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, rather arbitrarily, it seems, by the actor Kevin Bacon. An article about this appears in Math Horizons (“The Eccentricities of Actors” by John M. Harris and Michael J. Mossinghoff, February 1998, pages 23–25). Tim Hsu and David Grabiner have observed that since Dan Kleitman actually appears in and is a mathematical consultant for the movie Good Will Hunting, Bacon has a combined Erdös/Bacon number of 3, because 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. It was thought at one time that Paul Erdös himself had an official Bacon number of 4, by virtue of N is a Number (a documentary about him), but a supposed link through Tomasz Luczak is bogus. Some people claim that his number is 3, because Alec Guinness appears in N is a Number (he was one of the people getting an honorary degree at the same time Paul was), but he really had no role in that film. Here is a site that does the same thing for baseball players. 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). Recently a similar notion has been introduced for bridge players: Vanderbilt numbers (copy of article posted with permission from the Bridge Bulletin). Here is an article about similar links in surgery. Finally, there is a site for linking references on Wikipedia.

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 a play 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 book by Duncan Watts entitled Small Worlds; Grossman’s review of this book appears in the August, 2000 issue of The American Mathematical Monthly. Much more information along these lines is available on our page devoted to Research on Collaboration in Research.

One can also argue that the baseball player who broke Babe Ruth’s home run record, the late Henry L. “Hank” Aaron, has a joint publication with Paul Erdös. Carl Pomerance (a professor 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 article by Ivars Peterson).

Somewhat related to the issue of collaboration in mathematical research is the issue of academic roots. There is a wonderful website, the Mathematics Genealogy Project , which traces mathematicians' academic ancestors.

The branch of mathematics dealing with the kinds of issues raised in looking at collaboration and Erdös numbers is graph theory. Graph theory was one of Paul Erdös’s specialties, of course.

A portion of National Public Radio's Radiolab program broadcast in November, 2009 is about Paul Erdös and Erdös numbers. Details and podcasts are avaible.

Kristina Pfaff-Harris has written a delightful article called Six Degrees of Paul Erdös for

Kirsten Menger-Anderson has written a wonderful article called Who’s Important? A Tale from Wikipedia.

Aziz S. Inan has written an article exploring some numerological aspects of Paul Erdös’s birthdate (March 26, 1913).

This page was last updated on May 31, 2021.