John H. Coates

For other people named John Coates, see John Coates (disambiguation).
John Coates

John H. Coates
Born John Henry Coates
(1945-01-26) 26 January 1945[1]
New South Wales, Australia
Residence Cambridge, England
Nationality Australian
Fields Mathematics
Alma mater
Thesis The Effective Solution of Some Diophantine Equations (1969)
Doctoral advisor Alan Baker[2]
Doctoral students
Known for
Influences John Tate[3]
Notable awards
Spouse Julie Turner[1]

John Henry Coates, FRS[4] (born 26 January 1945) is a mathematician who was the Sadleirian Professor of Pure Mathematics at the University of Cambridge in the United Kingdom from 1986 to 2012.[2][5][6][7][8][9]

Early life and education

Coates was born the son of J. H. Coates and B. L. Lee[1] and grew up in Possum Brush (near Taree) in New South Wales, Australia. Coates Road in Possum Brush is named after the family farm on which he grew up.[10] Before university he spent a summer working for BHP Billiton in Newcastle, New South Wales, though he was not successful in gaining a university scholarship with the company. Coates attended Australian National University 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 in Paris, before moving again to England.


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 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 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.[11]

In 1977, Coates moved back to Australia, becoming a professor at the Australian National University, 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. In 1985, he returned to the École Normale Supérieure, this time as professor and director of mathematics.

Since 1986 Coates has worked in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) of the University of Cambridge. In the last ten years he has focused on the study of various aspects of non-commutative Iwasawa theory: for instance, on the study of the arithmetic of elliptic curves in nonabelian infinite extensions.

Awards and honours

Coates was elected a fellow of the Royal Society 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 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:

Distinguished for his contributions to the theory of numbers, in particular to the study of transcendence, cyclotomic fields and elliptic curves. In addition to his own important contributions he has been a stimulating influence on colleagues and students. Together with his pupil A. Wiles he achieved the first major breakthrough towards a proof of the Birch-Swinnerton-Dyer conjectures.[4]

Personal life

Coates married Julie Turner in 1966, with whom he had three sons.[1] He collects Japanese pottery and porcelain.[3]


  1. 1 2 3 4 5 "COATES, Prof. John Henry". Who's Who 2014, A & C Black, an imprint of Bloomsbury Publishing plc, 2014; online edn, Oxford University Press.(subscription required)
  2. 1 2 3 John H. Coates at the Mathematics Genealogy Project
  3. 1 2 John Coates interviewed by Alan Macfarlane, 15 February 2008, retrieved 30 March 2009
  4. 1 2 "EC/1985/08: Coates, John Henry". London: The Royal Society. Archived from the original on 27 May 2014.
  5. O'Connor, John J.; Robertson, Edmund F., "John H. Coates", MacTutor History of Mathematics archive, University of St Andrews.
  6. Emmanuel College profile: Professor John Coates
  7. John Coates interviewed by Alan Macfarlane 25 February 2008 (film)
  8. John H. Coates's publications indexed by the Scopus bibliographic database, a service provided by Elsevier. (subscription required)
  9. Coates, J.; Fukaya, T.; Kato, K.; Sujatha, R.; Venjakob, O. (2005). "The GL2 Main Conjecture for Elliptic Curves without Complex Multiplication". Publications mathématiques de l'IHÉS. 101: 163. doi:10.1007/s10240-004-0029-3.
  10. "Whereis: Possum Brush".
  11. Coates, J.; Wiles, A. (1977). "On the conjecture of Birch and Swinnerton-Dyer". Inventiones Mathematicae. 39 (3): 223. doi:10.1007/bf01402975.
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