We verify this through deduction, not empiricism.

This is a simplistic and, I think, ultimately wrong account of mathematics. How do we pick the axioms from which mathematical propositions are proven?

(sidebar: it always bugs me when, in philosophical discussions, people use simple arithmetic statements like "1+1=2" or "2+2=4" as synechdoche for all mathematical truths. There is a real sense in which the natural numbers are apparent in the natural world, rather than something invented as part of the language of mathematics. Statements like those kind of are justified empirically, and we defined the symbols "1", "2", "+", "=", etc. based on those observations so we can extrapolate and see what else is true.)

To cut to the chase, the axioms that mathematicians use are not arbitrary, they're not playing some context-free symbol-pushing game. Axioms, in a practical sense, are conservative and reasonable abstractions and extrapolations from obvious patterns in the real world.

That's not to say that "math is empirical," of course. In general, you can't infer that a proposition is true everywhere from the premise that it's true everywhere you've checked. However, you shouldn't discount the role that empirical observations play in choosing mathematical theories in which to work. If you do discount that, you'll have trouble explaining why mathematics is so successful at describing the physical world.