**John Coates** was an Australian mathematician who was the Sadleirian Professor at Cambridge and worked in algebraic number theory.

- By this time John was being educated at a very small school, with only one teacher, in a village about five miles away from the farm on which he lived.
- However, John failed to win a scholarship but he had also applied to the Australian National University for a scholarship and was invited for an interview.
- Kurt Mahler had also been appointed at A.N.U. and he taught Coates a course in elementary number theory during the second semester of his first year of study.
- Coates was fascinated by number theory and this course played a large role in his decision to move from physics to mathematics.
- In his final year as an undergraduate, Coates did an honours project supervised by Mahler which involved reading one of Mahler's unpublished papers.
- It was Coates' introduction to research.
- During his undergraduate studies, Coates met Julie Turner who was also an undergraduate at A.N.U. in the year below him.
- After the award of a B.Sc., Coates was awarded an A.N.U. scholarship and was advised by Kurt Mahler and Hanna Neumann to go to study for his doctorate at the École Normale Supérieure in Paris.
- However, Coates was unhappy with the areas of research in Paris feeling that he did not have the mathematical background to cope with the abstraction.
- Coates' thesis advisor at Cambridge was Alan Baker and, as soon as he arrived, he made the decision to start a new research project rather than continue the one he had begun in Paris.
- 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.
- 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.
- 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.
- Coates's first major mathematical publications were in 1966-67 when he published four articles on the algebraic approximation of functions.
- 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's 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.
- 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.

Born 26 January 1945, Possum Brush, Manning Valley, New South Wales, Australia. Died 9 May 2022, Cambridge, England.

View full biography at MacTutor

Origin Australia

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive