Timeline for Are there mistakes in the proof of FLT?
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11 events
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| Nov 24, 2021 at 20:26 | comment | added | Kevin Buzzard | In fact I found it interesting that this issue with Gross' work was very well known -- it is explicitly talked about in the introduction to his Duke paper on companion forms. Then Wiles used it and nobody seemed to make a fuss at all. And then the careful Taylor made sure that things were OK anyway... | |
| Nov 23, 2021 at 16:27 | comment | added | Olivier | Thanks a lot. The connection to Gross is exactly the kind of things I had in mind. @TimothyChow I do believe that most papers contain significant yet easily solved problems, but I also absolutely believe (know) that some papers don't and, in particular considering the level of scrutiny they received, it seemed entirely possible to me that those under discussion were in that category. | |
| Nov 23, 2021 at 15:15 | comment | added | Asaf Karagila♦ | @TimothyChow Well, to be fair, I'm way too young to have taken part of the actual debate. It's just my impression from all the stories and all the set theorists that talked about it around me over the years (of which there were plenty). | |
| Nov 23, 2021 at 15:13 | comment | added | Timothy Chow | @AsafKaragila My take on it was that the debate was a linguistic one, centered on what it means to "use" an axiom. See this MO question for more details. Experts reading the proof of FLT could "see" that universes were irrelevant; less expert readers got worried when they saw citations of (e.g.) SGA4 as a black box. | |
| Nov 23, 2021 at 10:54 | comment | added | Asaf Karagila♦ | The buzz from logicians was never "oh no, Wiles used inaccessible cardinals!", it was always "Oh, yes! Finally people just use inaccessible cardinals without fussing about them!!!! Woooo!!!!" | |
| Nov 22, 2021 at 22:28 | comment | added | Timothy Chow | Fascinating! Let me remark that, according to my reading of Oliver, he is not asking if there are any serious problems with the proof, nor he is even asking for anything "different to the usual kind of stuff which shows up in maths papers." Rather, he seems inclined to believe that the papers of almost everyone (except maybe Serre?) contain technically incorrect statements that the author(s) could readily correct upon demand, but that are not completely trivial. And he wants to know if his belief is correct for these papers. | |
| Nov 22, 2021 at 22:15 | comment | added | Kevin Buzzard | Probably also worth saying that if you'd asked me "is there a mistake in the proof of the Artin-Tate Lemma in Atiyah--Macdonald" then I would have said "no it's absolutely fine" but then one of my undergrads formalised it in Lean and this happened twitter.com/XenaProject/status/1308693991144206336 . So take everything I say about no errors with a pinch of salt! Humans are fallible! | |
| Nov 22, 2021 at 21:59 | comment | added | Kevin Buzzard | Of course if we formalise the Wiles and TW papers I might have to revise my answer later :P It's probably also worth mentioning that by 1996 everyone was reading Darmon-Diamond-Taylor, which was a summary of the proof + refinements which had shown up shortly afterwards. And that paper has a false proof in ;-) I spotted the issue after the paper had gone to press. But it's OK! The experts know how to get around it. So that's alright then. | |
| Nov 22, 2021 at 21:57 | comment | added | Kevin Buzzard | I don't believe that the comments I had with Ken represented issues that were any different to the usual kind of stuff which shows up in maths papers. When I was in Berkeley I knew a lot of the number theory involved but less of the arithmetic geometry, and it was there where I'd typically get stuck. I remember having to plough through a bunch of SGA7 :-/ But it's not unreasonable for a paper from the 80s to assume some familiarity with SGA7 I guess. | |
| Nov 22, 2021 at 14:03 | comment | added | Timothy Chow | Excellent answer. But let me ask this. The revision of the proof of the Kepler conjecture lists mistakes—a major one in Section 8, and lots of minor ones in Section 9 (page 35). If I understand Oliver correctly, he doesn't count the one-liners in Section 9, but he might count the longer entries (that take a paragraph or two). I gather that for FLT there is nothing as big as the gap of Section 8, but would any of the things you (as a postdoc) asked Ribet about be included in a meticulous list of errata, and require more than a single line? | |
| Nov 21, 2021 at 16:48 | history | answered | Kevin Buzzard | CC BY-SA 4.0 |