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. He published more papers during his life (at least 1400) than any other mathematician in history.
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; 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.
The Erdős number was most likely first defined in print by Casper Goffman, an analyst whose own Erdős number is 1. Goffman published his observations about Erdős's prolific collaboration in a 1969 article entitled "And what is your Erdős number?"
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