One day during the winter of 1998, mathematicians Duncan Watts and Steve Strogatz of Cornell University in Ithaca, New York, sat down at a table in Strogatz’s office and drew a series of dots on a piece of paper. They then connected some of the dots together with lines to produce a simple pattern that mathematicians refer to as a graph. This may not sound like serious mathematics; it certainly does not sound like a profitable way to go about making discoveries. But as the two mathematicians were soon to learn, they had connected their dots in a peculiar way that no mathematician had ever envisioned. In so doing, they had stumbled over a graph of an unprecedented and fascinating kind.