manthano

This root begins with the Greek verb manthanein — simply, 'to learn.' From the action of learning, Greek formed the noun mathēma, meaning 'that which is learned' — a lesson, a piece of knowledge, a branch of study. The plural ta mathēmata meant 'the things one learns,' i.e. the subjects of education.

Here is the surprising turn. Among the Pythagoreans, 'the things worth learning' came to mean, above all, the study of numbers, quantities, and shapes. So ta mathēmatika — literally 'the things that have to do with learning' — narrowed from 'learning in general' to one specific discipline: the study of number and magnitude. A word that started as 'whatever you study' became the name of a single subject. That is why English mathematics carries, hidden inside it, the older and broader idea of 'learning itself.'

Through Latin mathematica and Old French, the word reached English as mathematics — kept plural in form like physics and politics, even though we treat it as one subject. From it we get the adjective mathematical ('of mathematics; and by extension, exact, precise') and the older, now-archaic mathematic. Everyday speech then clipped the long word down: American English to math, British English to maths.

The root also survives in poly- + math: polymath, 'one who has learned many things' — a person whose knowledge spans many fields, the Leonardo-da-Vinci type. Two rarer relatives keep the original 'learning' sense more plainly: philomath, 'a lover of learning,' and chrestomathy, literally 'useful learning' — a collection of selected passages used to learn a language or subject. Across the whole family, the constant idea is the same: math is what you have learned. The Greeks just happened to decide that the thing most worth learning was number — and so 'learning' became 'mathematics.'