In the note "What St. Augustine didn't say about mathematicians" (which appeared sometime in 1991 in the pages of the Pi Mu Epsilon Journal), R. P. Boas, Jr. mentioned, among other things, that in the days of Augustine of Hippo the word "mathematicians" meant what we nowadays call "astrologers". Boas would even add the following: "The old usage seems to have occurred occasionally as recently as the 1700's, although the modern meaning goes back to around 1400."
The big, big question here is plain and simple to express:
How did R. P. Boas, Jr. find it all out?
Among his principal references one can find Marvin J. Greenberg's book on Euclidean and Non-Euclidean Geometries but, to be a hundred percent honest, I don't think that Mr. Greenberg touched upon the etymology of the word "mathematicians" at all in his book (of course, I'm always more than glad to be proven wrong).
By the way, the said article also appears in the (hilarious) book Lion hunting and other mathematical pursuits (A collection of mathematics, verse, and stories by Ralph P. Boas, Jr.)...
Let me thank you in advance for your insightful replies.