algebra

n. a system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.

My brother asked me in the car the other day if I knew what the -gebra portion of algebra meant; he knew it was Arabic in nature, and therefore almost certain a construction of the article al- (the equivalent of “the”). Assuming the original was more something like al-jibra, we puzzled for a few minutes before finally letting the matter drop.

We were right and wrong: the original Arabic was actually al-jebr, from the Arabic الجبر. Though I’m unsure its literal translation, the meaning comes to something like “the reunion” or “the resetting of broken parts.” The word was used in the 9th century by Abu Ja’far Muhammad ibn Musa al-Khwarizmi in his treatise on equations called Kitab al-Jabr w’al-Muqabala, or “Rules of Reintegration and Reduction”.

Evidence suggests that the word came into Europe via Arabs in Spain, who used the term to refer to setting broken bones; likely it was absorbed into Latin as algeber. from there, probably in the mid-16th century, and likely came to refer to equations once again. Eventually, metathesis appears to have brought the final syllable into the format we know.

While algebra comes from the Middle East, many of our other math words are entirely Latin and Greek.

Geometry is from the Greek root ge-, meaning “earth,” and -metria, meaning measurement; metria is likely from a Indo-European root med-, from the PIE me-.

Trigonometry is from the Greek trigonon, or “triangle,” which is itself from tri-, meaning “three,” and gonia, meaning angle (which also ultimately gives us “knee” and “genuflect”); add on the -metria and you’ve got the study of three-angled shapes.

Calculus as we know it (a shortening of either “differential calculus” or “integral calculus”), is a Latin term meaning “reckoning” or “accounting,” ultimately from a small stone used in counting. The word came from calcis, which is limestone, and also incidentally where we get “calcium” and “calcification.” The word in its mathematical context was first used in the mid-17th century.

One unforeseen entrant in this list is Statistics, which is from the German Statistik. The meaning we are familiar with (the general study or classification of organized numbers) didn’t arise until 1829; originally, the word was closely tied to demographic, political, or social data. The German political scientist Gottfried Aschenwall taught a course called Vorbereitung zur Staatswissenschaft in the mid-18th century, the word then referring to a lecture on state affairs. Ultimately, it goes back to Latin status, whose etymological legacy should be obvious.