What does ars mathematica or mathematicus mean?
From Augustine's commentary to the Genesis we have the following statement:
Quapropter bono christiano, sive mathematici, sive quilibet impie divinantium, maxime dicentes vera, cavendi sunt, ne consortio daemoniorum animam deceptam, pacto quodam societatis irretiant.
Or from the Codex Iustinianus:
Artem geometriae discere atque exerceri publice intersit. Ars autem mathematica damnabilis interdicta est
Surely we don't assume that mathematics is so bad.
If I didn't know anything else, from the context I would assume numerology is meant here.
But mathematici / ars mathematica is translated as astrologers/astrology.
And Thomas Aquinas did understand it that way, as he uses the quote from Augustine to support his views on astrology in the Summa Theologiae:
Et ideo astrologi in multis vera praenuntiant, et praecipue in communibus eventibus, qui dependent ex multitudine. Alio modo, propter Daemones se immiscentes. Unde Augustinus dicit, "Fatendum est, quando a mathematicis vera dicuntur, instinctu quodam occultissimo dici, quem nescientes humanae mentes patiuntur. [...]" Unde concludit, "quapropter bono Christiano sive mathematici, sive quilibet impie divinantium, et maxime dicentes vera, cavendi sunt, ne consortio Daemoniorum animam deceptam pacto quodam societatis irretiant."
Still, I find this puzzling. In the quote from the Codex Iustinianus, why was ars mathematica contrasted to ars geometriae?
It is often claimed that ars geometriae didn't mean geometry but mathematics in general. But that still doesn't make so much sense, too.
At some point much later, in modern Latin, mathematicus seems (from my cursory knowledge) to always just mean mathematical, for example in Newton's Philosophiae Naturalis Principia.
Thomas Aquinas again, as an example for medieval Latin, though he understood Augustine's use of mathematicus as meaning astrological himself uses mathematicus as just meaning mathematical. In De Substantiis Separatis he writes:
Unde Plato duo genera rerum a sensibilibus abstracta ponebat: scilicet mathematica, et universalia, quae species sive ideas nominabat. Inter quae tamen haec differentia videbatur: quod in mathematicis apprehendere possumus plura unius speciei, puta duas lineas aequales, vel duos triangulos aequilateros et aequales; quod in speciebus omnino esse non potest, sed homo in universali acceptus, secundum speciem est unus tantum.
So did ars mathematica also mean mathematics in classical (and late) Latin? Or did it only mean astrology?