Timeline for Would Euler's proofs get published in a modern math Journal, especially considering his treatment of the Infinite?
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| Apr 13, 2013 at 21:21 | comment | added | Igor Pak | @katz: There is a bit of misunderstanding. I actually read Euler's "infinite product" portion of "Introductio in analysin infinitorum". His starting point was divisibility of (a^n-b^n) by (a-b). He then substituted exponentials in place of a and b, and the rest by analogy. While it is indeed possible to justify that, Euler didn't think one needs this, which makes his potential paper submissions unacceptable in a modern research publication. That's all I was saying. | |
| Apr 10, 2013 at 15:02 | comment | added | Mikhail Katz | For Kanovei's paper see ams.org/mathscinet-getitem?mr=969566 | |
| Apr 10, 2013 at 15:01 | comment | added | Mikhail Katz | @Igor Pak: I don't think it is accurate to assert that "Euler's techniques by now are too well known and "standard" to be of interest..." Most of Euler's results are of course well understood, but his techniques, such as proof of the infinite product decomposition for the sine function, were properly interpreted only recently, through the work of Luxemburg, Kanovei, and others. The results are old, but the techniques are only beginning to be understood properly. | |
| Apr 10, 2013 at 14:32 | comment | added | Andy Putman | I'm very late to this party, but I think it is important to point out that Thurston had complete and rigorous proofs of all the results he claimed. He discussed them with many people, and whenever pressed was able to produce as many details as people needed. He just chose not to write papers containing all the details of his proofs. The paper that Greg Graviton refers to contains his justification for this decision. | |
| Sep 28, 2010 at 19:45 | comment | added | Greg Graviton | Thurston writes (in section 6) that his approach to rigor in the Geometrization program was intentional. He also argues that is was beneficial, for it mimics the way that people learn and live mathematics, which is actually quite different from what a stark formal proof or written paper might suggest. | |
| May 13, 2010 at 12:30 | comment | added | Lennart Meier | There also some famous mathematicians in modern times, whose standards of rigour and complete proofs do not please everyone. One example, which comes to my mind, is Thurston, where it took many years to fill his proofs in 'Geometry and Topology of 3-manifolds' with details and rigour (I don't know if it is done for everything). I've read that on these grounds, Serre was against to arward Thurston the Fields medal. Two other examples of mathematicians, who are more well-known for new ideas than complete and rigorous proofs are probably Gromov and Sullivan. | |
| May 12, 2010 at 19:41 | comment | added | Qiaochu Yuan | Perhaps a fairer interpretation of the question is about how a "modern-day Euler" would be received - someone whose education was up to date but whose sense of rigor was analogous to Euler's. One modern-day analogue I can think of is Feynman and the path integral. | |
| May 12, 2010 at 17:57 | history | answered | Igor Pak | CC BY-SA 2.5 |