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John Henry Coates

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26 Jan 1945

New South Wales, Australia

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John Coates was educated in Australia, obtaining a B.Sc. from the Australian National University. From Australia he went to France where he studied at the École Normale Supérieure in Paris. To work for his doctorate he moved to England where he undertook research at the University of Cambridge studying at Trinity College. His doctoral dissertation was an outstanding piece of work on p-adic analogues of Baker 's method.

Continuing to move round some of the leading centres for mathematical research, Coates obtained a position as assistant professor of mathematics at Harvard University in the United States in 1969. From Harvard he moved to Stanford University in 1972, where he was an associate professor, and, after a further three years he returned to England to take up a lectureship at the University of Cambridge in 1975. He became a fellow of Emmanuel College during this period at Cambridge and it was during this time that Andrew Wiles was his research student.

At this stage Coates had returned to work in one of the three universities that he had studied in and indeed he continued with this pattern in 1977 when he was appointed as professor at the Australian National University. However, he did not remain for long in his home country, moving back to France in 1978 to a professorship at the University of Paris XI at Orsay. In 1985 he took up the positions of professor and director of mathematics at the École Normale Supérieure. In the same year he was elected to a fellow of the Royal Society of London .

In 1986 Coates returned to Cambridge when he was appointed to the Sadleirian Chair of Mathematics and he was also elected a fellow of Emmanuel College in Cambridge for the second time. In 1991 he became Head of the Department of Pure Mathematics and Mathematical Statistics at Cambridge.

Coates's first major mathematical publications were in 1966-67 when he published four articles on the algebraic approximation of functions. Then, together with A Baker , he extended Mahler 's work on fractional parts of powers of rational numbers. In other work he looked at problems relating properties of algebraic number fields to algebraic K-theory.

He then proved certain special cases of Weil 's conjecture on elliptic curves. He worked on Iwasawa 's theory and wrote a number of articles with Andrew Wiles published around 1977-78 including Kummer's criterion for Hurwitz number, Explicit reciprocity laws and On p-adic L-functions and elliptic units. As stated in :

His 1977 article on the conjecture of Birch and Swinnerton-Dyer, written jointly with his research student Andrew Wiles , was a landmark contribution to number theory which introduced a panoply of new methods into the field of elliptic curves.

Wiles had studied for his doctorate under Coates at Cambridge from 1974 and this proved an important link in the various strands which led to Wiles ' proof of Fermat's Last Theorem . During the 1980s Coates's work was concerned with elliptic curves, Iwasawa theory and p-adic L-functions, all work closely related to the direction that would eventually yield the proof of Fermat's Last Theorem. From :

Coates's insights into the Iwasawa theory of the symmetric square of an elliptic curve were instrumental in the recent proof by Wiles of the Shimura- Taniyama conjecture for semistable elliptic curves over Q.

Not only is Coates an outstanding researcher but he also has a reputation as a teacher of the highest quality :

John Coates is an inspired teacher and expositor who has made decisive contributions to the training of research students and junior colleagues, many of whom have gone on to fruitful research careers.

Again his contribution as an editor is singled out for praise in :

He was for many years an energetic and active editor of Inventiones Mathematicae, one of the premier journals of research mathematics, often making decisive stylistic improvements to articles which he deemed important but insufficiently well crafted.

Coates served as president of the London Mathematical Society during 1988-90 and as vice-president of the International Mathematical Union from 1991 to 1995. During 1992-94 he served as a member of the Council of the Royal Society , then, in 1996, he served on a group set up by the Royal Society to examine the peer review system used for funding research. The London Mathematical Society awarded Coates their Senior Whitehead Prize in 1997:

... for his fundamental research in number theory and for his many contributions to mathematical life both in the UK and internationally.

Source:School of Mathematics and Statistics University of St Andrews, Scotland