Andrew Wiles is an English mathematician at Oxford University, who achieved international fame for his proof to Fermat's Last Theorem.

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English

Mathematics

Number theory, Fermat's last theorem

Whitehead Prize ,1988

Professor Wiles probably holds some sort of record for the number of prizes he has been awarded, in awe of his great achievement in providing the elusive proof for Fermat's Last Theorem, 1995-1998: Rolf Schock, Ostrowski, Fermat, Wolf, Royal Medal, NAS, cole, Wolfskehi, IMU silver plaque, King Faisal International Prize in Science.

Shaw Prize, 2005

Wiles had an asteroid (asteroid 9999 Wiles), named in his honour in 1999.

PhD, 1980, Cambridge University

Professor of Mathematics, Princeton University, 1981, 1991 - 2011

Guggenheim Fellow at Institut des Hautes Études Scientifiques, and École Normale Supérieure, Paris, 1985-6

Oxford University, Royal Society Research Professor, 1988-90, from 2011

Member of the US National Academy of Sciences, 1996

Wiles' solution to Fermat's Last Theorem came in two papers, published in 1993 and 1994, and both papers were published in *Annals of Mathematics* in 1995. The second paper includes a modification sparked by the discovery of a flaw in the first paper.

Arithmetic of elliptic curves with complex mulitplication, involving Iwasawa theory, generalising the main conjecture over rational numbers, and subsequently to totally real fields.

Modularity theorem

Proof of Fermat's Last Theorem

Proof of the main conjecture of Iwasawa theory

He says he first encountered Fermat's Last Theorem at the age of ten, and solved it 32 years later. He took up the task seriously in 1986, following Ken Ribet's proof of the epsilon conjecture. Despite even his own tutors and colleaques assuring him it was probably impossible, he proved Fermat's Last Theorem by proving the Taniyama-Shimura Conjecture for semistable elliptic curves.

The personal qualities one fellow researcher attributed to Wiles for why he alone was able to have the insight to see the solution was summed up in the word 'audacity'. Because of the intense importance of the theorem, Wiles worked largely in secret, until he published his result in a 1993 paper. A flaw was discovered the same year, and Wiles set about resolving it, initially to no avail. A second paper in September, 1994, however, demonstates an effective circumnavigation of the problem the flaw had exposed in his original paper.

(Biographies of famous scientists no. 75)

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1862 - 1943

David Hilbert, 1862 - 1943, was German, and is considered one of the greatest mathematicians ever, leaving a broad legacy in mathematics, physics and philosophy.

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