FOM: History of Pigeon-hole Principle
jlh at math.appstate.edu
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 http://members.aol.com/jeff570/mathword.html 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 jlh at math.appstate.edu
Associate Professor of Mathematics
Appalachian State University, Boone, NC 28608
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