Andrew Wiles
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Categories: 1953 births | 20th century mathematicians | 21st century mathematicians | Alumni of Clare College, Cambridge | Alumni of Merton College, Oxford | English mathematicians | Fellows of the Royal Society | Honorary Fellows of Merton College, Oxford | Living people | MacArthur Fellows | Members of the National Academy of Sciences | Number theorists | Princeton University faculty | Rolf Schock Prize laureates | Wolf Prize in Mathematics laureates | Members of the French Academy of Sciences | Knights Commander of the Order of the British Empire
For the French mathematician with work in the area of elliptic curves, see André Weil.
Sir Andrew John Wiles, KBE (born April 11 1953) is a British research mathematician at Princeton University, specialising in number theory. He is most famous for proving Fermat's Last Theorem.
Early workAndrew Wiles was born in Cambridge, England in 1953 and attended The Leys School, Cambridge and then earned his BA degree from Merton College, Oxford in 1974 and Ph.D. from Clare College, Cambridge in 1980. His graduate research was guided by John Coates beginning in the summer of 1975. Together they worked on the arithmetic of elliptic curves with complex multiplication by the methods of Iwasawa theory. He further worked with Barry Mazur on the main conjecture of Iwasawa theory over Q, and soon afterwards generalized this result to totally real fields. Taking approximately 7 years to figure it out, Wiles was the first person to prove Fermat's Last Theorem, going into history in doing so. Solution of Fermat's Last TheoremAndrew Wiles' most famous mathematical result is that all rational semistable elliptic curves are modular which, in particular, implies Fermat's Last Theorem. Wiles was introduced to Fermat's Last Theorem at the age of ten. He tried to prove the theorem using textbook methods and later studied the work of mathematicians who had tried to prove it. When he began his graduate studies he stopped trying to prove it and began studying elliptic curves under the supervision of John Coates. In the 1950s and 1960s a connection between elliptic curves and modular forms was conjectured by the Japanese mathematician Goro Shimura based on some ideas that Yutaka Taniyama posed. In the West it became well known through a paper by André Weil. With Weil giving conceptual evidence for it, it is sometimes called the Shimura-Taniyama-Weil conjecture. It states that every rational elliptic curve is modular. The full conjecture was proven by Christophe Breuil, Brian Conrad, Fred Diamond, and Richard Taylor in 1998 using many of the methods that Andrew Wiles used in his 1995 published papers.
A connection between Taniyama-Shimura and Fermat was made by Ken Ribet, following on work by Barry Mazur and Jean-Pierre Serre, with his proof of the epsilon conjecture showing that Frey's idea that the Frey curve could not be modular was correct. In particular, this showed that a proof of the semistable case of the Taniyama-Shimura conjecture would imply Fermat's Last Theorem. Wiles made the decision that he would work exclusively on the Taniyama-Shimura conjecture shortly after he had learned that Ribet had proven the epsilon conjecture in 1986. While many mathematicians thought the Taniyama-Shimura conjecture was inaccessible, Wiles resolved to follow that approach. When Wiles first began studying Taniyama-Shimura, he would casually mention Fermat to people, but he found that doing so created too much interest. He wanted to be able to work on his problem in a concentrated fashion, and if people were expressing too much interest then he would not have been able to focus on his problem. Consequently he let only Nicholas Katz know what he was working on. Wiles did not do any research that was not related to Taniyama-Shimura, though of course he did continue in his teaching duties at Princeton University; continuing to attend seminars, lecture undergraduates, and give tutorials. Cultural references
AwardsWiles has been awarded several major prizes in mathematics:
References
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