Bryan John Birch
Encyclopedia
Bryan John Birch F.R.S. (born 25 September 1931) is a British
mathematician
. His name has been given to the Birch and Swinnerton-Dyer conjecture
.
He 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
. More influenced by Harold Davenport
, he proved Birch's theorem
, one of the definitive results to come out of the Hardy–Littlewood circle method; it shows that odd-degree rational forms in a large enough set of variables must have zeroes.
He then worked closely with Peter Swinnerton-Dyer
on computations relating to the Hasse–Weil L-functions of elliptic curve
s. Their subsequently formulated conjecture relating the rank of an elliptic curve to the order of zero of an L-function was a major influence on the development of number theory
from the mid-1960s onwards. only partial results have been obtained.
In later work he contributed to algebraic K-theory
(Birch–Tate conjecture
). He then formulated ideas on the role of Heegner point
s (he had been one of those reconsidering Kurt Heegner
's original work, on the class number one problem, which had not initially regained acceptance). Birch put together the context in which the Gross–Zagier theorem was proved; the correspondence is now published.
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
.
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...
mathematician
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....
. His name has been given to 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...
.
He 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, Cambridge
Trinity College is a constituent college of the University of Cambridge. Trinity has more members than any other college in Cambridge or Oxford, with around 700 undergraduates, 430 graduates, and over 170 Fellows...
. He married Gina Margaret Christ in 1961. They have three children.
As a doctoral student 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...
, he was officially working under J. W. S. Cassels
J. W. S. Cassels
John William Scott Cassels , FRS is a leading English mathematician.-Biography:Educated at Neville's Cross Council School in Durham and George Heriot's School in Edinburgh, Cassels graduated from the University of Edinburgh with an MA in 1943.His academic career was interrupted in World War II...
. More influenced by Harold Davenport
Harold Davenport
Harold Davenport FRS was an English mathematician, known for his extensive work in number theory.-Early life:...
, he proved Birch's theorem
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:...
, one of the definitive results to come out of the Hardy–Littlewood circle method; it shows that odd-degree rational forms in a large enough set of variables must have zeroes.
He then worked closely with Peter Swinnerton-Dyer
Peter Swinnerton-Dyer
Sir Henry Peter Francis Swinnerton-Dyer, 16th Baronet KBE FRS , commonly known as Peter Swinnerton-Dyer, is an English mathematician specialising in number theory at University of Cambridge...
on computations relating to the Hasse–Weil L-functions of 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. Their subsequently formulated conjecture relating the rank of an elliptic curve to the order of zero of an L-function was a major influence on the development of number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
from the mid-1960s onwards. only partial results have been obtained.
In later work he contributed to algebraic K-theory
Algebraic K-theory
In mathematics, algebraic K-theory is an important part of homological algebra concerned with defining and applying a sequenceof functors from rings to abelian groups, for all integers n....
(Birch–Tate conjecture
Birch–Tate conjecture
The Birch–Tate conjecture is based on algebraic K-theory proposed by both Bryan John Birch and John Tate. It relates the value of a Dedekind zeta function at s = −1 to the order of K2 of the ring of integers, for a number field F....
). He then formulated ideas on the role of Heegner point
Heegner point
In mathematics, a Heegner point is a point on a modular elliptic 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 conjecture on imaginary quadratic fields of class...
s (he had been one of those reconsidering Kurt Heegner
Kurt Heegner
Kurt Heegner was a German private scholar from Berlin, who specialized inradio engineering and mathematics...
's original work, on the class number one problem, which had not initially regained acceptance). Birch put together the context in which the Gross–Zagier theorem was proved; the correspondence is now published.
He was elected a Fellow of the Royal Society in 1972; was awarded 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 1993 and the De Morgan Medal
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
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:* * *...
.
Selected publications
- Computers in Number Theory. (editor). London: Academic PressAcademic PressAcademic Press is an academic book publisher. Originally independent, it was acquired by Harcourt, Brace & World in 1969. Reed Elsevier bought Harcourt in 2000, and Academic Press is now an imprint of Elsevier....
, 1973. - Modular function of one variable IV (editor) with W. Kuyk. Lecture Notes in Mathematics 476. Berlin: Springer Verlag, 1975.
- The Collected Works of Harold Davenport. (editor). London: Academic Press, 1977.