> Deligne?s most spectacular results are on the interface of two areas > of mathematics: number theory and geometry. At first glance, the two > subjects appear to be light-years apart. As the name suggests, number > theory is the study of numbers, such as the familiar natural numbers > (1, 2, 3, and so on) and fractions, or more exotic ones, such as the > square root of two. Geometry, on the other hand, studies shapes, such > as the sphere or the surface of a donut. But French mathematician > André Weil had a penetrating insight that the two subjects are in > fact closely related. In 1940, while Weil was imprisoned for refusing > to serve in the army during World War II, he sent a letter to his > sister Simone Weil, a noted philosopher, in which he articulated his > vision of a mathematical Rosetta stone. Weil suggested that sentences > written in the language of number theory could be translated into the > language of geometry, and vice versa. ?Nothing is more fertile than > these illicit liaisons,? he wrote to his sister about the unexpected > links he uncovered between the two subjects; ?nothing gives more > pleasure to the connoisseur.? And the key to his groundbreaking idea > was something we encounter everyday when we look at the clock.