<begin quote>
To conclude this chapter, a few words about the so-called "Fermat's last
theorem." Whether Fermat knew a proof or not has been the subject of many
speculations. The truth seems obvious. Fermat made his famous remark in
the margin of his private copy of Bachet's edition of Diophantos in
1637(next to the problem of ... ).
<skip description of the well-known marginal note>
This statement was made at the time of his first letters concerning
number theory and we can assume that this was also the time his interest
awakened in the theory of numbers. As far as we know, he never repeated
his general remark but repeatedly made the statement for the cases n = 3
and n = 4 and posed these cases as problems to his correspondents. We
have already seen that he formulatd the case n = 3 in a letter to Carcavi
in 1659 (n = 4 obviously appeared too simple to be included in his
collection of important theorems). All these facts indicate that Fermat
quickly became aware of the incompleteness of the "proof" of 1637. Of
course, there was no reason for the public retraction of his privately
made conjecture.
<end quote>
Jack V. Wales, Jr.
The Thacher School
5025 Thacher Road
Ojai, CA 93023
(805) 646-4377