The Erdős number

The popular Erdős number of a mathematician is determined as the least number of steps between Erdős and the person when walking through a path where consecutive people coathored at least one paper. That is, Erdős has Erdős number zero, his coathors have one, the coauthors' coauthors, who themselves are not coauthors of Erdős, have two, etc. Finding the Erdős number of various persons is something similar to the party game ``Six degrees of separation''.

The Erdös Number Project , maintained by Jerry Grossman, is the most comprehensive and amusing source of information on Erdős number.

There is actually serious research on the science behind this so called "small world" phenomenon. Interestingly, this research heavily uses the mathematical theory of random graphs—created by Erdős himself.