[gambling8nt]

We can't guarantee anything about the world. Empirically, science seems to work, and that is all we can ever get from it. Math is true regardless of its utility in science, and we use it in science because it is convenient to do so.

There are no solid, incontrovertible definitions. Only solid incontrovertible proofs (even there, we don't generally actually know whether or not a proof is incontrovertible, because proofs are rarely verified on that level...but, within mathematics, it is at least POSSIBLE to either verify a proof on that level, or provide a verifiable flaw). Definitions are a matter of convenience.

That the semantics of mathematics sometimes change does not imply that any of its terminology are ever inherently complex in the sense that those who don't understand it, "Don't get it." Indeed, since semantics in mathematics are only ever a shorthand, every mathematical construct could conceivably be expanded into the language of logic, and every mathematician (modulo human error) would agree that the expansion was valid. This underlying agreement on meaning is precisely what is missing from fields like much of literary criticism and philosophy.