John Coates was an internationally renowned mathematician, who specialized in number theory. He grew up in Australia, but spent his career in the USA, France and the UK. He was best known for his promotion of Iwasawa theory as a method of studying elliptic curves, and in particular the conjecture of Bryan Birch (FRS 1972) and Peter Swinnerton-Dyer (FRS 1967). His celebrated theorem on this topic (jointly with his student Andrew Wiles (FRS 1989)) was the first general result on this problem, which remains unsolved to this day. He continued working in this area for much of his life and was extremely influential both as a teacher and as a researcher. He also travelled extensively in Asia and had an important effect on the development of algebraic number theory in South Korea and in China, as well as pursuing significant collaborations with mathematicians in Japan.
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