> All questions that find an answer will have come through a science by definition of what science is.

No, that's a definition of scientism, which is very much pseudoscience. Your idea is so wrong that is excludes all answers to mathematical questions, which are, in fact, unscientific.

> How are mathematical questions unscientific?

Because the essential quality of science is empirically testing hypotheses against physical observations, and math doesn't work like that at all.