Sir Andrew Wiles | |
![]() Sir Andrew John Wiles
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Born | 11 April 1953 Cambridge, England |
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Residence | United Kingdom United States |
Nationality | British |
Fields | Mathematics |
Institutions | Princeton University |
Alma mater | Oxford University Cambridge University |
Doctoral advisor | John Coates |
Doctoral students | Manjul Bhargava Brian Conrad Karl Rubin Chris Skinner Richard Taylor |
Known for | Proving Fermat's Last Theorem |
Notable awards | Fermat Prize (1995) Wolf Prize (1995/6) Royal Medal (1996) IMU Silver Plaque (1998) Shaw Prize (2005) |
Sir Andrew John Wiles KBE FRS (born 11 April 1953)[1] is a British mathematician and a professor at Princeton University, specialising in number theory. He is most famous for proving Fermat's Last Theorem.
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Andrew Wiles was born in Cambridge, England in 1953 and attended King's College School, Cambridge (where his mathematics teacher, David Higginbottom first introduced Fermat's Last Theorem to him) and The Leys School, Cambridge; and earned his BA degree in 1974 after study at Merton College, Oxford, and a Ph.D. in 1980 after research at Clare College, Cambridge. 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 seven years to complete the work, Wiles was the first person to prove Fermat's Last Theorem, earning him a place in history.
Andrew 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.
Fermat's Last Theorem states that no nontrivial integer solutions exist for the equation: xn + yn = zn if n is an integer greater than two. |
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The bridge between Fermat and Taniyama |
If p is an odd prime and a, b, and c are positive integers such that ap+bp= cp, then a corresponding equation y² = x(x - ap)(x + bp) defines a hypothetical elliptic curve, called the Frey curve, which must exist if there is a counterexample to Fermat's Last Theorem. Following on work by Yves Hellegouarch who first considered this curve, Frey pointed out that if such a curve existed it had peculiar properties, and suggested in particular that it might not be modular. |
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.
Wiles has been awarded several major prizes in mathematics and science
Wiles' father is Rev. Prof. Maurice Frank Wiles (1923-2005), Regius Professor of Divinity at the University of Oxford[12] and his mother Patricia Wiles (née Mowll). His father worked as Chaplain at Ridley Hall Cambridge for the period 1952-55. Wiles is married to Nada Canaan Wiles,[2] who has a PhD in microbiology from Princeton, and they have two daughters.[1] Since 1994 he has been Eugene Higgins Professor at Princeton. He is a Foreign member of the US National Academy of Sciences since 1996 (as he remains a British citizen).[1]
He is currently Chair of the Mathematics Department at Princeton.[13]
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Persondata | |
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NAME | Wiles, Andrew |
ALTERNATIVE NAMES | |
SHORT DESCRIPTION | Mathematician |
DATE OF BIRTH | April 11, 1953 |
PLACE OF BIRTH | Cambridge, England |
DATE OF DEATH | |
PLACE OF DEATH |