Timeline for Where are the second- (and third-)generation proofs of the classification of finite simple groups up to?
Current License: CC BY-SA 4.0
46 events
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| Oct 27 at 12:13 | comment | added | David Roberts♦ | @TimothyChow Oh, I see the preface ams.org/bookstore/pspdf/surv-40-10-pref.pdf does indeed have a good discussion of what the books cover so far, and what is left: In summary, the theorems to be proved in future volumes are Case B of Theorem $\mathcal{C}_4^*$ and Odd Uniqueness theorems. The end is in sight! | |
| Oct 27 at 12:00 | comment | added | David Roberts♦ | @TimothyChow cool! Do you know if there it has any detailed discussion about the path forward/what is left for future volumes? | |
| Oct 27 at 10:41 | comment | added | Timothy Chow | @DavidRoberts Volume 10 is already available. Our library just got a copy. | |
| Oct 13 at 22:24 | comment | added | Timothy Chow | @DavidRoberts Oh yes, for sure. I'm just saying that I expect one can get another thousand pages or more out of the other background results. Feit-Thompson is 255 pages right off the bat. Volume 1 mentioned several "general group theory" books, and later volumes added two more books by Aschbacher. | |
| Oct 13 at 22:18 | comment | added | David Roberts♦ | @TimothyChow the Aschbacher–Smith volumes are listed as background knowledge :-) I'd have to really go digging to find all the background stuff and how long it is. One day I will. Maybe after vol 10 comes out, so I can see what's listed in it | |
| Oct 13 at 17:16 | comment | added | Timothy Chow | @DavidRoberts If you're starting to count pages, then I'd argue for including the page counts of the "background results." These are mostly listed in Volume 1, but a few additional background results are listed in the introductory pages of Volumes 8 and 9 (and, apparently, in Chapter 16 of Volume 10). | |
| Oct 8 at 23:25 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
update on vol 10 to appear later this year; page lengths
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| Oct 8 at 23:02 | comment | added | David Roberts♦ | @colt_browning yay!! | |
| Oct 8 at 23:00 | comment | added | colt_browning | Meanwhile, volume 10 is available for pre-order: bookstore.ams.org/surv-40-10 | |
| Aug 21 at 7:37 | comment | added | David Roberts♦ | I think, from consulting the various published volumes, that vol 10 finishes off the proof of Theorem $\mathcal{C}_6$, and the last remaining row of the Classification Grid, Theorem $\mathcal{C}_4$, seems to split into two cases: $e(G)\leq 2$, which is covered by Aschbacher–Smith, and $e(G)= 3$. Then there's one more row of the Uniqueness Grid, to be covered by Stroth's volume, and the last volume (or two) by Lyons–Solomon. | |
| Jul 7 at 12:31 | comment | added | David Roberts♦ | Maybe Inna Capdeboscq's expertise that was used for volumes 9 and (I presume) 10 is orthogonal to what is needed for volume 11, but it's sad to see the team to go back down to two. | |
| Jul 7 at 12:18 | comment | added | David Roberts♦ | @TimothyChow (C)GLS (11 or 12) + Aschbacher–Smith (2) + Stroth (1). Lyons said Stroth's work will be the (singular) last volume, and since that manuscript is complete, I think that's an informed judgement. It's volume 11 that might spill over into 12. | |
| Jul 7 at 11:59 | comment | added | Timothy Chow | @DavidRoberts I don't understand what you mean by "11+2+1 (or 12+2+1)". Don't you mean "10+1+1 (or 10+2+1)"? Or maybe "11+1 (or 12+1)"? | |
| Jun 24 at 10:37 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
update with info from Lyons
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| Jun 10 at 3:18 | comment | added | Timothy Chow | @DavidRoberts My guess is that the "12 volumes" estimate assumes that Stroth's contribution will be a single volume, whereas Solomon's estimate of "13 volumes" assumes that it will be split into two volumes. Also, the estimate of 5,000 pages must exclude Aschbacher-Smith; even so, 5,000 pages sounds like a lowball estimate to me. | |
| May 14 at 23:20 | comment | added | David Roberts♦ | @colt_browning thanks. There was also a pair of talks relatively recently (but months before that one—maybe even last year), with the second one given by Capdeboscq, that gave a detailed examination of what is happening about now, and what has been one. I've watched them recently, and meant to give a link and a brief summary, so thanks for the prod. | |
| May 14 at 20:33 | comment | added | colt_browning | There was a talk a month ago: Remarks on CFSG and CGLSS (Richard Lyons, April 19, 2023) sites.math.rutgers.edu/~weibel/algebra.seminar.html#41923 Alas, I have no idea about its content. | |
| Mar 9 at 10:17 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
recent news
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| Apr 7, 2022 at 10:01 | comment | added | Nick Gill | @DavidRoberts, yes, I guess you're right... That's a shame.... And, yes, it seems likely that this cancellation is a result of the war in Ukraine. | |
| Apr 6, 2022 at 7:44 | comment | added | David Roberts♦ | @NickGill it appears the talk didn't happen? At the least, the last talk I find listed before the forum stopped operating (possibly related to current activities by the Russian government) is the 17th Feb. | |
| S Apr 6, 2022 at 1:09 | history | suggested | Vanni | CC BY-SA 4.0 |
New update
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| Apr 5, 2022 at 21:43 | review | Suggested edits | |||
| S Apr 6, 2022 at 1:09 | |||||
| Feb 24, 2022 at 23:40 | comment | added | David Roberts♦ | @NickGill oh, awesome! Especially the hints to avenues for improvements/optimisation for the CFSG, which, hopefully, will help to enliven the field. | |
| Feb 24, 2022 at 15:58 | comment | added | Nick Gill | Ron Solomon is due to give an update next week on this subject: mca.nsu.ru/kourovkaforum | |
| Dec 29, 2021 at 10:13 | history | edited | Denis Serre | CC BY-SA 4.0 |
edited body
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| Dec 29, 2021 at 10:02 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
added 168 characters in body
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| Sep 22, 2021 at 11:25 | history | bounty ended | Johannes Hahn | ||
| Sep 22, 2021 at 4:05 | comment | added | Yemon Choi | @Carl-FredrikNybergBrodda At the risk of derailing the comments (in which case I suppose there is always a chat) I find the page that's linked to and the wikipedia entry painting a rather pathetic picture. Which is not an excuse for the views, but this is not some highly influential mathematician (and AFAICT not a highly influential scientist). We can't police who reads our theorems | |
| Sep 21, 2021 at 23:19 | comment | added | Carl-Fredrik Nyberg Brodda | @DavidRoberts Yes, to be clear I think you’re right to put the link there, I just think it’s worth pointing out. His Wikipedia page is awful, too. | |
| Sep 21, 2021 at 22:59 | comment | added | David Roberts♦ | @Carl-FredrikNybergBrodda ugh. I was alread getting weird vibes from just the start of the posting I linked to, and I didn't dig further. But I'm loath to supply the email without some sort of provenance. | |
| Sep 21, 2021 at 18:10 | comment | added | Carl-Fredrik Nyberg Brodda | Hugo de Garis' blog is disgusting. It makes me feel ashamed to see something as beautiful as the CFSG be connected with the other material on his blog (sexism, bigotry, and anti-semitism, to name a few.). | |
| Sep 21, 2021 at 10:27 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
More info on projected rest of books, direct from Prof Solomon
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| Jun 16, 2021 at 5:06 | vote | accept | David Roberts♦ | ||
| Feb 25, 2021 at 14:29 | comment | added | Timothy Chow | @DavidRoberts Back in 1995, Barry Cipra wrote an article in Science entitled, "At math meetings, enormous theorem eclipses Fermat." At that time, the estimated length of the "second-generation proof" was between 3000 and 5000 pages. If we include Aschbacher and Smith, which seems fair to me, then the current estimated length would seem to be closer to 7000 pages. | |
| Feb 25, 2021 at 6:26 | comment | added | David Roberts♦ | Another note to self: volumes 1–9 fill 3941 pages, and there are at least two more volumes with specific plans, if not three, given the comment about volume 9. Then there is the "e(G)=3" problem, which is at least one more volume, but quite likely more. | |
| Feb 25, 2021 at 2:03 | history | edited | Timothy Chow | CC BY-SA 4.0 |
Added reference to volume 9
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| Jul 24, 2020 at 5:47 | comment | added | David Roberts♦ | Note to myself: volumes 1,2,3 cover Part I. Volume 4 is (the start of?) Part II. Volumes 5,7,8 cover "Part III: the generic case" (I think all of it). Volume 6 covers "Part IV: The Special Odd Case". | |
| Nov 13, 2019 at 22:46 | comment | added | David Roberts♦ | As a sample of the contribution of Capdeboscq–Lyons–Solomon to the project (i.e. what will probably be in volume 9), see this talk by Capdeboscq from 2015: youtube.com/watch?v=rSAKSP1C1-E | |
| Mar 27, 2019 at 21:12 | comment | added | David Roberts♦ | @Nick thanks! I don't mind at all. | |
| Mar 27, 2019 at 14:49 | history | edited | Nick Gill | CC BY-SA 4.0 |
Mar 2019 update.
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| Mar 27, 2019 at 14:45 | comment | added | Nick Gill | David, I'm just about to edit your answer to give an update, as Volume 8 is now available. I hope you don't mind -- I find it helpful that this page allows people to find out where things are up to. Please roll back the edits if you prefer. | |
| Jun 22, 2018 at 5:09 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
Added details of projected volumes
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| Mar 27, 2018 at 0:15 | history | edited | David Roberts♦ | CC BY-SA 3.0 |
added 219 characters in body
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| Oct 15, 2016 at 1:32 | comment | added | David Roberts♦ | My personal (vain) hope would be that the CFSG people start and embrace something like the Stacks project for writing up the second-generation proof. It would attract people to finite group theory and help iron out kinks faster with more potential contributors, as well as be a fantastic open resource. I guess the groupprops wiki is meant to be a little something along these lines, but I don't see it approaching the majesty of what de Jong and collaborators have put together. | |
| Oct 15, 2016 at 1:30 | history | edited | David Roberts♦ | CC BY-SA 3.0 |
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| Sep 4, 2015 at 2:43 | history | answered | David Roberts♦ | CC BY-SA 3.0 |