Birch and Swinnerton-Dyer conjecture
The Birch and Swinnerton-Dyer conjecture is an open problem in number theory linking the rational solutions of elliptic curves to their L-functions.
The Birch and Swinnerton-Dyer conjecture was proposed in the 1960s by British mathematicians Bryan Birch and Peter Swinnerton-Dyer on the basis of computer calculations. It predicts that the rank of the group of rational points on an elliptic curve over the rational numbers equals the order to which the curve's L-function vanishes at s = 1.
The general case remains unproven, and it is one of the seven Millennium Prize Problems announced by the Clay Mathematics Institute in 2000, each carrying a $1 million prize.
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