Andrew J. Wiles
Election Year: 1996
Primary Section: 11, Mathematics
Membership Type: Foreign Associate
My primary mathematical interests are in number theory. The three main areas that I have studied in depth are the arithmetic of elliptic curves, the theory of cyclotomic fields, and the Galois representations associated to modular forms. In the first area, my work was joint with Coates, and its main achievement was a proof of part of the Birch and Swinnerton-Dyer conjecture. In the theory of cyclotomic fields, in joint work with Mazur I proved the Iwasawa conjecture. I later extended this to cover the case of any totally real base field. Lastly, my work on modular forms culminated in a proof that many elliptic curves are modular, thereby finally giving a proof of Fermat's Last Theorem. This last field has occupied me since 1986, and the quest for the solution to FLT was what motivated this work.