Who invented the word “Mathematics”?

In its modern meaning of mathematics, the earliest citation Liddell–Scott give is the treatise of the same name by Archytas. (However, the German Wikipedia doubts that was the original title of his work.) The term comes into its own in its modern meaning in Aristotle, a generation later, who uses it extensively.

Plato was the exact same age as Archytas and his friend, but he only used the term to mean “fond of learning” (Timaeus 88c), or “scientific” (Sophist 219c). He does get close when he refers to the three mathemata (sciences) of arithmetic, geometry, and astronomy (Laws 817e), but he isn’t quite there yet, and his term for mathematics is logismos, “calculation”.