The ABC Conjecture
The ABC Conjecture, formulated in the mid-1980's by Oesterlé and Masser, is one of the most important conjectures in number theory. It has many deep consequences, but its basic formulation can be given in entirely elementary terms. In September 2012, a 500-page solution was announced by Shinichi Mochizuki (building on several thousand pages of work that he has carried out over the last 20 years). I will explain what the conjecture asserts, some evidence that supports it, a few of its consequences, and some of the circumstances surrounding the evaluation of the proof by the number theory community.