# Six degrees of Paul Erdős

The goal of the game Six Degrees of Kevin Bacon is to connect actors to Kevin Bacon in as few steps as possible. For example, Elvis Presley can be linked to Kevin Bacon in two steps: Elvis Presley made a movie with Ed Asner, and Ed Asner made a movie with Kevin Bacon. The game could be played with other actors, but the advantage of using Kevin Bacon is that he’s made movies with a lot of other actors.

Mathematicians have a similar and older game, connecting each other to Paul Erdős via a chain of papers. Like Kevin Bacon, Erdős was a social hub. He wrote more math papers than anyone else and usually collaborated with other authors.

The length of the smallest chain connecting someone to Paul Erdős is called that person’s  Erdős number. Erdős has Erdős number 0. Anyone who wrote a paper with Erdős has Erdős number 1, etc. My Erdős number is 4 because I wrote a paper with Ralph Showalter, who wrote a paper with Charles Radin, who wrote a paper with John Horton Conway, who wrote a paper with Erdős. I’ve written papers with other folks with Erdős number 3, but not with anyone with a lower number, so my number is 4. I calculated my Erdős number after learning about this  web site from Dave Richeson’s six degrees of separation blog post.

Paul Erdős was a pure mathematician. I wonder who might be the Paul Erdős of applied math, someone who has written a large number of applied math articles, especially with many collaborators. It would be hard to say since applied math is a fuzzy classification, blending into other disciplines. Still, any nominations?

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## 8 thoughts on “Six degrees of Paul Erdős”

1. Hm… Keith’s number is 4, according to your link site; he links through Kevin, whose number is 3. I’m not represented as an author on their page but I’ve co-authored with Kevin so I guess my number is also 4.

Papers in medicine typically have long lists of authors so perhaps the game isn’t as fun there. I guess one could do a Watson number or something…