Title:  The ABC conjecture
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Abstract:  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 Oesterle 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.