Mathematics is purely deductive. When something is said to be mathematically "proved," it means that the conclusion follows rigorously and necessarily from the axioms. Of itself, a mathematical system can't show anything as being "true" in the sense of describing the real world. All the shelves of volumes serve simply to make explicit what was contained in the assumptions. If some mathematical procedures happen to approximate the behavior of certain real-world phenomena over certain ranges sufficiently closely to allow useful predictions to be made, then obviously that can be of immense benefit in gaining a better understanding of the world and applying that knowledge to practical ends. But the only measure of if, and if so to what degree, a mathematical process does in fact describe reality can be actual observation. Reality is in no way obligated to mimic formal systems of symbol manipulation devised by humans.