Erdős numbers are named for the Hungarian-American mathematician Paul Erdős and are an application of graph theory, a field in which he published extensively. They treat collaboration among researchers — measured by publication of joint papers — as a graph. A researcher's Erdős number is the length of the shortest path, via co-author relationships, connecting him or her to Paul Erdős. Erdős was an amazingly prolific writer with over 1500 papers in diverse areas of mathematics and over 500 collaborators.
More explicitly, your Erdős number is the first number in the following list which applies to you:
- 0: You are Paul Erdős .
- 1: You have co-authored a paper with Erdős.
- 2: You have done a paper with someone of Erdős number 1.
- N+1 You have co-authored a paper with someone of Erdős number N.
If there is no chain of co-author relations connecting you to Erdős, your Erdős number is considered infinite.
Erdős number connections extend far outside mathematics. In Physics, Einstein has Erdős number two while Pauli, Feynman, Born and Gell-Mann among others are at three, Dirac and Heisenberg four. For some fields a few authors provide the main connection — Ron Rivest in cryptography, John Tukey in Statistics, Eugene Koonin, Eric Lander and Bruce Kristal in biology. They all have Erdős number two and several collaborators, so through them many people in their field get small numbers. Prominent people in many other fields also have finite Erdős numbers — from Piaget, Shannon, von Neumann, and both Google founders at three, to Chomsky, Popper, Pauling and Bill Gates at four. Watson and Crick are at five and six, respectively.
There are analogous measures in other fields. Actors calculate their Kevin Bacon number, based on appearing in films together, and Go players have a Shusaku number, the minimum number of games linking them to a great 19th century master. Similarly, chess players can calculate a Morphy number.
The The Erdős Number Project at Oakland University in Rochester, Michigan has much more information.