Timeline for Have there been any updates on Mochizuki's proposed proof of the abc conjecture?
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22 events
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| Apr 29, 2020 at 18:52 | comment | added | jjcale | Maybe this preprint of Taylor Dupuy and Anton Hilado is interesting : "THE STATEMENT OF MOCHIZUKI’S COROLLARY 3.12, INITIAL THETA DATA, AND THE FIRST TWO INDETERMINACIES", arxiv.org/pdf/2004.13228.pdf . | |
| Apr 15, 2020 at 22:41 | comment | added | santker heboln | The situation is pretty clear. Within Japan the abc conjecture is now a Theorem. Outside of Japan it is still a conjecture. So if you want to publish counterexamples this is only possible in non-Japanese Journals. Corollaries on the other hand can only appear in Japanese Journals. I am glad this entire matter is finally settled. | |
| Apr 10, 2020 at 14:17 | comment | added | Timothy Chow | The above link doesn't work properly now that the comments have spilled over to a second page. Use this link instead to go directly to Scholze's initial comment. | |
| Apr 6, 2020 at 16:18 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Apr 6, 2020 at 14:40 | comment | added | Timothy Chow | On Woit's blog, there is a very interesting comment by Peter Scholze that he has made in the light of the current press coverage. | |
| Apr 6, 2020 at 10:55 | comment | added | Thomas Sauvaget | @none: not at all an expert either, but back in late october (2019) the very long remark 3.9.5 (over 17 pages) was added to IUTpartIII and refered to at several places. It seems to be meant to adress details of the proof of corollary 3.12. Could this be what convinced the referee? | |
| Apr 6, 2020 at 9:33 | history | edited | manifold | CC BY-SA 4.0 |
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| Apr 4, 2020 at 12:04 | comment | added | Will Sawin | @none I'm not an expert and I only looked very quickly, but my impression was the new information was less than contained in Mochizuki's response to Scholze/Stix. As you (hopefully) already know, there was nothing that can be described as an attempt to fix the problems in that response, but rather a a series of arguements-by-analogy that the problem does not exist. | |
| Apr 4, 2020 at 3:39 | comment | added | none | @WillSawin do the new versions of the papers at least attempt to fix the problems called out in the Scholze/Stix report? MoziburUllah, the string theory comparison is bogus because physics papers are allowed some mathematical unsoundness but math papers are not. A mathematically unsound physics paper can still be interesting if it somehow describes nature in a new way, like QFT did. But math like this isn't about describing nature, so if it's unsound it's just not interesting. | |
| Apr 4, 2020 at 3:31 | comment | added | Mozibur Ullah | @Lucia: I happen to think that string theory is a reasonable idea - I'm just not interested in the hype; the point I'm making is that at the frontiers of science its difficult to make judgement calls. | |
| Apr 4, 2020 at 3:25 | comment | added | Lucia | @MoziburUllah: No one wants to be like string theory! And math doesn't have to go down that path. Anyway, I'm done with responding. | |
| Apr 4, 2020 at 3:15 | comment | added | Mozibur Ullah | @Lucia: Have you heard about String Theory? How many thousands of man-hours and hundreds of doctorates have been devoted to that theory without there being a shred of real evidence of its truth, physically speaking? | |
| Apr 4, 2020 at 2:00 | comment | added | Lucia | @MoziburUllah: You don't really know what you're talking about here. No one in the number theory community believes this result -- apart from acolytes of Mochizuki in Nottingham and Japan. And I don't think this sorry state of affairs has been seen in any of the other breakthroughs in mathematics that have happened over the last 20 years -- many of them quite complicated. | |
| Apr 4, 2020 at 1:46 | comment | added | Mozibur Ullah | @Lucia: I don't think the paper is questionable in any easy or simple way. That the paper is being published after eight years shows just how complex and difficult certain parts of modern mathematics has become. Moreover, the editors and referees are in a very difficult position themselves when the mathematical community as a whole can't come to a consensus. | |
| Apr 4, 2020 at 1:33 | comment | added | Lucia | @MoziburUllah: Journals don't publish questionable papers and hope that the community sorts itself out. At least no decent journal would willingly choose to do that. Something seriously wrong has happened here, and I can't imagine any editorial board being happy with this. This is not to say that journals won't make mistakes -- that'll of course happen -- just that no journal would/should walk into a situation like this. | |
| Apr 4, 2020 at 1:32 | comment | added | Mozibur Ullah | @Lucia: I'm not claiming that I can understand Mochizukis proof, nor am I an expert in number theory but I do understand English and what the article in Nature is saying is plain enough. | |
| Apr 4, 2020 at 1:26 | comment | added | Mozibur Ullah | ... [moreover] In the world of mathematics, a journal’s seal of approval is often not the end of the peer-review process. An important result only truly becomes an accepted theorem after the community has reached a consensus that it is correct, and this can go on for years after a paper’s official publication.' It looks like this will be case for this 'proof'. | |
| Apr 4, 2020 at 1:25 | comment | added | Mozibur Ullah | @Lucia: According to the link to Nature: 'mathematicians often publish papers in journals where they are editors. As long as the authors recuse themselves from the peer-review process ... and Mochizuki had recused himself from the review process, and had not attended any of the editorial board meetings about the paper. The journal has previously published papers from other members of the journals’ editorial board ... | |
| Apr 3, 2020 at 23:50 | history | edited | manifold | CC BY-SA 4.0 |
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| Apr 3, 2020 at 22:52 | comment | added | Lucia | What a disgrace! | |
| Apr 3, 2020 at 21:26 | comment | added | Will Sawin | A new version of IUT 2 and IUT 3 was posted to Mochizuki's website on March 22, and IUT 1 on March 10th. Since according to the article, the paper was accepted on February 5th, I would guess these are the final accepted versions. | |
| Apr 3, 2020 at 21:21 | history | answered | manifold | CC BY-SA 4.0 |