Erdős number

In order to be assigned an Erdős number, an author must co-write a mathematical paper with an author with a finite Erdős number. Paul Erdős has an Erdős number of zero. If the lowest Erdős number of a coauthor is X, then the author's Erdős number is X + 1.

Erdős wrote around 1500 mathematical articles in his lifetime, mostly co-written. He had 509 direct collaborators^[1]; these are the people with Erdős number 1. The people who have collaborated with them (but not with Erdős himself) have an Erdős number of 2 (6,984 people), those who have collaborated with people who have an Erdős number of 2 (but not with Erdős or anyone with an Erdős number of 1) have an Erdős number of 3, and so forth. A person with no such coauthorship chain connecting to Erdős has an undefined (or infinite) Erdős number. There is of course room for ambiguity over what constitutes a link between two authors; the Erdős Number Project website says "Our criterion for inclusion of an edge between vertices u and v is some research collaboration between them resulting in a published work. Any number of additional co-authors is permitted," but they do not include non-research publications such as elementary textbooks, joint editorships, obituaries, and the like.

The Erdős number was most likely first defined by Casper Goffman, an analyst whose own Erdős number is 1.^[2] Goffman published his observations about Erdős's prolific collaboration in a 1969 article entitled "And what is your Erdős number?"