[FOM] finite simple groups: no rumor known to me (fwd)

Timothy Y. Chow tchow at alum.mit.edu
Mon Nov 3 17:27:27 EST 2008

Steve Smith wrote:
>    Rumors about incompleteness seem to circulate about every couple of 
>    years; not based on any foundation known to me.  I've pretty much 
>    assigned it by now to some kind of would-be schadenfreude in the math 
>    community.

To be fair, the group-theoretic community did not do itself a service 
during the 1980's and even the 1990's when, in response to skepticism from 
outsiders, it firmly insisted that there was no gap in the proof.  As 
Serre puts it in his interview:

  Whenever I asked the specialists, they replied something like: "Oh no, 
  it is not a gap; it is just something which has not been written, but 
  there is an incomplete unpublished 800-page manuscript on it."  For me, 
  it was just the same as a "gap," and I could not understand why it was 
  not acknowledged as such.

I had similar experiences myself.  Small wonder that people keep asking 
now whether the proof is really complete.

On the positive side, here is an excerpt from Mark Ronan's excellent book 
"Symmetry and the Monster."

  Still some people wondered whether Janko, who had produced four 
  exceptions, might not have a fifth one up his sleeve.  Janko himself
  got in touch with Thompson to tell him where he thought another large 
  exception might be lying, in quasi-thin territory, so Thompson called 
  Smith in Chicago to make enquiries.  However, it seemed they had that 
  case well covered, and when I wrote to Janko to enquire what he now 
  thought, his reply was, "I have read ALL CRITICAL PLACES in the 
  Aschbacher-Smith book (on quasi-thin simple groups), and now I am 
  confident that the classification is absolutely OK!!"


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