Bryan John Birch FRS (born 25 September 1931) is a British mathematician. 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. He married Gina Margaret Christ in 1961. They have three children. As a doctoral student at the University of Cambridge, he was officially working under

J. W. S. Cassels John William Scott "Ian" Cassels, FRS (11 July 1922 – 27 July 2015) was a British mathematician. Biography Cassels was educated at Neville's Cross Council School in Durham and George Heriot's School in Edinburgh. He went on to study at ...

. 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 on computations relating to the Hasse–Weil L-functions of elliptic curves. 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 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 fo ...

s 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 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 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. In 2020 he was awarded the Sylvester Medal by the Royal Society.

Selected publications

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