| It's fairly commonly asserted nowadays in the mathematical community
| that Fermat's Last Theorem acquired its name because it was the last
| of Fermat's (valid) claims to be actually proved. This explanation
| makes some sense, but is it really all that well established? I have
| not seen this explanation anywhere in print in a source that is more
| than a decade old, so I am tempted to suppose that this sensible
| interpretation is a modern reconstruction.
|
In my opinion, there's infinitesimal doubt that "Fermat's Last Theorem"
acquired its name because it was in fact the *last* of Fermat's propositions
waiting (perhaps, anxiously expecting!) to be proved.
| ... it was brought to my attention by Pat Touhey that the phrase goes
| back at least as far as Gabriel Lame's "Memoire sur le dernier theoreme
| de Fermat", C.R. Acad. Sci. Paris, 9, 1839, pp. 45-46, eight years
| before Lame announced his false proof.
And, as far as I can tell, the phrase "dernier the/ore\me de Fermat"
[= "last theorem of Fermat"], which appears in the title of Lame's memoir
(1839), receives its clear explanation at the breaking lines of the same
article:
"De tous les the/ore\mes sur les nombres, e/nonce/s par Fermat,
un seul reste incomple/tement demontre/. Ce the/ore\me dit que
l'equation $ x^n + y^n = z^n $ est impossible en nombres entiers,
lorsque l'exposant $n$ est plus grand que 2."
Cauchy, who reviewed Lame's paper on September 16th, 1839, began his
_Rapport_ as follows:
"L'Acade/mie nous a charge/s, M. Liouville et moi, de lui rendre
compte d'un Me/moire de M. Lame/ sur le dernier the/ore\m de Fermat.
On sait que Fermat, l'un des plus beaux ge/nies qui aient illustre/
la France, a donne/ des e/nonce/s de plusieurs the/ore\mes, parmi
lesquels il en est deux dont la de/monstration a e/te/ pendant
long-temps recherche/e avec ardeur par divers ge/ome\tres. De ces
the/ore\mes il n'en reste plus qu'un seul qui ne soit pas aujourd'
hui comple/tement demontre/ : c'est le the/ore\me relatif aux
puissances des nombres entiers, et suivant lequel une puissance d'un
degre/ $n$ sup/erieur au second, ne peut re/sulter de l'addition de
deux puissances du me\me grade/."
With best regards,
Julio Gonzalez Cabillon