"Euclid alone has looked on Beauty bare," wrote the poet Edna St. Vincent Millay. And ever since Euclid's time, lovers of mathematics have marveled at its beauty, even if they have glimpsed it, as St. Vincent Millay wrote later in her sonnet, "once only and then from far away."

One of the beauties of mathematics is that it promises us eternal truths that do not depend on opinion or fashion. One plus one will never be three. But mathematics is not just about assertions of fact; the deeper truth usually lies in the explanation of the fact. A good definition of beauty in mathematics would be: simplicity that leads to insight. "Proof is beautiful," wrote the late Harvard mathematician Gian-Carlo Rota, "when it gives away the secret of the theorem, when it leads us to perceive the actual and not the logical inevitability of...