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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.

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From the article "Astrology", by Sheila J. Rabin, in Encyclopedia of the Scientific Revolution from Copernicus to Newton, p.77:

In fact, astrology was part of the mathematics curriculum of every Western university from their founding in the twelfth century to the seventeenth century, and mathematicus was a synonym for astrologer

Lynn Thorndike's magisterial A History of Magic and Experimental Science (8 volumes; volume 2 alone is over 1000 pages!) has a wealth of material (of which I've read only a smidgen). For example, he mentions Bernard Silvester's 12th C.

narrative poem whose plot hinges upon an astrologer's prediction and whose very title is Mathematicus (v.2, p.101).

Other medieval scholars made a careful lexical distinction. Hugh of St. Victor (also 12th C.) distinguishes mathematica (with an 'h' after the 't'), mathematics in our sense, and matesis (no 'h'), astrology ("that superstitious vanity which places the fate of man under the constellations") (v.2, p.11).

Michael Scot, a 13th C. astrologer at the court of Frederick II, in his Introduction to Astrology

distinguishes between mathesis, or knowledge, and matesis, or divination, and between mathematica, which may be taught freely and publicly, and matematica, which is forbidden to Christians [this being the version of astrology which denied the existence of free will]. (v.2, p.319)

Scot often uses astronomia to mean astrology.

Finally, after Scot's death the poet Henry of Avranches wrote a poem about him, in which he

explains how astrologers (mathematici) "reveal the secrets of things", by their art affecting numbers, by numbers affecting the procession of the stars, and by the stars moving the universe. (v.2, p.307-308)

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I knew I'd already heard this story that astrologers used to be called mathematicians, and now I've found where. Morris Kline mentions it in his celebrated Mathematical Thought from Ancient to Modern Times, the excerpt can be read here on page 179. You might find more details in the (short) bibliography a few pages further down.

However, I'm afraid I don't have any references for specific examples of this term being used by anyone, let alone as recently as the eighteenth century. All I can offer you is the above non-constructive existence proof.

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Originally (in Greece) the word mathematician was used in the same sense as today. Astrology penetrated Greece from Babylon during Alexander's conquests, and gradually became very popular. The use of the word "mathematicus" in the sense "astrologer" spread in the Roman empire, among the people who had no slightest idea about what mathematics is. In the late antiquity, when mathematics (in the proper sense of the word) completely disappeared, the only meaning of the word "mathematicus" was "astrologer".

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