The Birch and Swinnerton-Dyer conjecture is a famous unsolved problem in mathematics, specifically in the field of number theory. It relates to the study of elliptic curves, which are equations that describe certain shapes and have important applications in cryptography and algebraic geometry. The conjecture suggests a deep connection between the number of rational solutions to an elliptic curve and the behavior of a specific mathematical function called the L-function associated with that curve. According to the conjecture, the rank of the group of rational points on an elliptic curve can be determined by analyzing the L-function at a particular point. If the L-function equals zero at that point, it indicates that the curve has infinitely many rational solutions. The Birch and Swinnerton-Dyer conjecture is one of the seven Millennium Prize Problems, and solving it carries a reward of one million dollars.