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.

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 )