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Erdös numbers are not the only case of interest in links among
people. For a **related website, where the vertices are
actors** and the links are provided by appearance in the same
movie, take a look at the Oracle of Bacon. Here
the central position of Paul Erdös is assumed by the **actor
Kevin Bacon**. Tim Hsu and David Grabiner have observed that since
**Dan Kleitman** actually appears (briefly) in and is a mathematical consultant
for the movie *Good Will Hunting*, Bacon has a combined
Erdös/Bacon number of 3, since Kleitman has Bacon number 2 (via
Minnie Driver, who was in *Sleepers* with Kevin Bacon) and
Erdös number 1. Bruce
Reznick is in a similar position, with an Erdös number of 1 and a
Bacon number (by virture of being an extra in *Pretty Maids All in a
Row* with Roddy
McDowall) of 2. In fact, according to the Oracle of Bacon site, Paul
Erdös himself has an official Bacon
number of 4, by virtue of the *N is a
Number* (a documentary about him), and lots of other mathematicians have finite
Bacon number through this film. **However, we have recently
discovered
that this is bogus, because the link, named Gene Patterson, is not the
same person in N is a
Number as in the film Box of Moonlight, where the link
supposedly lies. Thus it remains an open question as to what Paul
Erdös’s Bacon number is.**
In a similar vein, William Montbleau has a
site devoted
to links among

Click here
for a chuckle.

A serious look at the phenomenon of networks like these (often
referred to with the phrase *six degrees of separation*, in
reference to the idea, originating in Stanley Milgram's
research in the 1960s ("The Small World Problem", Psychology Today,
May 1967, 60-67), that you can connect (almost) any two people in the
world by a path of six acquaintances, as well as aplay and movie with that title
mildly
related to this concept) appears in *Nature*, 4 June 1998, Vol. 393, No.
6684, pp. 409 and 440.
See also a recent book by
**Duncan Watts** entitled Small
Worlds; Grossman’s review
of this book appears in the August, 2000
issue of The
American Mathematical Monthly.
(There is also an
audio
report on this from National Public Radio.)
See also this article in SIAM News. Much more
information along these lines is available on our page devoted to research on collaboration.

One can also argue that the **baseball player** who broke
Babe Ruth’s home run record, Henry L.
“Hank” Aaron, has a joint publication with Paul Erdös.
Carl Pomerance (now at
Dartmouth College), who
had
a long and fruitful collaboration with Paul, reports having a baseball
autographed by both of them, occasioned by their both having received
honorary degrees at Emory University in 1995 (it’s a long story,
having to do with a property of the numbers 714 and 715, reported by Carl
at the Paul Erdös memorial session held at the 1997 annual AMS/MAA
meeting in San Diego, and recounted in an article in the *Notices of the
American Mathematical Society*, January 1998, page 22, as well as
in an Ivar
Peterson article).

Somewhat related to the issue of collaboration in mathematical research
is the issue of **academic roots**. At least two academic
genealogical websites exist, which try to trace people’s academic
ancestors, one in mathematics,
and one in theoretical computer science
(which quickly gets back to mathematicians, of course).

The branch of mathematics dealing with the kinds of issues raised in
looking at collaboration and Erdös numbers is *graph theory*.
Here is a
link to some graph theory resources, including people, research, writings
(with some interesting statistics like the average number of papers per
author), conferences, and the famous Four Color Theorem. Graph theory was
one of Paul Erdös’s specialties, of course.

Kristina Pfaff-Harris has written a delightful article called “Six Degrees of Paul Erdös” for linux.com.

Dave Rusin has a Web page devoted to all the proper names that appear in the Mathematics Subject Classification, such as in "Kan extensions" or "Erdös problems".

URL = http://www.oakland.edu/enp/related.html

This page was last updated on August 12, 2005.

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