Erdős—who had a lifelong affair with caffeine, and later amphetamines—regularly worked 20 hours a day. Into his 70s, Erdős was publishing more papers per year than many good mathematicians publish during their lifetimes. During a short break he had taken from amphetamines to prove he wasn’t addicted, Erdős noted a drop in his productivity, and proclaimed that mathematics had been set back a month.
This tremendous volume of work, spread out over various disciplines and all over the world, has left the mathematician with a very fitting legacy: the Erdős number.
By the simplest definition, a person’s Erdős Number is their degree of separation from Erdős via a published paper. If you collaborated with him on a paper, your Erdős number is 1. If you’re a co-author with someone who was a co-author with Erdős, you get a 2, and so on. Only Erdős’ has 0 as an Erdős number. If you have no collaborative connection, your Erdős number is infinite. As time has gone on the highest reported Erdős number has increased: from 8 in 2000 to 15 in 2013.
Other versions demand that publications may only have two authors in order to be counted toward an Erdős number. There is an Erdős-Bacon number that sums a person’s Erdős number with their Bacon number: a degree-of-separation value based on the same postulate but applied to a person’s film connection to actor Kevin Bacon (some players allow non-film connections) . The first recorded source noting the idea of counting degrees of separation from Erdős was in a mathematics paper published in 1969 by a colleague. The Erdős Number Project, founded by Jerrold Grossman and Patrick Ion, and hosted by Oakland University in Michigan, started in 1995 and is the most extensive resource on Erdős’s publications and Erdős numbers.
Erdős numbers have no actual consequence—it’s a game. And like most games, it pops up, I’ve found, between classes, over drinks at meetings and during work breaks. Paul Erdős believed that mathematics was a collaborative activity, and the Erdős number, perhaps unintentionally, reflects that. It brings people together; gives them something to share. Sometimes when a great scientist dies, he or she is remembered with a statue, an institute, a street name or a school, but Erdős has been immortalized with something highly unique: a game derived from his work, and reflecting his collaborative spirit.
(Please note that a large portion of the research for this article comes from Paul Hoffman’s book on Erdős, The Man Who Loved Only Numbers.)