In classic Greek, μάθημα is a neuter noun, formed by a standard procedure from the root of the verb μανθάνω, to learn, and denotes in general the object of learning. Also standard is the derivation of the adjective μαθηματικός, "what concerns the object of learning". Plato refers this adjective to persons still in the generic sense of wishful to learn. Aristoteles uses the neuter plural, τὰ μαθηματικά, to denote theoretical studies, including mathematics, mathematical physics, astronomy. As far as I know, Aristoteles is also the first who uses μαθηματικός as a substantive, ὁ μαθηματικός, the mathematician, of course in the wider acceptation of "theoretical scientist" that this word had in all ancient science. In fact, throughout all medieval times, in this sense "Mathematici" especially denoted the followers of Aristotheles in natural sciences, (often as opposed to "Medici", the followers of Hippocrates, scientists with an empiric approach based on observations).
The noun akousmatikos, that however we know from later authors, like Porphyry (born 230 AC) and Iamblichus (born 245AC) has a parallel formation: ἀκούω (to listen) > ἀκουσμα (oral teaching) > ἀκουσματικός (listener, follower of oral lectures). The distinction is between advanced students and not initiated, simple listeners, and also emanated the two branches after the scission of the Pythagorean school: one more interested in scientific aspects of Pythagorism, the other attached to the religious aspects of it.