The popular Erdős number of a mathematician is determined as the
least number of steps between Erdős and the person when walking through a
path where consecutive people coathored at least one paper.
That is, Erdős has Erdős number zero,
his coathors have one, the coauthors' coauthors, who themselves are not
coauthors of Erdős, have two, etc.
Finding the Erdős number of various persons is something similar
to the party game ``Six degrees of separation''.
The Erdös Number Project
, maintained by
Jerry Grossman, is the most comprehensive and amusing source of
information on Erdős number.
There is actually serious research on the science behind this so called
"small world" phenomenon.
Interestingly, this research heavily uses the mathematical theory
of random graphs—created by Erdős himself.

Stanley Milgram:
The Small World Problem,
Psychology Today, May 1967, 6067.

Mark Buchanan:
Nexus, Small Worlds and the Grounbreaking Science of Networks
, W. W. Norton and Comp., 2002, 256 pp., ISBN 0393041530

Tom Odda [R. Graham]: On properties of a wellknown graph or what is your Ramsey number?
in: Topics in graph theory, (New York, 1977),
Ann. New York Acad. Sci., 328,
New York Acad. Sci., New York, 1979. 166172,

Paul Erdős:
On the fundamental problem of mathematics,
American Mathematical Monthly, 79(1972), 149150.

Caspar Goffman: And what is your Erdős number?
American Mathematical
Monthly, 76 (1969), 791.

J. J. Collins, C. C. Chow:
It's
a small world
, Nature, 393(1998), 409410

Kristina PfaffHarris:
Six Degrees of Paul Erdős
,
linux.com

Simon Singh:
ErdosBacon Numbers, Daily Telegraph, April 2002

Erica Klarreich:
Theorems for
Sale,
Science News Online

Ivars Peterson:
Groups, graphs, and Erdős numbers,
Science News,
165>
(2004), June 12,

Duncan J. Watts:
The Dynamics of Networks between Order and Randomness,
Princeton University Press, 1999, xvi+262 pp.

Greg Martin's Erdős number is
2

Jörg Winkelmann's Erdős number is
5

Kenrick Mock's Erdős number is
6