John Henry Coates (26 January 1945 – 9 May 2022) was an Australian mathematician who was the

Sadleirian Professor of Pure Mathematics The Sadleirian Professorship of Pure Mathematics, originally spelled in the statutes and for the first two professors as Sadlerian, is a professorship in pure mathematics within the DPMMS at the University of Cambridge. It was founded on a beque ...

at the

University of Cambridge The University of Cambridge is a public collegiate research university in Cambridge, England. Founded in 1209 and granted a royal charter by Henry III in 1231, Cambridge is the world's third oldest surviving university and one of its most pr ...

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 Taree is a town on the Mid North Coast, New South Wales, Australia. Taree and nearby Cundletown were settled in 1831 by William Wynter. Since then Taree has grown to a population of 26,381, and is the centre of a significant agricultural distr ...

) 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 BHP Group Limited (formerly known as BHP Billiton) is an Australian multinational mining, metals, natural gas petroleum public company that is headquartered in Melbourne, Victoria, Australia. The Broken Hill Proprietary Company was founded ...

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 area ...

, 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 an ...

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 establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, S ...

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 transcendental number theory, a mathematical discipline, Baker's theorem gives a lower bound for the absolute value of linear combinations of logarithms of algebraic numbers. The result, proved by , subsumed many earlier results in transcendent ...

. 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 Sir Andrew John Wiles (born 11 April 1953) is an English mathematician and a Royal Society Research Professor at the University of Oxford, specializing in number theory. He is best known for proving Fermat's Last Theorem, for which he was awa ...

, and together they proved a partial case of the

Birch and Swinnerton-Dyer conjecture In mathematics, the Birch and Swinnerton-Dyer conjecture (often called the Birch–Swinnerton-Dyer conjecture) describes the set of rational solutions to equations defining an elliptic curve. It is an open problem in the field of number theory an ...

for

elliptic curve In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If ...

s 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 visible wh ...

. 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 Paris-Sud University (French: ''Université Paris-Sud''), also known as University of Paris — XI (or as Université d'Orsay before 1971), was a French research university distributed among several campuses in the southern suburbs of Paris, in ...

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 centur ...

. 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 In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite towers of number fields. It began as a Galois module theory of ideal class groups, initiated by (), as part of the theory of cyclotomic fields. In th ...

, number theory and arithmetical algebraic geometry. He served on the Mathematical Sciences jury for the

Infosys Prize The Infosys Prize is an annual award given to scientists, researchers, engineers and social scientists of Indian origin (not necessarily born in India) by the Infosys Science Foundation and ranks among the highest monetary awards in India to r ...

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, re ...

of London in 1985, and was President of the London Mathematical Society from 1988 to 1990. The latter organisation awarded him the

Senior Whitehead Prize The Senior Whitehead Prize of the London Mathematical Society (LMS) is now awarded in odd numbered years in memory of John Henry Constantine Whitehead, president of the LMS between 1953 and 1955. The Prize is awarded to mathematicians normally ...

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 , is one of the oldest Japanese crafts and art forms, dating back to the Neolithic period. Kilns have produced earthenware, pottery, stoneware, glazed pottery, glazed stoneware, porcelain, and blue-and-white ware. Japan has an exceptionally ...

. 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