Much in the way the rest of us measure the degree to which we are Hollywood royalty by the closeness of our kinship to Kevin Bacon, mathematicians start their family tree with the ubiquitous Paul Erdos at the root.
Erdos (1913-1996) was a Hungarian mathematician known for his eccentricity and prolific output of publications. His (approximately) 1,475 articles and 511 collaborators on those articles serve as the basis for calculating so-called "Erdos numbers."
One's Erdos number is a decidedly tongue-in-cheek measure of a mathematician's (or anyone else's for that matter) collaborative distance from Paul Erdos. What follows is a guide to calculating an Erdos number.
The most basic way to calculate an Erdos number is fairly straightforward and simple. To start with, Paul Erdos himself is assigned an Erdos number of 0 (zero). Each of his collaborators has an Erdos number of 1; in other words, there is one step from Erdos himself to someone who directly collaborated with him on an article. Anyone collaborating on an article with one of his collaborators would then have an Erdos number of 2, and so on.
Put in mathematical terms, if one writes an article with a mathematician with a particular Erdos number x, then one's own Erdos number can be expressed by the formula x+1. Since Erdos himself collaborated with so many people, and collaboration on articles is such a common practice anyway, a list of everyone with an Erdos number would be truly staggering. In addition, because there is a great deal of interdisciplinary work done by mathematicians (especially statisticians) and other scientists, Erdos numbers can be assigned to people in fields as diverse as genetics, political science, and linguistics.
But what of that handful of people on the planet who have not coauthored a scholarly paper with someone having Erdos number x? If no connection to Paul Erdos can be shown to exist, one is said to have an Erdos number of infinity.
As stated earlier, the above method of calculating an Erdos number is simple and straightforward. However, mathematicians being what they are (intelligent, crazed, mischievous, and easily bored), other methods of calculation have been put forward as well. For example, there are the "rational Erdos numbers" proposed by Michael Barr, which take into account whether or not people coauthored multiple articles with Erdos or their other collaborators. Such complex operations are, however, outside the scope of this guide.