The meaning of mathematics from an etymological point of view

I study mathematics and I wonder what mathematics means. I've been searching for the definition and until now I haven't found something clear, so I decided to begin from the start. On Wikipedia I found this:

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") includes the study of such topics as quantity, structure, space, and change.

What do you think was the meaning of mathematics for ancients? If you have a definition that one can tell to a person that is not in math, please share it.

• Could make for a great question if supported by research effort.
– Kris
Commented Sep 20, 2018 at 8:15
• We often find fossils of the old meaning in modern English. en.wikipedia.org/wiki/Polymath defines a polymath as (Greek: πολυμαθής, polymathēs, "having learned much", Latin: homo universalis, "universal man") is a person whose expertise spans a significant number of different subject areas, such a person is known to draw on complex bodies of knowledge to solve specific problems. This illustrates a meaning closer to the original Greek. Commented Sep 21, 2018 at 11:48

2 Answers

The ultimaste root appears to be

from mathema (genitive mathematos)

a Greek term with a wider meaning:

"science, knowledge, mathematical knowledge; a lesson,"literally "that which is learnt;

whose supposed PIE root is found in other related terms:

mendh-

Proto-Indo-European root meaning "to learn." It forms all or part of: chrestomathy; mathematic; mathematical; mathematics; opsimathy; polymath.

It is the hypothetical source of/evidence for its existence is provided by: Greek menthere "to care," manthanein "to learn," mathema "science, knowledge, mathematical knowledge;" Lithuanian mandras "wide-awake;" Old Church Slavonic madru "wise, sage;" Gothic mundonsis "to look at," German munter "awake, lively."

(Etymonline )

According to the Oxford English Dictionary, the term in English originally was:

(a collective term for) geometry, arithmetic, and certain physical sciences involving geometrical reasoning, such as astronomy and optics; spec[ifically] the disciplines of the quadrivium collectively.

The earliest example they listed is from 1545 (although this may be an example of the noun "mathematic" which is defined as "a mathematician; an astrologer"):

Nature hath prouyded the hart to be set so egallye in the middest of the brest, as is possyble to be deuysed, by al the mathematikes in the worlde
An introduction into phisycke wyth an vniuersal dyet, gathered by Christofer Langton.

There's also a 1573 example:

Amonge other studies..he cheefly applied himself to Physick and Mathematickes.
Virgil's Whole .xii. Books Æneidos

As for its etymology, the OED says it was formed within English from the adjective mathematic (and was modeled "probably after physics, metaphysics, etc., rather than ancient Greek τὰ μαθηματικά"). "Mathematic", however, is "Partly a borrowing from French. Partly a borrowing from Latin." Specifically, it's from the French word mathematique and the Latin words mathēmaticus, mathēmatica.