John Coates
Encyclopedia
John Henry Coates, FRS (born 26 January 1945) is a mathematician
who holds (since 1986) the position of Sadleirian Professor of Pure Mathematics at the University of Cambridge
in the United Kingdom
.
) in New South Wales
, Australia
. 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 B.Sc. degree. He then moved to France
, doing further study at the École Normale Supérieure
in Paris, before moving again to England.
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 curve
s with complex multiplication
.
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.
He 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".
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, the study of the arithmetic of elliptic curves in nonabelian infinite extensions.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who holds (since 1986) the position of Sadleirian Professor of Pure Mathematics at the University of Cambridge
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
in the United Kingdom
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
.
Early life and education
Coates was born the son of J. H. Coates and B. L. Lee and grew up in Possum Brush (near TareeTaree, New South Wales
Taree is a city 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 around 20,000 people and is the centre of a significant agricultural district. It is 16 km from the sea coast,...
) in New South Wales
New South Wales
New South Wales is a state of :Australia, located in the east of the country. It is bordered by Queensland, Victoria and South Australia to the north, south and west respectively. To the east, the state is bordered by the Tasman Sea, which forms part of the Pacific Ocean. New South Wales...
, Australia
Australia
Australia , officially the Commonwealth of Australia, is a country in the Southern Hemisphere comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands in the Indian and Pacific Oceans. It is the world's sixth-largest country by total area...
. Before university he spent a summer working for BHP Billiton
BHP Billiton
BHP Billiton is a global mining, oil and gas company headquartered in Melbourne, Australia and with a major management office in London, United Kingdom...
in Newcastle, New South Wales
Newcastle, New South Wales
The Newcastle metropolitan area is the second most populated area in the Australian state of New South Wales and includes most of the Newcastle and Lake Macquarie Local Government Areas...
, though he was not successful in gaining a university scholarship with the company. Coates attended Australian National University
Australian National University
The Australian National University is a teaching and research university located in the Australian capital, Canberra.As of 2009, the ANU employs 3,945 administrative staff who teach approximately 10,000 undergraduates, and 7,500 postgraduate students...
on scholarship as one of the first undergraduates, from which he gained a B.Sc. degree. He then moved to France
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
, doing further study at the École Normale Supérieure
École Normale Supérieure
The École normale supérieure is one of the most prestigious French grandes écoles...
in Paris, before moving again to England.
Career
In England he did postgraduate research at the University of Cambridge, his doctoral dissertation being on p-adicP-adic number
In mathematics, and chiefly number theory, the p-adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a way different from the extension of the rational number system to the real and complex number systems...
analogues of Baker's method. In 1969, Coates was appointed assistant professor of mathematics at Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
in the United States, before moving again in 1972 to Stanford University
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
where he became an associate professor.
In 1975, he returned to England where he was made a fellow
Fellow
A fellow in the broadest sense is someone who is an equal or a comrade. The term fellow is also used to describe a person, particularly by those in the upper social classes. It is most often used in an academic context: a fellow is often part of an elite group of learned people who are awarded...
of Emmanuel College
Emmanuel College, Cambridge
Emmanuel College is a constituent college of the University of Cambridge.The college was founded in 1584 by Sir Walter Mildmay on the site of a Dominican friary...
, and took up a lectureship. Here he supervised the PhD of Andrew Wiles
Andrew Wiles
Sir Andrew John Wiles KBE FRS is a British mathematician and a Royal Society Research Professor at Oxford University, specializing in number theory...
, and together they proved a partial case of the Birch and Swinnerton-Dyer conjecture
Birch and Swinnerton-Dyer conjecture
In mathematics, the Birch and Swinnerton-Dyer conjecture is an open problem in the field of number theory. Its status as one of the most challenging mathematical questions has become widely recognized; the conjecture was chosen as one of the seven Millennium Prize Problems listed by the Clay...
for elliptic curve
Elliptic curve
In mathematics, an elliptic curve is a smooth, projective algebraic curve of genus one, on which there is a specified point O. An elliptic curve is in fact an abelian variety — that is, it has a multiplication defined algebraically with respect to which it is a group — and O serves as the identity...
s with complex multiplication
Complex multiplication
In mathematics, complex multiplication is the theory of elliptic curves E that have an endomorphism ring larger than the integers; and also the theory in higher dimensions of abelian varieties A having enough endomorphisms in a certain precise sense In mathematics, complex multiplication is the...
.
In 1977, Coates moved back to Australia, becoming a professor at the Australian National University
Australian National University
The Australian National University is a teaching and research university located in the Australian capital, Canberra.As of 2009, the ANU employs 3,945 administrative staff who teach approximately 10,000 undergraduates, and 7,500 postgraduate students...
, 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
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 center of Paris.Inhabitants of Orsay are known as Orcéens.-History:...
. In 1985, he returned to the École Normale Supérieure, this time as professor and director of mathematics.
He was elected a fellow of the Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
of London in 1985, and was President of the London Mathematical Society
London Mathematical Society
-See also:* American Mathematical Society* Edinburgh Mathematical Society* European Mathematical Society* List of Mathematical Societies* Council for the Mathematical Sciences* BCS-FACS Specialist Group-External links:* * *...
from 1988 to 1990. The latter organisation awarded him the Senior Whitehead Prize
Senior Whitehead Prize
The Senior Whitehead Prize of the London Mathematical Society is currently 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 resident in the United Kingdom on 1 January of the...
in 1997, for "his fundamental research in number theory and for his many contributions to mathematical life both in the UK and internationally".
Since 1986 Coates has worked in the Department of Pure Mathematics and Mathematical Statistics
Faculty of Mathematics, University of Cambridge
The Faculty of Mathematics at the University of Cambridge comprises the Department of Pure Mathematics and Mathematical Statistics and the Department of Applied Mathematics and Theoretical Physics . It is housed in the Centre for Mathematical Sciences site in West Cambridge, alongside the Isaac...
(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
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 Kenkichi Iwasawa, in the 1950s, as part of the theory of cyclotomic fields. In the early 1970s, Barry Mazur...
, for instance, the study of the arithmetic of elliptic curves in nonabelian infinite extensions.