ANDREW WILES

'Sir Andrew John Wiles' (born April 11 1953) is a British-American research mathematician at Princeton University, specialising in number theory. He is most famous for solving Fermat's Last Theorem.

Contents

Early work

Solution of Fermat's Last Theorem

Cultural references

Awards

Quotations

References

External links

Early work

Andrew 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 generalised this result to totally real fields.

Solution of Fermat's Last Theorem

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.

____________________________________

'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.

Cultural references

★ Wiles's work on Fermat's Last Theorem was commemorated (in fictional form) in the musical Fermat's Last Tango, written by Joanne Sydney Lessner and Joshua Rosenblum.[1]

★ Wiles and his work on Fermat's last theorem were mentioned in the '' episode "Facets". This also served as a correction for Fermat's last theorem being said to be unsolved in the earlier '' episode "The Royale".

★ Wiles is mentioned in Tom Lehrer's song "That's Mathematics"

★ Information about Wiles' proof of Fermat's Last Theorem appears in ''The Parrot's Theorem''

★ Wiles was interviewed for an episode of BBC's documentary series ''Horizon'', which focused on Fermat's Last Theorem

★ One of two multiple choice questions, on a fake television quiz show watched in episode 15 of the anime series ''Lucky Star'', concerns "Princeton's Sir Wiles", and asks which theorem he proved in 1994.

Awards

Wiles has been awarded several major prizes in mathematics:

★ Schock Prize (1995)

★ Cole Prize (1996) [2]

★ National Academy of Sciences Award in Mathematics from the American Mathematical Society (1996) [3]

★ Ostrowski Prize (1996) [4][5]

★ Royal Medal (1996)

★ Wolf Prize (1996)

★ Wolfskehl Prize (1997) [6] - see Paul Wolfskehl

★ A silver plaque from the International Mathematical Union (1998) recognizing his achievements, in place of the Fields Medal, which is restricted to those under 40 (Wiles was born in 1953 and proved the theorem in 1994). [7]

★ King Faisal Prize (1998) [8]

★ Clay Research Award (1999)

★ Named Knight Commander of the Order of the British Empire (2000).

★ Shaw Prize (2005) [9]

Quotations

★ "I think I'll stop here." -- immediately after presenting the proof of Fermat's Last Theorem, Cambridge, 23 June, 1993

References

★ Princeton home page

★ Andrew Wiles' bibliography

★ Modular elliptic curves and Fermat's Last Theorem, Andrew Wiles, , , Annals of Mathematics, 1995

★ Ring-theoretic properties of certain Hecke algebras, Richard Taylor and Andrew Wiles, , , Annals of Mathematics, 1995

★ The Proof of Fermat's last theorem by R. Taylor and A. Wiles, Gerd Faltings, , , Notices of the AMS, 1995

★ Wiles Receives NAS Award in Mathematics, John Coates, , , Notices of the AMS, 1996

★ Fermat's Enigma, , Simon, Singh, , 1997, ISBN 0-8027-1331-9

★ The Fermat Diary, , Charles, Mozzochi, , 2000, ISBN 0-8218-2670-0

★ NOVA Online: The Proof

★

★ Bluff your way in Fermat's Last Theorem

★ Fermat's Last Tango

External links

★

★ List of Publications