Andrew Wiles
Sir Andrew John Wiles is an
English-
American research mathematician at
Princeton University in number theory. He attended
The Leys School, Cambridge and then earned his BA degree from
Merton College,
Oxford University in 1974 and Ph.D. from
Clare College,
Cambridge University 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.
Quotations
I think I'll stop here.
After finishing writing the proof to Fermat's Last Thereom (1993)
More Quotes >>
Encyclopedia
- Andrew Wiles should not be confused with André Weil, another famous mathematician who, like Wiles, did important work in the area of elliptic curves.
Sir Andrew John Wiles is an
English-
American research mathematician at
Princeton University in number theory. He attended
The Leys School, Cambridge and then earned his BA degree from
Merton College,
Oxford University in 1974 and Ph.D. from
Clare College,
Cambridge University 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 made major breakthroughs in the study of rational elliptic curves associated with modular forms. He is most famous for finally proving
Fermat's Last Theorem.
Solution of Fermat's Last Theorem
| Fermat's Last Theorem states that no nontrivial solutions in integers exist for the equation: xn + yn = zn if n is 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 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. |
|
Andrew 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
Wiles's work on Fermat's Last Theorem was commemorated in the musical Fermat's Last Tango, written by Joanne Sydney Lessner and Joshua Rosenblum.
Wiles and his work on Fermat's last theorem were mentioned in the
episode "Facets".
Awards
Wiles has been awarded several major prizes in mathematics:
- Schock Prize
- Cole Prize
- National Academy of Sciences Award in Mathematics from the American Mathematical Society
- Ostrowski Prize
- Royal Medal
- Wolf Prize
- Wolfskehl Prize
- A silver plaque from the International Mathematical Union recognizing his achievements, in place of the Fields Medal, which is restricted to those under 40 .
- King Faisal
...
Prize
Quotations
- "I think I'll stop there."
References
External links
