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Items of Interest Related to Erdös Numbers

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 musicians in rock bands. Here is a site that does the same thing for baseball players. Here is a report on a study of such phenomena in acquaintances among classmates at a college. And in the game of chess there are notions of Morphy number and Kasparov number, connecting people who have played each other (in the latter case, it's a directed graph, based on one player's beating another).

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

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".

This page was last updated on August 12, 2005.
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