Informally, the Birch--Swinnerton-Dyer conjecture identifies the set of rational points on an elliptic curve via the order of vanishing of an associated holomorphic function, called the L-function. In this talk, we will give a precise statement of this conjecture and discuss it's relation to the famous Congruent number problem. The talk will be especially useful if you're planning to attend Alexander Smith's RSG lecture series. Speaker(s): Alex Horawa (UM)