Fermat’s last theorem is strikingly different and much more difficult to prove than the analogous problem for n = 2… The fact that the problem’s statement is understandable by schoolchildren makes it all the more frustrating, and it has probably generated more incorrect proofs than any other problem in the history of mathematics. No correct proof was found for 357 years, when a proof was finally published by Andrew Wiles in 1994. The term “last theorem” resulted because all the other theorems proposed by Fermat were eventually proved or disproved, either by his own proofs or by other mathematicians, in the two centuries following their proposition.”
Fermat claims to have proven it in his letter:
Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet.
I have discovered a truly marvelous proof that it is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second into two like powers. This margin is too narrow to contain it.
Right. Andrew Wiles has successfully proven the last theorem with techniques not made available to Fermat during his time. Fermat’s proof probably never existed.