Mathematics got its name from "
teach" since one had to be "
taught" it, unlike rhetoric, poetry or music.
Arithmetic: 2 + 3 * 5 (push button calculator)
Mathematics: x + 3 = y (create and then solve)
English: The Peripatetics say that rhetoric and poetry and the whole of popular music can be understood without any course of instruction, but no one can acquire knowledge of the subjects called by the special name mathematics unless he has first gone through a course of instruction in them; and for this reason the study of these subjects was called mathematics. …” Loeb 335, p. 2.
Greek: “Οἱ μὲν ἀπὸ τοῦ Περιπάτου φάσκοντες ῥητορικῆς μὲν καὶ ποιητικῆς συμπάσης τε τῆς δημώδους μουσικῆς δύνασθαί τινα συνεῖναι καὶ μὴ μαθόντα, τὰ δὲ καλούμενα ἰδίως μαθήματα οὐδένα εἰς εἴδησιν λαμβάνειν μὴ οὐχὶ πρότερον ἐν μαθήσει γενόμενον τούτων, διὰ τοῦτο μαθηματικὴν καλεῖσθαι τὴν περὶ τούτων θεωρίαν ὑπελάμβανον. …”