The Erdős number is used as a tool to study how mathematicians cooperate to find answers to unsolved problems. But what is the history behind the Erdős number?
According to the USNA website Erdös Numbers, it is named after a most prolific and supremely talented mathematician,
Paul Erdös (1913-1996) was a phenomenally prolific mathematician, who combined extraordinary talent with near-total devotion to mathematical research. For most of his career he did not have a conventional position; he was a mathematical nomad who disdained property, power, and even family life as distractions from what he really wanted to do: prove theorems.
His work in number theory, set theory, various kinds of combinatorics (including graph theory), analysis, and probablility theory resulted in well over 1500 publications, with over 500 collaborators, giving rise to the Erdös Number, which was started by his friends (Vienna University of Technology), and is described as:
All those mathematicians who co-authored a paper or book with Erdös are said to have Erdös number 1; those who have co-authored with someone of Erdös number 1 (but not with Erdös himself) have Erdös number 2; and so on.
According to the USNA website, the number of people is almost 10,000.
Oakland University have a dedicated The Erdös Number Project webpage, essentially exploring the 'six degrees of separation' in mathematics based research, there is even a facility to find out your own Erdös Number.
In terms of timeframes, according to Oakland's webpage Research on Collaboration in Research,
The earliest discussion we could find on Erdös numbers are articles by Casper Goffman [And what is your Erdos number?, American Mathematical Monthly 76 (1969), 791] and Ron Graham (writing under the pseudonym Tom Odda) [On properties of a well-known graph or what is your Ramsey number?, Topics in Graph Theory (New York, 1977) 166-172]. According to MELVIN HENRIKSEN, the idea was suggested by John Isbell at Princeton University around 1957.
(Incidently, John Isbell has an Erdös number of 2)
An interesting part of the website is the correlation of Fields Medal and Nobel Prize recipients and their Erdös Number - Some Famous People with Finite Erdös Numbers, that many have a low Erdös Number - read into that what you will.
One thing is clear though, the Erdös Number and the associated project is a fitting tribute, started by his friends (according to the Vienna University of Technology) to a great scholar and a way to show that in some way, we are all linked in our drive for knowledge.