First posed by the ancient Greeks, there are compass and straightedge problems—squaring the circle, trisecting an angle, doubling the cube—that have served as muses for mathematicians for more than two millennia. In this engaging and refreshingly opinionated survey, David Richeson investigates how Euclid, Archimedes, Descartes, Newton, Gauss, and Leonardo da Vinci labored to understand these challenges and how some of their major mathematical discoveries emerged from their explorations. Here too are answers to such questions as: why did the Indiana state legislature pass a bill setting an incorrect value for pi?