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

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 from the mid-1960s onwards.

[1] Birch was a visiting scholar at the Institute for Advanced Study in the fall of 1983.