# Erdős number

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The Erdős number (Hungarian pronunciation: [ˈɛrdøːʃ]) describes the "collaborative distance" between a person and mathematician Paul Erdős, as measured by authorship of mathematical papers.

It was created by friends as a humorous tribute to the enormous output of Erdős, one of the most prolific modern writers of mathematical papers, and has become well-known in scientific circles as a tongue-in-cheek measurement of mathematical prominence.

Paul Erdős was an influential and itinerant mathematician, who spent a large portion of his later life living out of a suitcase and writing papers with those of his colleagues willing to give him room and board.[1] He published more papers during his life (at least 1400) than any other mathematician in history.[1]

## Contents

### Definition

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. Anybody else's Erdős number is k + 1 if the lowest Erdős number of any coauthor is k.

Erdős wrote around 1,400 mathematical articles in his lifetime, mostly co-written. He had 511 direct collaborators;[2] 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 (8,162 people as of 2007), 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 Erdős number of infinity (or an undefined one).

There is room for ambiguity over what constitutes a link between two authors; the Erdős Number Project web site says:

but they do not include non-research publications such as elementary textbooks, joint editorships, obituaries, and the like. The “Erdős number of the second kind” restricts assignment of Erdős numbers to papers with only two collaborators.[3]

The Erdős number was most likely first defined in print by Casper Goffman, an analyst whose own Erdős number is 1.[4] Goffman published his observations about Erdős's prolific collaboration in a 1969 article entitled "And what is your Erdős number?"[5]