>Possible research topic: sift through what Fermat did publish or write to his
>correspondents and see if anything fits as a counterexample or demonstration
>of a logical fallacy in a would-be proof of the Last Theorem. If you find
>anything plausible, then try to reconstruct the idea of the fallacious proof
>from Fermat's announcement of the fallacy in it.
Mahoney, Michael S. (Michael Sean)
TITLE The mathematical career of Pierre de Fermat (1601-1665)
IMPRINT Princeton, N. J., Princeton University Press [1973]
DESCRIPT'N xviii, 419 p. illus. 25 cm.
does that. The book was lately re-released with some additions.
Mahoney reaches the same conclusion that Jack Wales quoted in an
earlier post today, from _From Fermat to Minkowski: Lectures on the Theory
of Numbers and Its Historical Development_ by Winfried Scharlau and Hans
Opolka, Springer-Verlag 1985, page 13. Fermat quickly realized he had no
good proof in general but he could prove it for n =3 or =4.
On the other hand, a few years ago someone on the newsgroup sci.math
gave an interesting argument that Fermat may actually have had something
like Wile's proof in mind. Recall Fermat says his proof would not fit in the
margin--and certainly the Wiles proof would not.
Colin