John H. Coates (1945 - 2022)#

Professor John H. Coates, a very distinguished mathematician and a member of the Academia Europaea Mathematics section since 2015 passed away on 9 May 2022 at the age of 77. Read the commemorative words by Prof. Pierre Colmez and Prof. Philippe Michel, the Chair of the Mathematics section of Academia Europaea.

Born on January 26, 1945 in Australia, John Coates started his mathematical career under the supervision of Fields medalist and 1988 AE member Alan Baker. He wrote a number of papers on themes related to Baker's work (diophantine approximation, linear forms in logarithms of algebraic numbers) before turning to algebraic number theory (and especially Iwasawa theory) to which he devoted the rest of his career. His most spectacular achievement is the so-called theorem of Coates-Wiles which he proved with his student Andrew Wiles, around 1975, and was the first general result towards the Birch and Swinnerton-Dyer conjecture (one of the 7 millenium problems).

Shortly after proving this result he moved to University Paris-Sud Orsay where his teaching had a deep impact on french Number Theory

He then moved to Cambridge where he became the Sadleirian Professor of pure Mathematics until his retirement. After several years as head of the Mathematics department during which he devoted a lot of energy to the planning of the new buildings of the department, he had the hindsight that Iwasawa's ideas could be also used in a non-abelian setting; this led him to create non-abelian Iwasawa Theory which he developped with the help of many collaborators. His Cambridge years were as fruitful as his years in France as far as mentoring goes. Altogether the mathgenealogy Project lists 35 students and over 400 descendants (several of which are now AE members) but many are missing: a telling testimony of his influence.