page_title: Pigeonhole principle
section_title: Etymology
hierarchical_section_title: Pigeonhole principle / Etymology
caption_attribution_description: English: Pigeon-hole messageboxes at Stanford University, California, USA
context_page_description: In mathematics, the pigeonhole principle states that if items are put into containers, with, then at least one container must contain more than one item. In layman's terms, if you have more "objects" than you have "holes," at least one hole must have multiple objects in it. A real-life example could be, "if you have three gloves, then you have at least two right-hand gloves, or at least two left-hand gloves," because you have 3 objects, but only two categories to put them into. This seemingly obvious statement, a type of counting argument, can be used to demonstrate possibly unexpected results. For example, if you know that the population of London is greater than the maximum number of hairs that can be present on a human's head, then the pigeonhole principle requires that there must be two people in London who have the same number of hairs on their heads.
  Although the pigeonhole principle appears as early as 1624 in a book attributed to Jean Leurechon, it is commonly called Dirichlet's box principle or Dirichlet's drawer principle after an 1834 treatment of the principle by Peter Gustav Lejeune Dirichlet under the name Schubfachprinzip.
context_section_description: Dirichlet published his works in both French and German, using either the German Schubfach or the French tiroir. The strict original meaning of these terms corresponds to the English drawer, that is, an open-topped box that can be slid in and out of the cabinet that contains it. (Dirichlet wrote about distributing pearls among drawers.) These terms were morphed to the word pigeonhole in the sense of a small open space in a desk, cabinet, or wall for keeping letters or papers, metaphorically rooted in structures that house pigeons.
  Because furniture with pigeonholes is commonly used for storing or sorting things into many categories (such as letters in a post office or room keys in a hotel), the translation pigeonhole may be a better rendering of Dirichlet's original drawer metaphor. That understanding of the term pigeonhole, referring to some furniture features, is fading—especially among those who do not speak English natively but as a lingua franca in the scientific world—in favour of the more pictorial interpretation, literally involving pigeons and holes. The suggestive (though not misleading) interpretation of "pigeonhole" as "dovecote" has lately found its way back to a German back-translation of the "pigeonhole principle" as the "Taubenschlagprinzip".
  Besides the original terms "Schubfachprinzip" in German and "Principe des tiroirs" in French, other literal translations are still in use in Bulgarian ("принцип на чекмеджетата"), Chinese ("抽屉原理"), Danish ("Skuffeprincippet"), Dutch ("ladenprincipe "), Hungarian ("skatulyaelv"), Italian ("principio dei cassetti"), Japanese ("引き出し論法"), Persian ("اصل لانه کبوتری"), Polish ("zasada szufladkowa"), Swedish ("Lådprincipen"), and Turkish ("çekmece ilkesi").
caption: Pigeon-hole messageboxes at Stanford University
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