Where does the word "algorithm" come from?

From a person. "Algorithm" is what happens to the name of Muhammad ibn Musa al-Khwarizmi (c. 780 to c. 850) after centuries of being copied from Arabic into Latin into English. His name means "from Khwarazm", a region of Greater Iran, and although he was probably of Khwarezmian origin he wrote his scientific works entirely in Arabic. Around 820 he worked at the House of Wisdom in Baghdad.

Here is the path of the word. Numbers written with ten digits including zero were invented by Indian mathematicians between the 1st and 4th centuries. By the 9th century Arabic mathematicians had adopted the system, and al-Khwarizmi's book On the Calculation with Hindu Numerals (c. 825) helped make it widely known. In the early 12th century it was translated into Latin, and the text began Dixit Algoritmi, "Thus spoke Al-Khwarizmi". Algoritmi is the Latinized form of his name. In English the word first meant calculating with this place-value notation, then in the 15th century it was reshaped under the influence of the Greek arithmos into algorithmus, and by 1596 Thomas Hood was writing "algorithm".

The meaning drifted far from digits. In computing, an algorithm is a well-defined set of instructions that terminates after a finite number of steps and solves a given problem. Al-Khwarizmi's name also survives in Spanish guarismo and Portuguese algarismo, which mean "digit", and the word "algebra" comes from the title of his other great book.

So the word hides a small chain of translations: a scholar of Persian descent in Baghdad, writing in Arabic about an Indian invention, rendered into Latin for European readers.