[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
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there is an incomplete unpublished 800-page manuscript on it."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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