FOM: Expert error

[Colin McLarty]

Friedman's anonymous expert was simply wrong.

        Wiles's article "Modular elliptic curves and Fermat's last theorem"
uses Grothendieck duality over fields, and cites Altman and Kleiman
INTRODUCTION TO GROTHENDIECK DUALITY THEORY on page 486, just about in the
middle of the body of the paper. Altman and Kleiman use sets whose existence
is equivalent to existence of a Grothendieck Universe. So Friedman was
misinformed when he says:

>>I have been told that there is absolutely no trace back from the references
>>used in the body of the Wiles paper to Universes (of Grothendieck).

       This is only the first entry in Wiles's bibliography. I have not
tried to find every entry in the body of the paper that uses universes. 

        This proves two things about the expert: He or she is not devoted to
memorizing bibliographic references. And he or she is not obsessed with
finding who uses Grothendieck universes. Hardly surprising. It is surprising
that Friedman would use this kind of impressionistic evidence in a serious
investigation of foundations.