Timeline for What problem in pure mathematics required solution techniques from the widest range of math sub-disciplines?
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| Jun 13, 2020 at 12:14 | history | edited | user44143 |
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| S Jun 19, 2017 at 23:04 | history | bounty ended | David G. Stork | ||
| S Jun 19, 2017 at 23:04 | history | notice removed | David G. Stork | ||
| Jun 17, 2017 at 16:38 | vote | accept | David G. Stork | ||
| Jun 17, 2017 at 16:23 | comment | added | David G. Stork | @Manfred Weis: Excellent suggestion. Even though the sub-disciplines may or may not overlap, the axioms may or may not be shared. I wonder, though, how easy it would be for those answering my question to list the axioms used in a given complex proof or result. I won't change this question (since there has been much refinement and I must award the reputation points soon), but perhaps there will be an opportunity for another question, focused on axioms. Thanks. | |
| Jun 17, 2017 at 7:16 | comment | added | Manfred Weis | @S.Carnahan one way to make the question perfectly meaningful, would be to count as different areas of mathematics, those that are based on different sets of axioms, leaving open the possibility, that individual axioms of different systems are equal like e.g. those related to ordering of elements. Asking for the number of different axioms, that a proof relies on, would however be an undisputable criterion. | |
| Jun 13, 2017 at 22:53 | comment | added | David G. Stork | @TimothyChow: Thanks... I'll look at Marguli's work (which others, outside of MathOverflow have recommended). I am not sure, though, that I'm sufficiently expert to single out Margulis' most "diverse" paper. | |
| Jun 13, 2017 at 22:30 | comment | added | Timothy Chow | Grigory Margulis is often cited as a mathematician who has a talent for bringing together techniques from apparently widely separated fields of mathematics in order to solve problems. I believe that Tits said that in the year he spent studying the work of Margulis, he learned more mathematics than in all the preceding years. I'm not competent to evaluate Margulis's work but you might want to look at this summary of his work for potential answers to your question: math.lsa.umich.edu/~lji/margulis.pdf | |
| Jun 13, 2017 at 7:51 | answer | added | ThiKu | timeline score: 4 | |
| Jun 13, 2017 at 6:12 | answer | added | Wlod AA | timeline score: 3 | |
| Jun 13, 2017 at 5:05 | answer | added | Ian Agol | timeline score: 12 | |
| S Jun 12, 2017 at 23:26 | history | bounty started | David G. Stork | ||
| S Jun 12, 2017 at 23:26 | history | notice added | David G. Stork | Canonical answer required | |
| Jun 12, 2017 at 19:00 | comment | added | David G. Stork | My view is that mathematics classification is more than human sociology as different sub-disciplines may employ different fundamental concepts: point, line, measure space, etc. have no relevance (as far as I know) to mathematical logic, and a logician can work without reference to them. One may apply results from logic to a problem in differential topology (say), but that doesn't mean the sub-field's differences are just sociology. Given the fundamental unity of physics, we nevertheless consider astro-physics as "distinct" from bio-physics, even though astro-biologists might rely on both. | |
| Jun 12, 2017 at 18:49 | history | edited | David G. Stork | CC BY-SA 3.0 |
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| Jun 12, 2017 at 18:49 | comment | added | Paul Siegel | @S.Carnahan If I go to the home page of a big math department there will be distinct research groups specializing in "Number Theory", "Analysis", "Topology", etc. There are journals which cater specifically to each of these areas, and the papers within are about different problems and use different techniques. And these papers are by and large presented by different experts at different conferences. All of these are objective, factual statements. It is highly doubtful that these classifications are rooted in anything more that human sociology, but this question doesn't require them to be. | |
| Jun 12, 2017 at 17:20 | history | edited | David G. Stork | CC BY-SA 3.0 |
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| Jun 12, 2017 at 17:12 | history | edited | David G. Stork | CC BY-SA 3.0 |
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| Jun 12, 2017 at 10:24 | answer | added | მამუკა ჯიბლაძე | timeline score: 9 | |
| Jun 12, 2017 at 8:18 | answer | added | Lennart Meier | timeline score: 21 | |
| Jun 11, 2017 at 23:17 | comment | added | S. Carnahan♦ | I don't speak for John Pardon, but I think it is safe to remove (1) all references to Mathematics Subject Classification as well as the ArXiv, (2) all defenses of the use of MSC as an objective measure, (3) all references to objectivity and the claim that this question is not based on opinion. That would make your question more concise and, at least to me, more interesting. You also seem to have an implicit question about how much breadth is changing over time, by reference to an analogous phenomenon in technology, and perhaps that can be made more explicit. | |
| Jun 11, 2017 at 19:19 | history | edited | David G. Stork | CC BY-SA 3.0 |
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| Jun 11, 2017 at 19:18 | comment | added | David G. Stork | @JohnPardon: Interesting... I added the reference to arxiv solely based on Paul Siegel's comment and am happy to take it out. | |
| Jun 11, 2017 at 18:56 | comment | added | John Pardon | I think this is a good question and should stay open, but it would be much better if it were formulated without reference to "the most msc or arxiv subject tags" (which, taken literally, seems unlikely to be an interesting or useful measure of mathematical breadth). | |
| Jun 11, 2017 at 18:21 | history | edited | David G. Stork | CC BY-SA 3.0 |
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| Jun 11, 2017 at 15:06 | history | edited | David G. Stork | CC BY-SA 3.0 |
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| Jun 10, 2017 at 21:13 | answer | added | Alain Valette | timeline score: 17 | |
| Jun 10, 2017 at 20:12 | review | Close votes | |||
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| Jun 10, 2017 at 19:06 | history | reopened |
Alexander Chervov Henry.L Leo Alonso Gro-Tsen Will Sawin |
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| Jun 10, 2017 at 15:56 | history | edited | David G. Stork | CC BY-SA 3.0 |
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| Jun 10, 2017 at 15:46 | history | edited | David G. Stork | CC BY-SA 3.0 |
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| Jun 10, 2017 at 15:36 | review | Reopen votes | |||
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| Jun 10, 2017 at 12:48 | history | closed |
Felipe Voloch Steven Landsburg Will Jagy Alexandre Eremenko Andrés E. Caicedo |
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| Jun 10, 2017 at 9:47 | answer | added | Libli | timeline score: 36 | |
| Jun 10, 2017 at 9:22 | answer | added | S. Carnahan♦ | timeline score: 25 | |
| Jun 10, 2017 at 9:01 | history | made wiki | Post Made Community Wiki by S. Carnahan♦ | ||
| Jun 10, 2017 at 9:01 | comment | added | S. Carnahan♦ | I disagree with the claim that this question is fact-based in any meaningful way, since quantitative measures would rely on rather arbitrarily chosen divisions between mathematical areas. On the other hand, we could just use it as an opportunity to list our favorite theorems whose proofs involve a large number of unexpected techniques. For this purpose, I am imposing "community wiki" mode. | |
| Jun 10, 2017 at 7:43 | comment | added | Paul Siegel | @alexandreeremenko: A perfectly reasonable objective interpretation of this question is "What math paper's citation list has the largest total number of distinct arxiv subject tags?" I don't expect anyone will answer the question this way, but it is rooted in something factual. | |
| Jun 10, 2017 at 7:35 | comment | added | Paul Siegel | Regarding the analogy with technology: a really important driver of progress is that the foundations of mathematics are periodically rewritten to organize knowledge more efficiently. As a result sub-disciplines are created, destroyed, and reorganized to accommodate important results, and so when an important result spans a large number of disciplines it is often taken as a sign that the foundations need to be revisited. A counterpart of this in technology might be something like docker containers, which reorganized and consolidated the various tools people used to deploy software. | |
| Jun 10, 2017 at 7:28 | comment | added | Alexandre Eremenko | I disagree with the statement that this question has any objective meaning: all possible answers will be based on an opinion. | |
| Jun 10, 2017 at 7:09 | answer | added | Paul Siegel | timeline score: 27 | |
| Jun 10, 2017 at 4:57 | history | edited | David G. Stork | CC BY-SA 3.0 |
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| Jun 10, 2017 at 1:47 | review | Close votes | |||
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| Jun 10, 2017 at 1:09 | comment | added | David G. Stork | @PaulGarrett: Thanks for your note. I'm happy to entertain problems that use the most modern understanding or definition of number theory. Given that, what such problem would require a very broad range of techniques? Note that an acceptable problem might be posed in geometry (say), but require a wide range of techniques from modern number theory. | |
| Jun 10, 2017 at 0:58 | comment | added | paul garrett | I think a more genuine, sophisticated, professional version of "number theory" may use/require the greatest range of other bits of mathematics for substantial success. (Part of the point is that an entry-level or elementary notion of "number theory" is typically 200 years out of date, or based on inaccurate if popular premises... seeming to make the subject a special case of elementary abstract algebra and elementary combinatorics... which will not get anyone very much farther than Euler 250 years ago...) Is such a response of interest? | |
| Jun 10, 2017 at 0:32 | history | edited | David G. Stork | CC BY-SA 3.0 |
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| Jun 10, 2017 at 0:06 | history | asked | David G. Stork | CC BY-SA 3.0 |