Bryan John Birch FRS (born 25 September 1931) is a British mathematician. His name has been given to 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 ...

Biography

Bryan John Birch was born in

Burton-on-Trent Burton upon Trent, also known as Burton-on-Trent or simply Burton, is a market town in the borough of East Staffordshire in the county of Staffordshire, England, close to the border with Derbyshire. At the 2021 United Kingdom census, 2021 censu ...

, the son of Arthur Jack and Mary Edith Birch. He was educated at Shrewsbury School and

Trinity College, Cambridge Trinity College is a Colleges of the University of Cambridge, constituent college of the University of Cambridge. Founded in 1546 by King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any ...

. He married Gina Margaret Christ in 1961. They have three children. As a doctoral student 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 ...

, he was officially working under J. W. S. Cassels. More influenced by

Harold Davenport Harold Davenport FRS (30 October 1907 – 9 June 1969) was an English mathematician, known for his extensive work in number theory. Early life and education Born on 30 October 1907 in Huncoat, Lancashire, Davenport was educated at Accringto ...

, he proved Birch's theorem, one of the results to come out of the Hardy–Littlewood circle method. He then worked with Peter Swinnerton-Dyer on computations relating to the Hasse–Weil L-functions of

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. Their subsequently formulated conjecture relating the rank of an elliptic curve to the order of zero of an L-function has been an influence on the development of

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

from the mid-1960s onwards. He introduced modular symbols in about 1971. In later work he contributed to algebraic ''K''-theory ( Birch–Tate conjecture). He then formulated ideas on the role of Heegner points (he was one of those reconsidering

Kurt Heegner Kurt Heegner (; 16 December 1893 – 2 February 1965) was a German private scholar from Berlin, who specialized in radio engineering and mathematics. He is famous for his mathematical discoveries in number theory and, in particular, the Stark–H ...

's original work on the class number one problem, which had not initially gained acceptance). Birch put together the context in which the Gross–Zagier theorem was proved; the correspondence is now published. Birch was a visiting scholar at the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

in the fall of 1983. He was elected a Fellow of the Royal Society in 1972; was awarded 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 1993 and the

De Morgan Medal The De Morgan Medal is a prize for outstanding contribution to mathematics, awarded by the London Mathematical Society. The Society's most prestigious award, it is given in memory of Augustus De Morgan, who was the first President of the society ...

in 2007 both 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 ...

. In 2012 he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. In 2020 he was awarded the

Sylvester Medal The Sylvester Medal is a bronze medal awarded by the Royal Society for the encouragement of mathematical research, and accompanied by a £1,000 prize. It was named in honour of James Joseph Sylvester, the Savilian chair of geometry, Savilian Prof ...

by 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 ...

Selected publications

*''Computers in Number Theory.'' (editor). London:

Academic Press Academic Press (AP) is an academic book publisher founded in 1941. It launched a British division in the 1950s. Academic Press was acquired by Harcourt, Brace & World in 1969. Reed Elsevier said in 2000 it would buy Harcourt, a deal complete ...

, 1973.
''Modular function of one variable IV''
(editor) with W. Kuyk. Lecture Notes in Mathematics ''476''. Berlin:

Springer Verlag Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in ...

, 1975. *''The Collected Works of Harold Davenport.'' (editor). London: Academic Press, 1977.

References

International Who's Who

External links

* {{DEFAULTSORT:Birch, Bryan John 1931 births 20th-century British mathematicians 21st-century British mathematicians Alumni of Trinity College, Cambridge Fellows of Brasenose College, Oxford Fellows of the American Mathematical Society Fellows of the Royal Society Institute for Advanced Study visiting scholars Living people