Abstract: The idea that people are connected through just "six degrees of separation," based on Stanley Milgram's "small world study," has become part of the intellectual furniture of educated people. New evidence discovered in the Milgram papers in the Yale archives, together with a review of the literature on the "small world problem," reveals that this widely-accepted idea rests on scanty evidence. Indeed, the empirical evidence suggests that we actually live in a world deeply divided by social barriers such as race and class. An explosion of interest is occurring in the small world problem because mathematicians have developed computer models of how the small world phenomenon could logically work. But mathematical modeling is not a substitute for empirical evidence. At the core of the small world problem are fascinating psychological mysteries.