Ok I'll bite. Why is "creating the right model for thinking about a problem and devising the appropriate mechanizable techniques to solve it" a subset of mathematics?
Because the mathematics is basically distilled, formalized art of precise thinking. It's the art of manipulating and morphing mental models. It's as much about numbers as astronomy is about telescopes ;).
Higher math requires a great deal of lateral thinking. Also, music an math are often closely related but I don't see the connection between music an say computer vision.
Computer vision practitioners do mostly math, are we calling them computer scientists also? Sheesh :). Whenever I get in the same room with one, we are talking completely different languages (and we do have a sizeable computer vision team in our lab).