In the early 1980's W. Stothers and (independently) R. Mason discovered a new and simple inequality about the zeros of polynomials. The proof uses only basic facts about derivatives. As a corollary Mason obtained a very simple proof of "Fermat's Last Theorem" for polynomials. Inspired by Mason's observations, Masser and Oesterl e proposed an analogous inequality for integers, which has come to be known as the ABC conjecture. In this talk I will discuss Mason's inequality, some of its applications, and the resulting ABC conjecture for integers. The talk should be accessible to a general mathematical audience.