In De Motu Animalium, Aristotle says there is an unmoved mover in the animal’s leg joint, and proceeds to a geometrical description of the axis of rotation of the joint. More famously, he says there are unmoved movers in the apparent motion of the fixed stars and planets, and there too associates them with geometrical axes of circular motions. What is going on here? This is a good illustration of several points.
First, Aristotle is perfectly happy to use mathematics in natural science. (He just correctly judged that early Greek arithmetic and geometry generally had little to contribute to the intelligibility of becoming, and wisely objected to the Pythagorean numerology that found a place in the Platonic Academy.)
Second, there is nothing mysterious about what he calls an unmoved mover. In the best-known cases, it refers to something that is in fact not only observable but mathematically describable. (This is not the only way a concept can have value, but that is not the point here.)
Third, he calls the unmoved mover a “mover” in the sense that it is the descriptive law or form of the physical motion in question, not a driving impulse or force. In a similar move, Leibniz famously said God is the law of the series.