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 beques ...

at the

University of Cambridge The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

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 city on the Mid North Coast, New South Wales, Australia. It and nearby Cundletown were settled in 1831 by William Wynter. Since then it has grown to a population of 26,381, and commands a significant agricultural district. Situ ...

) in

New South Wales New South Wales (commonly abbreviated as NSW) is a States and territories of Australia, state on the Eastern states of Australia, east coast of :Australia. It borders Queensland to the north, Victoria (state), Victoria to the south, and South ...

, 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, founded as the Broken Hill Proprietary Company, is an Australian multinational mining and metals corporation. BHP was established in August 1885 and is headquartered in Melbourne, Victoria. As of 2024, BHP was the world� ...

Newcastle, New South Wales Newcastle, also commonly referred to as Greater Newcastle ( ; ), is a large Metropolitan area, metropolitan area and the second-most-populous such area of New South Wales, Australia. It includes the cities of City of Newcastle, Newcastle and Ci ...

, 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 university, public research university and member of the Group of Eight (Australian universities), Group of Eight, located in Canberra, the capital of Australia. Its main campus in Acton, A ...

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 or Ecole may refer to: * an elementary school in the French educational stages normally followed by Secondary education in France, secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing i ...

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 A baker is someone who primarily bakes bread. Baker or Bakers may also refer to: Business * Bakers Coaches, trading name BakerBus, a bus and coach operator in Staffordshire, England * Baker Hughes, an oilfield services company * Baker McKenzie, ...

. In 1969, Coates was appointed assistant professor of mathematics at

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

in the United States, before moving again in 1972 to

Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...

where he became an associate professor. In 1975, he returned to England, where he was made a

fellow A fellow is a title and form of address for distinguished, learned, or skilled individuals in academia, medicine, research, and industry. The exact meaning of the term differs in each field. In learned society, learned or professional society, p ...

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, specialising in number theory. He is best known for Wiles's proof of Fermat's Last Theorem, proving Ferma ...

, 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 ...

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 the ...

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 at

Orsay Orsay () is a Communes of France, commune in the Essonne Departments of France, department in Île-de-France in northern France. It is located in the southwestern suburbs of Paris, France, from the Kilometre Zero, centre of Paris. A fortifie ...

. 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 Tower of fields, towers of number fields. It began as a Galois module theory of ideal class groups, initiated by (), as part of the theory of cyclotomic ...

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

Infosys Prize The Infosys Prize is an annual award granted 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 for researc ...

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

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 r ...

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. Types have included earthenware, pottery, stoneware, porcelain, and blue-and-white ware. Japan has an exceptionally long and successful history of cer ...

. He died on 9 May 2022.

References

External links

* {{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 Department of Mathematics faculty Number theorists People from Taree Sadleirian Professors of Pure Mathematics Stanford University Department of Mathematics faculty