Some math is actually invented, like transfinite numbers. But feel free to empirically construct one of those...

I'm familiar with the underlying concepts in philosophy, but I can't be sure what _you_ mean here. Care to explain?

Math is an empirical science.

If it is a science, it can't have theorems.

Empiricism is often involves in mathematical discoveries but the key difference is math isn't reliant on empiricism and at least in theory the current body of mathematical knowledge can reasoned entirely from simple axioms.

Why do you say this? What do you mean?

You recognize that "empirical science" has a clear meaning to most scientists, right? This idea is quite different than formal reasoning (e.g. deduction over theorems).