a difficult problem, and since then the Polymath Project has grown to describe a particular
70:
of his blog. Along with the math problem itself, Gowers asked a question which was included in the title of his blog post, "is massively collaborative mathematics possible?" This post led to his creation of the
Polymath Project.
616:
1007:
Barany, Michael J. (2010). "'ut this is blog maths and we're free to make up conventions as we go along': Polymath1 and the modalities of 'massively collaborative mathematics'".
535:. From the Polymath14 project. The journal and arXiv versions use the Polymath pseudonym, though the author names appear in the journal's table of contents and on the DOI page.
539:
Polymath, D. H. J. (2019), "Effective approximation of heat flow evolution of the
Riemann $ \xi$ function, and a new upper bound for the de Bruijn-Newman constant",
104:
The initial proposed problem for this project, now called
Polymath1 by the Polymath community, was to find a new combinatorial proof to the density version of the
42:
problems by coordinating many mathematicians to communicate with each other on finding the best route to the solution. The project began in
January 2009 on
194:(the least gap between primes with m-1 primes between them that is attained infinitely often), by combining the Polymath8a results with the techniques of
356:. From the Polymath4 project. Although the journal editors required the authors to use their real names, the arXiv version uses the Polymath pseudonym.
467:
66:
by choosing an important unsolved mathematical problem and issuing an invitation for other people to help solve it collaboratively in the
717:
155:. It was active for much of 2010 and had a brief revival in 2012, but did not end up solving the problem. However, in September 2015,
1088:. Guest Editors: Harry Halpin and Alexandre Monnin. Volume 43, Issue 4, pp 480–498, July 2012, DOI: 10.1111/j.1467-9973.2012.01758.x
739:
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1136:
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625:
206:
Both components of the
Polymath8 project produced papers, one of which was published under the pseudonym D. H. J. Polymath.
761:
1116:
642:
17:
179:
on the least gap between consecutive primes that was attained infinitely often, by developing the techniques of
1141:
195:
124:
of the
Polymath1 project have been successful, producing at least two new papers to be published under the
152:
401:
Polymath, D.H.J. (2014), "Variants of the
Selberg sieve, and bounded intervals containing many primes",
1146:
459:
321:
105:
878:
113:
88:
220:, Bolyai Soc. Math. Stud., vol. 21, János Bolyai Math. Soc., Budapest, pp. 689–753,
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Proceedings of the 6th
International Symposium on Wikis and Open Collaboration (WikiSym '10)
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Polymath8b, "Bounded intervals with many primes", was a project to improve the value of H
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Proceedings of the SIGCHI Conference on Human
Factors in Computing Systems (CHI '11)
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198:. This project concluded with a bound of H = 246, as well as additional bounds on H
175:
Polymath8a, "Bounded gaps between primes", was a project to improve the bound H = H
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460:"The "bounded gaps between primes" Polymath project: A retrospective analysis"
433:
259:
Polymath, D. H. J. (2012), "A new proof of the density Hales-Jewett theorem",
1130:
946:"Variants of the Selberg sieve, and bounded intervals containing many primes"
591:
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Polymath, D. H. J. (2014), "New equidistribution estimates of Zhang type",
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117:
80:
308:
156:
109:
39:
780:
1092:. Reprinted in the collection: Harry Halpin and Alexandre Monnin (Eds)
1080:
Stefaneas Petros, Vandoulakis Ioannis "The Web as a Tool for Proving",
666:
Gowers, T.; Nielsen, M. (2009). "Massively collaborative mathematics".
84:
498:
Polymath, D. H. J. (2018), "Homogeneous length functions on groups",
216:
Polymath, D. H. J. (2010), "Density Hales-Jewett and Moser numbers",
168:
125:
858:
Polymath (2009). "A new proof of the density Hales-Jewett theorem".
687:
50:
process of using an online collaboration to solve any math problem.
553:
512:
167:
The Polymath8 project was proposed to improve the bounds for small
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226:
1096:. Wiley-Blackwell, 2014, 149–167. DOI: 10.1002/9781118700143.ch10
891:
Polymath (2014). "New equidistribution estimates of Zhang type".
27:
Series of public experiments on mass collaboration in mathematics
1089:
1111:
718:""Crowdmath" project for high school students opens on March 1"
1122:
An introduction to the Polymath Project for non-mathematicians
837:
Polymath (2010). "Density Hales-Jewett and Moser numbers".
63:
620:. Princeton NJ: Princeton University Press. pp. 1–3.
1094:
Philosophical Engineering: Toward a Philosophy of the Web
800:
Polymath (2012). "Deterministic methods to find primes".
617:
Reinventing discovery: the new era of networked science
74:
151:
This project was set up in order to try to solve the
112:'s blog, focused on calculating bounds on density of
183:. This project concluded with a bound of H = 4,680.
762:"A combinatorial approach to density Hales-Jewett"
643:"Is massively collaborative mathematics possible?"
131:, where the initials refer to the problem itself (
1128:
319:(2012), "Deterministic methods to find primes",
307:
468:Newsletter of the European Mathematical Society
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781:"The Polymath project: scope of participation"
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79:Since its inception, it has now sponsored a "
1107:Current central hub of the Polymath Project
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75:Projects for high school and college
1050:. New York: ACM. pp. 1865–74.
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38:to solve important and difficult
83:" project in collaboration with
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576:. From the Polymath15 project.
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1:
1090:http://web-and-philosophy.org
1011:. New York: ACM. Article 10.
597:
397:. From the Polymath8 project.
304:. From the Polymath1 project.
255:. From the Polymath1 project.
1137:Projects established in 2009
547:(3): 67 pp. (paper no. 31),
236:10.1007/978-3-642-14444-8_22
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893:Algebra & Number Theory
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500:Algebra & Number Theory
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362:Algebra & Number Theory
285:10.4007/annals.2012.175.3.6
10:
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322:Mathematics of Computation
981:10.1186/s40687-014-0012-7
614:Nielsen, Michael (2012).
564:10.1007/s40687-019-0193-1
434:10.1186/s40687-014-0012-7
171:. It has two components:
153:Erdős discrepancy problem
53:
34:is a collaboration among
523:10.2140/ant.2018.12.1773
1056:10.1145/1978942.1979213
1017:10.1145/1832772.1832786
923:10.2140/ant.2014.8.2067
393:10.2140/ant.2014.8.2067
89:Art of Problem Solving
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1112:Polymath Project blog
262:Annals of Mathematics
190:further, as well as H
120:for low dimensions.
114:Hales–Jewett numbers
106:Hales–Jewett theorem
972:2014arXiv1407.4897P
915:2014arXiv1402.0811P
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491:2014arXiv1409.8361P
425:2014arXiv1407.4897P
384:2014arXiv1402.0811P
169:gaps between primes
329:(278): 1233–1246,
1147:Research projects
1084:. Special Issue:
1065:978-1-4503-0228-9
1026:978-1-4503-0056-8
944:Polymath (2014).
879:Polymath8 project
674:(7266): 879–881.
627:978-0-691-14890-8
313:Croot, Ernest III
265:, Second Series,
218:An irregular mind
129:D. H. J. Polymath
60:social experiment
18:Polymath projects
16:(Redirected from
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