FOM: History of Pigeon-hole Principle

Jeff Hirst jlh at
Mon Dec 4 17:35:17 EST 2000


Matt Frank asked:
>What I'd like to know about the pigeonhole principle is:  when did it come
>to be associated with pigeons?

The following account appears on the Earliest Known Uses of some Words in Mathematics
Page maintained by Jeff Miller
(see and click on p for pigeon.)

>PIGEONHOLE PRINCIPLE. The principle itself is attributed to Dirichlet in 1834, although he apparently used the term Schubfachprinzip.
>The French term is "le principe des tiroirs de Dirichlet," which can be translated "the principle of the drawers of Dirichlet."
>Pigeon-hole principle occurs in English in Paul Erdös and R. Rado, "A partition calculus in set theory," Bull. Am. Math. Soc. 62 (Sept. 1956):
>       Dedekind's pigeon-hole principle, also known as the box argument or the chest of drawers argument (Schubfachprinzip) can be described, rather
>       vaguely, as follows. If sufficiently many objects are distributed over not too many classes, then at least one class contains many of these objects.
>In the above, the authors apparently intended to use the name Dirichlet; E. C. Milner and R. Rado, "The pigeon-hole principle for ordinal numbers," Proc. Lond.
>Math. Soc., III. Ser. 15 (Oct., 1965) begins similarly:
>       Dirichlet's pigeon-hole principle (chest-of-drawers principle, Schubfachprinzip) asserts, roughly, that if a large number of objects is distributed in any
>       way over not too many classes, then one of these classes contains many of these objects.

A Mathscinet search for the use of pigeon hole principle in review text yields
the Erdos-Rado paper as the earliest source (after the 1940 MR starting date).
Perhaps pigeons were introduced to avoid discussions of Dirichlet's drawers.

-Jeff Hirst

Jeff Hirst   jlh at
Associate Professor of Mathematics
Appalachian State University, Boone, NC  28608
vox:828-262-2861    fax:828-265-8617 

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