John H. Coates

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John H. Coates

Coates in 2006
John Henry Coates

(1945-01-26)26 January 1945
Possum Brush, New South Wales, Australia
Died9 May 2022(2022-05-09) (aged 77)
Cambridge, England
Alma mater
Known for
SpouseJulie Turner[1]
Scientific career
ThesisThe Effective Solution of Some Diophantine Equations (1969)
Doctoral advisorAlan Baker[2]
Doctoral students

John Henry Coates FRS[4] (26 January 1945 – 9 May 2022) was an Australian 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[edit]

Coates was born the son of J. H. Coates and B. L. Lee on 26 January 1945[1] and grew up in Possum Brush (near Taree) in New South Wales, Australia.[3] 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 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, this time to England.[11][7]


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.[11]

In 1975, he returned to England, where he was made a fellow of Emmanuel College,[12] 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.[13]

In 1977, Coates moved back to Australia, becoming a professor at the Australian National University,[12] 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.[11]

From 1986 until his death, Coates worked in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) of the University of Cambridge.[11] He was head of DPMMS from 1991 to 1997.[14]

His research interests included Iwasawa theory, number theory and arithmetical algebraic geometry.[11][15]

He served on the Mathematical Sciences jury for the Infosys Prize in 2009.[16]

Awards and honours[edit]

Coates was elected a fellow of the Royal Society of London in 1985,[17] and was President of the London Mathematical Society from 1988 to 1990.[18] The latter organisation awarded him the Senior Whitehead Prize in 1997,[11] for "his fundamental research in number theory and for his many contributions to mathematical life both in the UK and internationally".[19] 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[edit]

Coates married Julie Turner in 1966, with whom he had three sons.[1] He collected Japanese pottery and porcelain.[7] He died on 9 May 2022.[11][14]


  1. ^ a b c d "COATES, Prof. John Henry". Who's Who 2014, A & C Black, an imprint of Bloomsbury Publishing plc, 2014; online edn, Oxford University Press. Archived from the original on 10 May 2022. Retrieved 27 May 2014.(subscription required)
  2. ^ a b c John H. Coates at the Mathematics Genealogy Project
  3. ^ a b Singh, S. (2017). Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem. Knopf Doubleday Publishing Group. p. 215. ISBN 978-0-525-43532-7. Retrieved 10 May 2022.
  4. ^ a b "EC/1985/08: Coates, John Henry". London: The Royal Society. Archived from the original on 8 July 2019.
  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". Archived from the original on 29 August 2012. Retrieved 17 November 2007.
  7. ^ a b c "interviewed by Alan Macfarlane 25 February 2008 (video)". Archived from the original on 6 May 2021. Retrieved 13 August 2019.
  8. ^ John H. Coates's publications indexed by the Scopus bibliographic database. (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: 163–208. arXiv:math/0404297. doi:10.1007/s10240-004-0029-3. S2CID 13996298.
  10. ^ "Whereis: Possum Brush". Archived from the original on 30 June 2013. Retrieved 5 March 2013.
  11. ^ a b c d e f g "Emmanuel College website, retrieved 9 May 2022". Archived from the original on 10 May 2022. Retrieved 9 May 2022.
  12. ^ a b "Department of Mathematics – On the arithmetic of the Gross family of elliptic curves with complex multiplication". KIT. Retrieved 10 May 2022.
  13. ^ Coates, J.; Wiles, A. (1977). "On the conjecture of Birch and Swinnerton-Dyer". Inventiones Mathematicae. 39 (3): 223. Bibcode:1977InMat..39..223C. doi:10.1007/bf01402975. S2CID 189832636.
  14. ^ a b "Department of Pure Mathematics and Mathematical Statistics | Welcome to DPMMS". University of Cambridge. Retrieved 10 May 2022. Professor John Coates (26th January 1945 to 9th May 2022) We are sad to learn of the death of John Coates FRS, Sadleirian Professor 1986-2012. John was a distinguished number theorist and a dynamic Head of DPMMS 1991-97. He was instrumental in shaping the current Department and in the establishment of the Kuwait Professorship and the Kuwait Foundation Lectures.
  15. ^ "Professor John Coates". University of Cambridge. Archived from the original on 7 July 2021. Retrieved 10 May 2022.
  16. ^ "Infosys Prize 2009" (PDF). Infosys Science Foundation. p. 13. Archived (PDF) from the original on 9 September 2021. Retrieved 10 May 2022.
  17. ^ "John Coates". Royal Society. 2 December 2019. Retrieved 10 May 2022.
  18. ^ "John Coates – Biography". Maths History. 26 January 1945. Retrieved 10 May 2022.
  19. ^ "Records of Proceedings at Meetings". Bulletin of the London Mathematical Society. 30 (4): 442. July 1998. doi:10.1112/S0024609398004445. S2CID 247660423.