# What's Your Erdős Number?

Five. The path of descent is as follows with the Erdős numbers of authors in the path shown as [n].

1. Erdős, P.[0], Silverman, R.[1], Stein, A.  “Intersection properties of families containing sets of nearly the same size.” Ars Combin. 15 (1983): 247-259.
2. Bumby, R.[2], Fisher, R., Levinson, H., Silverman, R.[1]  “Topologies on finite sets.” Proceedings of the Ninth Southeastern Conference on Combinatorics, Graph Theory, and Computing: Florida Atlantic Univ., Boca Raton, Fla. (1978): 163-170. Congress. Numer., XXI, Utilitas Math., Winnipeg, Man. (1978).
3. Bumby, Richard[2], Ellentuck, Erik[3].  “Finitely additive measures and the first digit problem.” Fund. Math. 65 (1969): 33-42.
4. Ellentuck, Erik[3], Rucker, R. v. B.[4]  “Martin's axiom and saturated models.” Proc. Amer. Math. Soc. 34 (1972): 243-249.
5. Rucker, R. v. B.[4], Walker, J.[5]  Exploring Cellular Automata. Sausalito, CA: Autodesk, Inc., 1989.

## Other People with Erdős Numbers of Five

According to Erdős Number Facts, approximately 268,000 people are known to have finite Erdős numbers. Among these, 5 is both the median (value with the closest to equal numbers above and below) and the mode (most common value), with 87,760 people having number 5. Here are some well-known names with Erdős number 5 from Some Famous People with Finite Erdős Numbers.

• Luis W. Alvarez
• John Bardeen
• Niels Bohr
• Louis de Broglie
• Alexander Grothendieck
• Tsung-dao Lee
• Paul A. Samuelson
• Arthur L. Schawlow
• Glenn T. Seaborg
• Arnold Sommerfeld
• Alan Turing

Note that in most cases Erdős numbers are an upper bound. Particularly for people with higher numbers, there's always the possibility an obscure publication or unexplored path will reduce their numbers. An individual's number may decrease if any of the authors in their path publishes a paper with anybody whose number is less than their previous predecessor, or if a new shorter path is created when an individual's Erdős number is reduced.

by John Walker
December 6th, 2004
Revised March 13th, 2012