The ABC conjecture

Abstract: 

The ABC conjecture is a simple, elementary statement about whole numbers and their prime factorisations. Nevertheless, it has numerous striking consequences. Recently, S. Mochizuki announced a proof of this conjecture, but its correctness is not yet fully verified. In this talk, I will state the conjecture, motivate it, explain some of its consequences and try to explain the parts of Mochizuki's strategy that I understand.