Thanks -- the prompts for my asking were the WP
Mathematics entry:
The word mathematics comes from Ancient Greek μάθημα (máthēma), meaning "that which is learnt",[23] "what one gets to know", hence also "study" and "science". The word for "mathematics" came to have the narrower and more technical meaning "mathematical study" even in Classical times.[FN: Both senses can be found in Plato. μαθηματική. (citing L&S)]
and Etymonline's
mathematics entry:
"the science of quantity; the abstract science which investigates the concepts of numerical and spatial relations," 1580s; see mathematic (the older form of the word in English, attested from late 14c.) + -ics. Originally one of three branches of Aristotelian theoretical science, along with first philosophy (or metaphysics) and physics (or natural philosophy).
I'm trying to discern who deserves credit for use of 'mathematics' in its modern sense between Archytas, Plato, and Aristotle. Re Archytas, thx again — I had missed that the L&S cite was to the title of Archytas's Fragment I.
Re that Fragment -- Iiuc, it was Porphyry who titled it 'On Mathematics' while Nicomachus titled it 'Harmonics' (per
Huffman and Johnson's
review of Huffman) The translations shown on Huffman's pp. 105 and 108 (last para) and Johnson's p. 5 (which cites Huffman 105) do not include 'mathematics' in the body of the fragment.
So while the 3rd sentence, "Indeed concerning the speed of the stars and their risings and settings as well as concerning geometry and numbers and not least concerning music, they handed down to us a clear set of distinctions. For these sciences seem to be akin. (Fr. 1.1-7; 105-106)" is the source of what became known in the Middle Ages as the 'quadrivium' (mathematical arts/sciences: logistic (arithmetic), geometry, astronomy and music), there is no record of Archytas's use of the term.