Timeline for What are some correct results discovered with incorrect (or no) proofs?
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| Jan 2, 2025 at 15:01 | answer | added | Ben Golub | timeline score: 4 | |
| Jul 25, 2022 at 16:23 | comment | added | LSpice | I am not sure whether @JoséHdz.Stgo.'s link in a comment was meant to point to a specific part of the question, but here's a clickable link to the referenced question: Nice proof of the Jordan curve theorem?. | |
| Jul 25, 2022 at 13:36 | answer | added | Michael_1812 | timeline score: 2 | |
| Jul 25, 2022 at 4:31 | answer | added | Sam Hopkins♦ | timeline score: 2 | |
| Feb 21, 2014 at 3:08 | history | edited | Andrés E. Caicedo |
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| Jun 9, 2013 at 20:01 | answer | added | Margaret Friedland | timeline score: 1 | |
| Jun 8, 2013 at 21:42 | answer | added | Amir Asghari | timeline score: 1 | |
| May 31, 2013 at 18:28 | comment | added | Zsbán Ambrus | The earlier question mathoverflow.net/questions/35468/… is very similar. | |
| Apr 7, 2011 at 17:23 | answer | added | anonymous | timeline score: 11 | |
| Apr 5, 2011 at 16:55 | answer | added | quim | timeline score: 1 | |
| Apr 4, 2011 at 18:30 | answer | added | anonymous | timeline score: 2 | |
| S Apr 4, 2011 at 13:24 | answer | added | David Harris | timeline score: -2 | |
| S Apr 4, 2011 at 13:24 | history | made wiki | Post Made Community Wiki | ||
| Apr 3, 2011 at 17:58 | answer | added | Vladimir Kalitvianski | timeline score: -2 | |
| Nov 14, 2010 at 14:18 | answer | added | Andrey Rekalo | timeline score: 27 | |
| Nov 5, 2010 at 15:14 | answer | added | Abhishek Parab | timeline score: 3 | |
| Nov 5, 2010 at 14:07 | answer | added | Franz Lemmermeyer | timeline score: 18 | |
| Nov 5, 2010 at 8:07 | answer | added | Anixx | timeline score: 48 | |
| Jul 8, 2010 at 21:16 | answer | added | Andy Putman | timeline score: 10 | |
| Jun 22, 2010 at 13:01 | answer | added | Franz Lemmermeyer | timeline score: 6 | |
| Jun 11, 2010 at 21:01 | answer | added | Daniel Asimov | timeline score: 20 | |
| Jun 11, 2010 at 19:25 | answer | added | Jack Lee | timeline score: 47 | |
| Jun 11, 2010 at 17:25 | answer | added | Roland Bacher | timeline score: 3 | |
| Jun 11, 2010 at 15:31 | answer | added | Someone | timeline score: 10 | |
| Jun 11, 2010 at 13:18 | answer | added | Diego Matessi | timeline score: 6 | |
| Jun 11, 2010 at 12:32 | comment | added | Steve Huntsman | I would argue that (although it came after the drive for rigor had already started thanks to Cantor, Weierstrass, et al.) the dawn of modern statistical and quantum physics had a great deal to do with the consolidation of rigor throughout mathematics. Indeed, ergodic theory and functional analysis owe a great deal to these disciplines, and neither could have existed in the time of (say) Euler because the approach to mathematics was different. | |
| Jun 11, 2010 at 12:28 | comment | added | Steve Huntsman | In response to the clarification: I would argue that physical intuition and lack of foundations are often very strongly connected. Mathematics is not the subject it once was. In the 18th and early 19th centuries, just about every mathematician could be regarded as a theoretical physicist in some sense. Because of the "unreasonable effectiveness of mathematics", the need for rigor was diluted here precisely because the physics supplied well-behaved problems. | |
| Jun 11, 2010 at 9:06 | answer | added | Andrei Halanay | timeline score: 0 | |
| Jun 11, 2010 at 8:35 | comment | added | José Hdz. Stgo. | @Emerton: Point taken, Sire. Nevertheless, I'd like to add, just to set the record straight, that I never tried to imply that the claim was original with Hales. It was clear that by actually looking at the paper the interested reader was to find out whose opinion it was. | |
| Jun 11, 2010 at 8:18 | answer | added | Victor Protsak | timeline score: 30 | |
| Jun 11, 2010 at 5:59 | comment | added | Emerton | A further remark: I think that is important to distinguish between polishing an argument, or perhaps interpreting it in terms of contemporary language and formalism, which will almost always be required when reading arguments (especially subtle ones) from 100 or more years ago, and genuinely incomplete arguments. As an example of the latter, one can think of Riemann's arguments with the Dirichlet principle, where this result was simply taken as an axiom. Additional work was genuinely required to validate the Dirichlet principle, and thus complete Riemann's arguments. | |
| Jun 11, 2010 at 5:54 | comment | added | Emerton | Dear J.H.S., The quotation you give is not from Hales, but is a quote within Hales's manuscript, that he attributes to Reeken. Hales himself makes even stronger assertions regarding the correctness of Jordan's argument. If an argument is correct modulo polishing the presentation, then I think it is fair to say that it is correct. (I should say that I haven't read Jordan's argument myself, but I have confidence in Hales's evaluation.) | |
| Jun 11, 2010 at 5:36 | answer | added | Michael Greinecker | timeline score: 64 | |
| Jun 11, 2010 at 4:40 | answer | added | Andy Putman | timeline score: 38 | |
| Jun 11, 2010 at 4:28 | comment | added | José Hdz. Stgo. | Doesn't the previous assertion hint at the fact that the modern standards will never regard Jordan's argument as a proof in its own right? | |
| Jun 11, 2010 at 4:18 | history | edited | John Stillwell | CC BY-SA 2.5 |
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| Jun 11, 2010 at 4:06 | comment | added | José Hdz. Stgo. | @Stillwell: Stand corrected? But you never implied that Jordan's proof was wrong. Your remark "the first rigorous proof was found some decades later than Jordan's attempt" is as true as it gets. According to an asseveration that appears in the Hales manuscript mentioned here (mathoverflow.net/questions/8521/…), "Jordan's proof is esentially correct... Jordan's proof does not present the details in a satisfactory way. But the idea is right and with some polishing the proof would be impeccable". | |
| Jun 11, 2010 at 3:59 | history | edited | John Stillwell | CC BY-SA 2.5 |
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| Jun 11, 2010 at 3:27 | answer | added | paul Monsky | timeline score: 19 | |
| Jun 11, 2010 at 3:18 | comment | added | Steve Huntsman | My series of very brief answers is essentially intended to convey the fact that this question (as currently stated) does not admit any reasonably navigable set of answers. As stated, conjectures that have been proven could be interpreted as valid answers. And as one answer points out, much of theoretical physics supplies answers as well. | |
| Jun 11, 2010 at 3:09 | comment | added | John Stillwell | @Emerton. I stand corrected. Maybe Jordan's proof should be in the same category as Heegner's: thought to be incorrect, but essentially correct when properly understood. | |
| Jun 11, 2010 at 2:49 | comment | added | Emerton | In Tom Hales account of Jordan's proof, he states that there is essentially no problem with Jordan's original proof, and that claims to the contrary are themselves wrong or based on misunderstandings. As far as I can tell, he is correct, and there is no reason to impugn Jordan's original proof. (See "Jordan's proof of the Jordan curve theorem" at math.pitt.edu/~thales/papers ) | |
| Jun 11, 2010 at 2:44 | answer | added | jeremy | timeline score: 11 | |
| Jun 11, 2010 at 2:35 | answer | added | Steve Huntsman | timeline score: 6 | |
| Jun 11, 2010 at 2:31 | answer | added | Steve Huntsman | timeline score: 22 | |
| Jun 11, 2010 at 2:28 | answer | added | Steve Huntsman | timeline score: -1 | |
| Jun 11, 2010 at 2:27 | answer | added | Steve Huntsman | timeline score: 0 | |
| Jun 11, 2010 at 2:23 | answer | added | Timothy Chow | timeline score: 11 | |
| Jun 11, 2010 at 2:16 | answer | added | Steve Huntsman | timeline score: 4 | |
| Jun 11, 2010 at 1:01 | comment | added | Steve Huntsman | I was thinking also of stuff like Witten. | |
| Jun 11, 2010 at 0:44 | answer | added | Andrey Rekalo | timeline score: 24 | |
| Jun 11, 2010 at 0:35 | answer | added | Guy Katriel | timeline score: 15 | |
| Jun 11, 2010 at 0:31 | answer | added | Richard Stanley | timeline score: 37 | |
| Jun 11, 2010 at 0:19 | comment | added | John Stillwell | @Steve. I guess the Jordan curve theorem is a nice example of physical intuition. | |
| Jun 11, 2010 at 0:12 | history | edited | John Stillwell | CC BY-SA 2.5 |
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| Jun 11, 2010 at 0:04 | answer | added | Gerhard Paseman | timeline score: 14 | |
| Jun 10, 2010 at 23:54 | comment | added | Steve Huntsman | Physical motivation and/or intuition. | |
| Jun 10, 2010 at 23:50 | answer | added | Adrian Barquero-Sanchez | timeline score: 17 | |
| Jun 10, 2010 at 23:44 | history | asked | John Stillwell | CC BY-SA 2.5 |