∞ Open Problems
Algebraic GeometryNeeds more backgroundMillennium Prize: $1,000,000Open since 1965
Birch and Swinnerton-Dyer Conjecture
The rank of an elliptic curve over the rationals (the number of independent rational points of infinite order) equals the order of vanishing of its L-function at s = 1. It links the curve's rational points to an analytic function.
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