Etymology of Mathematical Terms

Ordinary technical vocabulary preserves the transmission history like tree rings. Each entry below gives the standard etymology; where an etymology is folk or disputed, that is said.

algebra

From al-jabr ("the restoring/completion"), the first operation in the title of al-Khwarizmi's treatise al-Kitab al-mukhtasar fi hisab al-jabr wa-l-muqabala. In medieval Spanish and Italian, an algebrista could also mean a bone-setter, one who restores what is broken, the same Arabic sense applied to fractures. The mathematical meaning won.

algorithm / algorism

From Algorismi/Algoritmi, the Latinization of al-Khwarizmi's name in the translations of his arithmetic (Dixit Algorizmi). Medieval algorism = computation with Hindu-Arabic numerals; the modern spelling and generalized sense (any effective procedure) were influenced by false association with Greek arithmos (number). A ninth-century Baghdad civil servant's hometown surname (Khwarazm, the region south of the Aral Sea) is now the central noun of computer science.

cipher, zero

Both from Arabic sifr ("empty"), translating Sanskrit sunya (the empty place in positional notation). Latin cifra/cephirum split into two words: Italian zefiro → zero (the digit), and cipher (first meaning the zero, then any numeral, then secret writing, the last sense probably because encoded text looked like meaningless numerals). One Arabic word, two fundamental modern terms in mathematics and cryptography.

sine

The famous mistranslation. Sanskrit jya/jiva (bow-string, the half-chord) was transliterated into Arabic as j-y-b; read as the genuine Arabic word jayb (fold, pocket, bosom of a garment), it was translated into Latin as sinus (fold, bay). See Trigonometry. The other function names are Latin add-ons: cosinus (complement's sine), tangens and secans (touching and cutting lines, introduced by Thomas Fincke, 1583), but tangent and cotangent as functions originate as the Islamic shadow functions (zill, shadow).

zenith

From Arabic samt al-ra's ("direction of the head," the point overhead). In manuscript Latin, samt was miscopied, an m read as ni, yielding senit/cenit → zenith. A scribal error is permanently installed in every astronomy textbook.

nadir

From nazir ("opposite"), as in nazir al-samt, the point opposite the zenith. Clean transmission, no scribal accident this time.

azimuth

From al-sumut, plural of the same samt (direction): the compass bearings along the horizon.

almanac

From Arabic al-manakh, attested in al-Andalus for astronomical calendars/tables; the word's own deeper origin is uncertain (this is the standard but debated etymology, flagged as such in the OED).

almagest

Ptolemy's Syntaxis became, in the Islamic world, al-majisti (from Greek megiste, "the greatest"), and returned to Europe as Almagest, a Greek superlative wearing an Arabic article, the whole transmission story in a single word.

Other survivals

Alidade (the sighting rule of an astrolabe, al-idada); alcohol and alkali and alchemy/chemistry from the allied sciences; nucha (anatomy) and a hundred medical terms; and the star names: Aldebaran (al-dabaran, "the follower"), Altair (al-ta'ir, "the flying [eagle]"), Betelgeuse (yad al-jawza, "the hand of Orion," mangled in transliteration), Deneb (dhanab, "tail"), Rigel (rijl, "foot"), Vega (from al-nasr al-waqi, "the swooping eagle"), Fomalhaut (fam al-hut, "the fish's mouth"), Algol (ra's al-ghul, "the demon's head"). Roughly two hundred named stars carry Arabic names, most fixed in European usage through Latin translations of Arabic astronomical tables.

And the letter x?

The claim that the algebraic x descends from Arabic shay ("thing," the unknown), via Old Spanish transcription with x (then pronounced "sh"), is attractive and repeated widely; the sober assessment is that direct documentary proof is lacking, and Descartes' typographic conventions in the Géométrie (1637) are the proximate source of x-y-z for unknowns. This reference reports the shay story as plausible but unproven.

Sources: OED etymologies; Katz; Berggren; Kunitzsch, The Arabs and the Stars (star-name scholarship); standard histories of mathematical notation (Cajori).