The Erdős number is a way of describing the "collaborative distance" between an author and the prolific mathematician Paul Erdős, who was famous for his widespread collaboration. It is a concept from graph theory that has become famous both in and outside of the academic world, particularly for its playful insight into the interconnectedness of researchers across the globe. The smaller an author's Erdős number, the closer they are to Paul Erdős through their coauthorships. You may have heard of a similar exercise in terms of the Degrees of Kevin Bacon.
Erdős numbers start with Paul Erdős himself at 0. His immediate coauthors have an Erdős number of 1, and their coauthors (not including Erdős) have an Erdős number of 2, and so on. Notable figures such as Bill Gates have an Erdős number of 4.
I'm not sure how rigorously statistics on Erdős numbers are kept, but there's an interesting disucssion in Chalkdust Magazine. A histogram of the number of people with each Erdős number is also on their site and reproduced below. Needless to say, if you have coauthored a paper with me, then your Erdős number is at most 5. Correspondingly, if you have an Erdős number of 2 or less, then let's find a project to work on together!
