Bryan John Birch FRS (born 25 September 1931) is a British

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. 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 an ...

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. In 2011, it had a population of 72,299. Th ...

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

Trinity College, Cambridge Trinity College is a 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 college at either Cambridge or Oxford. ...

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

University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

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

Birch's theorem In mathematics, Birch's theorem, named for Bryan John Birch, is a statement about the representability of zero by odd degree forms. Statement of Birch's theorem Let ''K'' be an algebraic number field, ''k'', ''l'' and ''n'' be natural numbers, ' ...

, one of the results to come out of the Hardy–Littlewood circle method. He then worked with

Peter Swinnerton-Dyer Sir Henry Peter Francis Swinnerton-Dyer, 16th Baronet, (2 August 1927 – 26 December 2018) was an English mathematician specialising in number theory at the University of Cambridge. As a mathematician he was best known for his part in the ...

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. I ...

s. Their subsequently formulated conjecture relating the

rank of an elliptic curve In mathematics, the rank of an elliptic curve is the rational Mordell–Weil rank of an elliptic curve E defined over the field of rational numbers. Mordell's theorem says the group of rational points on an elliptic curve has a finite basis. This ...

to the order of zero of an L-function has been an influence on the development of

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Ma ...

from the mid-1960s onwards. only partial results have been obtained. He introduced

modular symbol In mathematics, modular symbols, introduced independently by Bryan John Birch and by , span a vector space closely related to a space of modular forms, on which the action of the Hecke algebra can be described explicitly. This makes them useful for ...

s in about 1971. In later work he contributed to algebraic ''K''-theory ( Birch–Tate conjecture). He then formulated ideas on the role of

Heegner point In mathematics, a Heegner point is a point on a modular curve that is the image of a quadratic imaginary point of the upper half-plane. They were defined by Bryan Birch and named after Kurt Heegner, who used similar ideas to prove Gauss's conjectu ...

s (he was one of those reconsidering Kurt Heegner's original work on the

class number one problem In mathematics, the Gauss class number problem (for imaginary quadratic fields), as usually understood, is to provide for each ''n'' ≥ 1 a complete list of imaginary quadratic fields \mathbb(\sqrt) (for negative integers ''d'') having ...

, 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), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent schola ...

in the fall of 1983. He was elected a Fellow of the Royal Society in 1972; was awarded the Senior Whitehead Prize in 1993 and the De Morgan Medal in 2007 both of the

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

. 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, meeting ...

. In 2020 he was awarded the

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

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 was acquired by Harcourt, Brace & World in 1969. Reed Elsevier bought Harcourt in 2000, and Academic Press is now an imprint of Elsevier. Academic Press publishes refer ...

, 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 i ...

, 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