WILES, ANDREW J. / Mathématiques / Chercheurs

Centre International de Recherche Scientifique

Chercheurs

Mathématiques / WILES, ANDREW J.


Position

Eugene Higgins Professor of Mathematics,
Chair of the Department of Mathematics at Princeton University, Princeton, USA.

Thèmes de recherche

His fields of research are number theory and arithmetic geometry.

In the late 1630s, a French mathematician named Pierre de Fermat wrote a note in a book regarding the statement: For each whole number n, greater than 2, the equation xn + yn = zn has no solutions which are positive whole numbers. Then, Fermat wrote, \"I have a truly marvelous demonstration of this proposition which this margin in too narrow to contain.\"

Wiles himself first read about the theorem as a boy, and he spent a total of eight years in search of a proof. He first announced a solution on June 23, 1993, at the conclusion of a lecture at the Isaac Newton Institute in Cambridge, England. When mathematicians raised questions about his proof, Wiles himself noticed a flaw. That sent him back to work for nearly a year. Finally, in October 1994, Wiles unveiled his revised proof, which has been confirmed by experts in the field.

Prix et récompenses

LMS Whitehead Prize (1988)
Fellow of the Royal Society (1989)
Fermat Prize (1995)
Wolf Prize (1995/6)
British Mathematical Colloquium plenary speaker (1996)
NAS Award in Mathematics (1996)
AMS Colloquium Lecturer (1996)
Royal Society Royal Medal winner (1996)
AMS Cole Prize in Number Theory (1997)
AMS Cole Prize for number theory (1997)
LMS Honorary Member (2001)
Shaw Prize (2005)

Publications

(with J. Coates) Kummer’s criterion for Hurwitz numbers, Algebraic Number Theory, Kyoto, (1977), 9-23.

(with J. Coates) Explicit reciprocity laws, Soci´et´e Math. France, Ast´erisque, 41-42,(1977), 7-17.

(with J. Coates) On the conjecture of Birch and Swinnerton-Dyer, Inventiones Mathematicae, 39 (1977), 223-251.

Higher explicit reciprocity laws, Annals of Mathematics, 107 (1978), 235-254.

(with J. Coates) On p-adic L-functions and elliptic units, Jour. Aus. Math. Soc., 26 (1978), 1-26.

On modular curves and the class group of Q(p), Inventiones Mathematicae, 58 (1980), 1-35.

(with K. Rubin) Mordell-Weil groups of elliptic curves over cyclotomic fields, Proceedings of a Conference on Number Theory related to Fermat’s Last Theorem, Boston: Birkhauser, (1982), 237-254.

(with B. Mazur) Analogies between function fields and number fields, American Journal of Mathematics, June (1983), 507-521.

(with B. Mazur) Class fields of abelian extensions of Q, Inventiones Mathematicae, 76 (1984), 179-330.

On p-adic representations of totally real fields, Annals of Mathematics, 123 (1986), 407-456.

(with B. Mazur) On p-adic analytic families of Galois representations, Compositio Mathematicae, 59 (1986), 231-261.

On ordinary -adic representations associated to modular forms, Inventiones Mathematicae, 94 (1988), 529-573.

The Iwasawa conjecture for totally real fields, Annals of Mathematics, 131 (1990), 493-540.

On a conjecture of Brumer, Annals of Mathematics, 131 (1990), 555-565.

Modular Elliptic Curves and Fermat’s Last Theorem, Annals of Mathematics, 141, (1995), 443-551.

(with R. Taylor) Ring-theoretic properties of Hecke Algebras, Annals of Mathematics, 141, (1995), 553-572.

Modular Forms, Elliptic Curves, and Fermat’s Last Theorem, Proc. of Int. Congress of Mathematicians, Zurich, (1994), Vol. I, 243-245, published (1996).

(with C. Skinner) Ordinary Representations and Modular Forms, Proceedings of the National Academy of Sciences, 94, (1997), 10520-10527.

(with C. Skinner) Residually Reducible Representations and Modular Forms, Publications
of the I.H.E.S., 89, (1999), 5-126.

Twenty Years of Number Theory published by the A.M.S. in a book entitled Mathematics: Frontiers and Perspectives, Arnold, Atiyah, Lax, and Mazur (editors), (Y2000), pp. 329-342.

(with C. Skinner) Buse Change and a problem of Serre, Duke Math. J., 107, No. 1, (2001), 15-25.

(with C. Skinner), Nearly ordinary deformations of irreducible residual representations, Ann. Fac. Sci. Toulouse Math (6), 10, No. I, (2001), 185-215.

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