Birch and Swinnerton-Dyer conjecture

The Birch and Swinnerton-Dyer Conjecture connects the behavior of certain mathematical objects called elliptic curves with number theory and algebra. Specifically, it suggests that the number of rational solutions (solution pairs with whole numbers) to an elliptic curve can be linked to the properties of a related mathematical function, called the L-function. If the L-function has specific features, it implies there are infinitely many rational solutions. This conjecture is one of the seven Millennium Prize Problems, meaning its proof or disproof could have profound implications for mathematics.