# Mathematics Colloquia and Seminars

In 1991 the physicists Candelas, de la Ossa, Green and Parkes made an astonishing prediction, based on "mirror symmetry" in string theory, of the number of rational curves of all degrees on a quintic threefold $Q \subset \Bbb{P}^4$. This sparked a huge amount of mathematical activity, which has since resulted in a precise formulation and proof of their prediction. I will describe some of the mathematics involved, and outline a new proof of this "mirror theorem". This is joint work with Alexander Givental.