# Where are the second- (and third-)generation proofs of the classification of finite simple groups up to?

According the the Wikipedia page, the second generation proof is up to at least nine volumes: six by Gorenstein, Lyons and Solomon dated 1994-2005, two covering the quasithin business by Aschbacher and Smith in 2004, and one by Aschbacher, Lyons, Smith and Solomon in 2011. However, this latter book is really just the second part of an outline of the proof, the first part of which was written by Gorenstein in the 80s (the reason for the delay is, of course, that the quasithin case hadn't actually been settled at the time of the announcement of completion). Hence the last update on the second-generation proof is really 2005.

With the recent formal proof in Coq of the Odd-order Theorem, it would be good to know where the traditional proof is up to.

EDIT 6 August 2013: Any news as to the completion of that seventh volume as mentioned in the comments?

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I asked this on the group-pub about a year ago, and I received the following email from Mark Lewis (forwarded from Ron Solomon): Richard and I HOPE to complete Book 7 by the end of 2012. Richard, Inna Capdeboscq and I have a lot of work completed on Book 8 as well. We might be able to complete it in one to 1 1/2 years after the completion of Book 7. That still leaves Books 9, 10, and 11. (The current best estimate is 11 total.) Gernot Stroth has a first draft of Book 11 written. Some work has been done on Book 9, but I would not hazard a guess on when that will see the light of day. –  Steve D Nov 30 '12 at 1:27
@Steve, would you care to post this as an answer? –  David Roberts Dec 3 '12 at 1:48
@SteveD - any more news of late? –  David Roberts Feb 10 '14 at 23:26
unfortunately, no. Book 7 should be out by now, but I haven't heard anything about an upcoming release. –  Steve D Feb 15 '14 at 3:53

## 1 Answer

With respect to the second generation proof you can get an answer from the horse's mouth' if you like: Ron Solomon gave an update on the program at BIRS recently and a video of his talk is here.

He starts the talk by comparing its progress to the receding of the glaciers'! In reality, though, they've made very significant headway into the later volumes. (In particular he mentions, around 9:30, that volume 7 is in preparation, and it is mainly this volume that he's discussing in the talk.)

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