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Mathematics

Elliptic Curves and the Birch and Swinnerton-Dyer Conjecture

Quick fact

The Birch and Swinnerton-Dyer conjecture is one of the Clay Mathematics Institute's Millennium Prize Problems, rewarding a $1 million prize for a proof. It predicts that the rank of an elliptic curve—the number of independent infinite-order rational points—is exactly the order of vanishing of its L-function at the point s=1.

Why this is interesting

We all know that some equations have finitely many solutions and others have infinitely many. But what if the 'number of solutions' to a certain kind of equation could be predicted by a seemingly unrelated analytic function?