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

Erdős,
P.[0],
Silverman, R.[1], Stein, A.
“Intersection properties of families containing sets of
nearly the same size.” Ars Combin. 15
(1983): 247259.
 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): 163170.
Congress.
Numer., XXI, Utilitas Math., Winnipeg, Man. (1978).
 Bumby, Richard[2],
Ellentuck, Erik[3].
“Finitely additive measures and the first digit problem.”
Fund. Math. 65 (1969): 3342.
 Ellentuck, Erik[3],
Rucker, R. v. B.[4]
“Martin's axiom and saturated models.”
Proc. Amer. Math. Soc. 34 (1972): 243249.
 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 wellknown 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
 Tsungdao 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