Mathematics

Andrew John Wiles

Date of birth: 11.04.1953

Place of birth: Cambridge, Great Britain

Citizenship: Great Britain

Mr Wiles is an English and American mathematician, Professor of Mathematics at Princeton University, Head of the Department for Mathematics in it, member of the Research Council at Clay Mathematics University). He was conferred with Bachelor’s degree in 1974 at Murton College of Oxford University. Mr Wiles began his academic career in summer 1975 headed by the Professor John Coates at Clare College of Cambridge University, where he got Doctor’s degree. In the period from 1977 to 1980, Andrew Wiles worked as the Junior Research Worker at Clare College and Associate Professor at Harvard University. He worked on the arithmetic of elliptic curves with complex multiplication using the methods from Iwasawa theory in cooperation with John Coates. In 1982 Mr Wiles left Great Britain for the USA.

One of the most important events in his career became a statement about proving Fermat’s Great Theorem in 1993 and discovery of an elegant method which enabled to complete the proving in 1994. Andrew Wiles began his professional work on Fermat’s Great Theorem in summer 1986 after Kenneth Ribet proved the hypothesis regarding a connection of semi-stable elliptic curves (a special case of Taniyama-Shimura theorem) with Fermat’s theorem.

History of Proving

Andrew Wiles got acquainted with Fermat’s Great Theorem at the age of 10. At that time he made an attempt to prove it using the methods from the school textbook. Later he began studying works of mathematicians who tried to prove this theorem. When Mr Wiles entered the College, he gave up his attempts to prove Fermat’s Great Theorem and devoted his time to studying of elliptic curves under the guidance of John Coates.

In the 1950s and 1960s a Japanese mathematician Shimura made a suggestion that there is a connection between elliptic curves and modular forms. Shimura relied on the ideas expressed by another Japanese mathematician - Taniyama. This hypothesis was known in the western academic circles thanks to work of Andre Weil who found a lot of fundamental data which supported the aforementioned hypothesis as a result of Weil’s thorough analysis of it. Therefore this theorem is often called “Shimura-Taniyama-Weil theorem”. The theorem says that each elliptic curve above the field of rational numbers is a modular. The theorem was completely proved in 1998 by Christoph Broyle, Brian Conrad, Fred Diamond and Richard Taylor who used the methods published by Andrew Wiles in 1995.

A connection between Taniyama-Shimura and Fermat’s theorems was ascertained by Kenneth Ribet who relied on works of Barry Mazur and Jean-Pierre Serra. Ribet proved that Frey curve was not modular. It meant that proving of a semi-stable case of Taniyama-Shimura theorem confirms truthfulness of Fermat’s Great Theorem. After Wiles found out that Kenneth Ribet got the proving in 1986, he decided to pay all his attention to proving of Taniyama-Shimura theorem. While the attitude of many mathematicians to the possibility of finding this proving was very skeptical, Andrew Wiles believed that the hypothesis may be proved using the methods of the XX^{th }century.

At the very beginning of his work on Taniyama-Shimura theorem, Wiles mentioned Fermat’s Great Theorem casually in the conversation with colleagues, and they became greatly interested in it. But Andrew Wiles wanted to concentrate himself on the problem as much as possible, and excessive attention could disturb him only. In order to exclude these cases, Mr Wiles decided to keep in secret the true essence of his research, revealing his secret to Nicolas Catz only. At that time Andrew Wiles, although he continued teaching at Princeton University, did not make any researches which were not connected with Taniyama-Shimura theorem.

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