Etude on the Chromatic Number of the Plane

Abstract

The Borsuk Conjecture survived for sixty-one years from 1932 to its negative resolution in 1993. The problem I am going to share with you here is now sixty years old. It may require another century, may be centuries, to be settled. This is my favorite unsolved problem in all of mathematics, because it is so easy to understand — I have presented it to middle school audiences — but very hard, if it is even possible, to solve.