Critique of the Pigeon-Hole Principle's Elevated Status in Mathematics
By
tosh
Lightly browned and well buttered. A solid pick from the rack.
Summary
This article critiques the elevated status of the pigeon-hole principle in mathematics, arguing that it's an elementary combinatorial observation that doesn't deserve the special reverence it receives. The author examines how the principle is treated with undue mystique across different languages and mathematical communities, noting that proofs using it are often regarded as particularly ingenious when they shouldn't be. The piece explores the principle's proper place in mathematical reasoning and questions why such a basic concept has achieved such elevated status.
Key quotes
· 4 pulledRight at the moment I was introduced to the pigeon-hole principle, I understood that there was something very special about it, for the Englishman from whom I learned it told it to me under its German name 'das Schubfach prinzip'.
Later I learned that also in other languages it is honoured by a special name.
It is, indeed, surrounded by some mystique, for proofs using it are often regarded as something special, something particularly ingenious.
This feeling of awe is, for instance, nicely reflected by Ross Honsberger when he concludes
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