The twentysomething daughter of a friend of mine recently ordered half a dozen new dresses. She wasn’t planning to keep the lot; she’d been invited to the wedding of a college classmate and knew in ...

Mona Lisa’s smile. Mary Lou Retton’s Olympic vault. Mariah Carey’s musical pitch. All are considered perfect. So are the numbers 6 and 28. With feats of artistry and athleticism, perfection lies in ...

Let r₂(n) denote the number of representations of the positive integer n as a sum of two squares, and let d(n) denote the number of positive divisors of n. Gauss and Dirichlet were evidently the first ...