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, mathematical structure, structure, space, Mathematica ...

. His name has been given to the Birch and Swinnerton-Dyer conjecture.

Biography

Bryan John Birch was born in Burton-on-Trent, 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, 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 curves. 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 (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, "Math ...

from the mid-1960s onwards. only partial results have been obtained. He introduced modular symbols in about 1971. In later work he contributed to algebraic ''K''-theory (

Birch–Tate conjecture The Birch–Tate conjecture is a conjecture in mathematics (more specifically in algebraic K-theory) proposed by both Bryan John Birch and John Tate. Statement In algebraic K-theory, the group ''K''2 is defined as the center of the Steinberg g ...

). 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 conje ...

s (he was one of those reconsidering Kurt Heegner'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), 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 scholar ...

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 S ...

. 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 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, r ...

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 refere ...

, 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