What question did this study set out to answer?

To celebrate the life and contributions of John Coates in the field of number theory.

January 16, 2026Biographical Memoirs of Fellows of the Royal Society0 citationsOpen Access

John Coates

AWAndrew WilesUniversity of Oxford LSLeila SchnepsCentre National de la Recherche Scientifique

Key Points

To celebrate the life and contributions of John Coates in the field of number theory.
Career overview covering Coates' work in various countries.
Focus on his influence on number theory, particularly Iwasawa theory.
Highlight extensive collaborations in Asia and their impact on algebraic number theory.
Coates promoted Iwasawa theory, contributing to studies on elliptic curves.
Collaborated with Andrew Wiles on notable theorems related to Birch-Swinnerton-Dyer conjecture.
Influenced the development of algebraic number theory in South Korea and China.

Abstract

Abstract 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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