John Henry Coates (26 January 1945 – 9 May 2022) was an Australian mathematician who was the Sadleirian Professor of Pure Mathematics at the

University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

in the United Kingdom from 1986 to 2012.

Early life and education

Coates was born the son of J. H. Coates and B. L. Lee on 26 January 1945 and grew up in Possum Brush (near Taree) in

New South Wales ) , nickname = , image_map = New South Wales in Australia.svg , map_caption = Location of New South Wales in AustraliaCoordinates: , subdivision_type = Country , subdivision_name = Australia , established_title = Before federation , es ...

, Australia. Coates Road in Possum Brush is named after the family farm on which he grew up. Before university he spent a summer working for BHP in

Newcastle, New South Wales Newcastle ( ; Awabakal: ) is a metropolitan area and the second most populated city in the state of New South Wales, Australia. It includes the Newcastle and Lake Macquarie local government areas, and is the hub of the Greater Newcastle ar ...

, though he was not successful in gaining a university scholarship with the company. Coates attended

Australian National University The Australian National University (ANU) is a public research university located in Canberra, the capital of Australia. Its main campus in Acton encompasses seven teaching and research colleges, in addition to several national academies and ...

on scholarship as one of the first undergraduates, from which he gained a BSc degree. He then moved to France, doing further study at the

École Normale Supérieure École may refer to: * an elementary school in the French educational stages normally followed by secondary education Secondary education or post-primary education covers two phases on the International Standard Classification of Education sca ...

in Paris, before moving again, this time to England.

Career

In England he did postgraduate research at the University of Cambridge, his doctoral dissertation being on ''p''-adic analogues of Baker's method. In 1969, Coates was appointed assistant professor of mathematics at

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of high ...

in the United States, before moving again in 1972 to Stanford University where he became an associate professor. In 1975, he returned to England, where he was made a

fellow A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...

of Emmanuel College, and took up a lectureship. Here he supervised the PhD of Andrew Wiles, and together they proved a partial case of the Birch and Swinnerton-Dyer conjecture for elliptic curves with

complex multiplication In mathematics, complex multiplication (CM) is the theory of elliptic curves ''E'' that have an endomorphism ring larger than the integers. Put another way, it contains the theory of elliptic functions with extra symmetries, such as are visibl ...

. In 1977, Coates moved back to Australia, becoming a professor at the

, where he had been an undergraduate. The following year, he moved back to France, taking up a professorship at the University of Paris XI at

Orsay Orsay () is a commune in the Essonne department in Île-de-France in northern France. It is located in the southwestern suburbs of Paris, France, from the centre of Paris. A fortified location of the Chevreuse valley since the 8th century a ...

. In 1985, he returned to the École Normale Supérieure, this time as professor and director of mathematics. From 1986 until his death, Coates worked in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) of the University of Cambridge. He was head of DPMMS from 1991 to 1997. His research interests included Iwasawa theory, number theory and arithmetical algebraic geometry. He served on the Mathematical Sciences jury for the Infosys Prize in 2009.

Awards and honours

Coates was elected a fellow of the

Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, r ...

of London in 1985, and was President of the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

from 1988 to 1990. The latter organisation awarded him the 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". His nomination for the Royal Society reads:

Personal life

Coates married Julie Turner in 1966, with whom he had three sons. He collected Japanese pottery and porcelain. He died on 9 May 2022.

References

{{DEFAULTSORT:Coates, John 1945 births 2022 deaths 20th-century Australian mathematicians 21st-century Australian mathematicians Alumni of Trinity College, Cambridge Australian National University alumni Academic staff of the École Normale Supérieure Fellows of Emmanuel College, Cambridge Fellows of the Royal Society Harvard University faculty Number theorists People from Taree Sadleirian Professors of Pure Mathematics Stanford University Department of Mathematics faculty