[prance]

I would go further: is "Axioms exist" true? You don't find them lying around in nature. They exist only in people's minds. I would argue that this is an inherent metaphysical question.

The scientismist's (?) standpoint could be that it exists because it is manifested as a concept in human brains. But by the same argument, wouldn't they then need to acknowledge that God exists?

The crux of the matter is to do science, you need formalism to express your theories, to interpret measurement results etc. Those formalisms are what we usually call "math". But any mathematical system has axioms, i.e. something we need to just "believe" in in the first place, and those believes are not themselves provable by science.

[AstralStorm]

Axioms can be shown to be useful or not. This is why some mathematicians reason with or without axiom of choice. Likewise, systems of axioms can be shown to be consistent or not.