Andrew Wiles was born and educated in England but emigrated to the United States and is still, I believe, a professor at Princeton University. In 1993 he presented a proof of the "Taniyama-Shimura" conjecture. It asserted that every one of a certain type of elliptic function could be associated in a specific way with a modular form. Not at all an elementary subject and not obviously connected with Fermat's Last Theorem. However, Gerhard Frey had earlier proved that Fermat's Last Theorem was true if and only if the Taniyama-Shimura conjecture was true!
Clearly, it was a group effort and a remarkable achievement.
Probably the most accessible discussion is still Simon Singh's book "Fermat's Enigma".
Until you can get that book (check your local library), here is a website with links to several sites talking about Fermat's Last Theorem:
The 1993 proof contained some errors though. Well, it is very long piece of mathematics. It took a couple of years tidying up by various people. He gave the first talk on it at Cambridge, there is I believe a reference to it in one of Tom Korner's writings: what it was like realizing that at the end of a very technical discussion that Wiles had just written, Corollary, x^n+y^n=z^n has no solutions in positive integers for n > 2. There had been a rumour about that being the real purpose of the talk and consequently he got a much larger audience than one might expect for such a topic. (Elliptic Modular Forms.)
If you are in the UK there is a Panorama program on it that might be available somehow; it interviews him, Conway (a colleague at Princeton), and several others, including John Coates (Wiles's PhD supervisor).
As far as I'm aware Wiles is still at Princeton.
He is a very clever and humble man, who came to a question and answer session for a group of High School (A-level) students I was working with once. I don't think that the students quite understood just what he had done, but equally I don't think he could grasp that they didn't know any higher pure mathematics when he tried to answer some of their questions. His modesty at his acheivement makes a refreshing change.