The way to the proof of Fermat's theorem

Abstract

In the mid-17th Century Pierre de Fermat stated on the margin of a copy of Diophantine's work the conjecture: there are no natural numbers n/spl ges/3,x,y,z such that x/sup n/+y/sup n/=z/sup n/ (Fermat's last theorem, FLT). In 1993 Andrew Wiles announced the theorem: semi-stable elliptic curves over Q are modular. The present paper explains the meaning of Wiles' theorem, his strategy to prove it, and why it settles Fermat's conjecture. We begin by sketching the history of the attempts to prove FLT which reflect its fascination as a challenge for testing the power of the mathematics available.