The Evolution of Numbers

I’ve always loved word origins. Often, knowing where a word comes from can provide you with insight on what it means today. At the very least, it makes you look smart at parties (e.g., “Did you know that the word apocalypse shares the same Greek root as calypso…”).

This post is the first in a series on mathematical word origins. Since math(s) is an old subject, many mathematical terms have ancient roots (for English, this usually means Greek and Latin). For today, we’ll explore the origins of the English words for counting and arithmetic. For all posts in this series, my primary source is Steven Schwartzman’s The Words of Mathematics, with an occasional assist from the Online Etymology Dictionary.

  1. One through Ten. I’m actually going to skip these; most Indo-European languages have a base 10 system whose words are in rough correspondence with each other (for instance, the word for 6 is six, sechsseiseis, and seks, in French, German, Italian, Spanish, and Norwegian, respectively). If you’re interested in exactly how those consonants correspond, go read up on Grimm’s law.
  2. Eleven and Twelve. These words have a particularly Germanic origin: for example, in French you’d use onze and douze while in German it’s elf and zwölf. The English word eleven comes from the Old English endleofon, which basically translates as “one left over.” If you were counting up 11 items, you’d get to ten, and then say “and there’s one left over.” Eventually, this got condensed down into our modern eleven. (It makes a certain amount of sense, no?) The same thing goes for twelve: the Old English twelf comes from the Proto-Germanic twa-lif, which means “two left.”
  3. Thousand and Million. The word thousand comes from the Germanic thus (thick) and hund (hundred), making a thousand a “thick hundred.” In the Romance languages, though, the word thousand comes from the Latin mille. The English word million originally meant “a great thousand.” Interestingly, there appears to be a connection between the words thousand and dozen (e.g., the Dutch word for a thousand is duizend), leading some scholars to speculate that some Germanic cultures had a mixed base-10 and base-12 system. This may also be seen in the fact that in the UK, a “hundredweight” is 112 lbs.
  4. Zero. This one’s a relatively new addition to English—according to Schwartzman, the first appearance in print of the word zero was in Philippi Calandri’s De Arithmetica Opusculum (1491). The word itself was borrowed from the Arabic صفر (sifr) which means “empty.” Interestingly, the word cipher has the same origin. One other point: in most European languages, zero is treated a plural (“I have zero apples” instead of “I have zero apple”). I’d be interested if this is the case in Arabic and other semitic languages.

Up next: the operations of arithmetic…

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3 thoughts on “The Evolution of Numbers

  1. Pingback: The Evolution of Arithmetic |

  2. Pingback: The Evolution of Plane Curves |

  3. Pingback: The Evolution of Weights and Measures |

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