In a 1959 paper, Richard Kadison and I.M. Singer asked a question about the extreme points of a certain compact convex set in the set of bounded operators on l_2. Over time, many conjectures in disparate areas were found to be equivalent. Last summer, a preprint was posted with a solution (positively vetted by some experts, though not yet published). I plan to give two talks about the result. The first will concentrate on the equivalent problems, the second on the main constructions in the proof.