**Title:** Four Tales of Impossibility

**Abstract:** "Nothing is impossible!" It is comforting to believe this greeting card sentiment; it is the American dream. Human flight and the four-minute mile were proclaimed to be impossible, but both came to pass. Yet there are impossible things, and it is possible to prove that they are so. In this talk we will look at some of the most famous impossibility theorems—the so-called "problems of antiquity." The ancient Greek geometers tried and failed to square circles, trisect angles, double cubes, and construct regular polygons using only a compass and straightedge. So did future generations of great mathematicians. It took two thousand years to prove conclusively that all four of these are mathematically impossible. No, not even Chuck Norris can square the circle.