Even when theoretical physics is neatly tied up into an axiomatic form, the axioms are normally suggested by experience, or at the very least by physical intuition, and in any event they remain subject to future revisions, should any evidence arise that contradicts them. Pure mathematics (though the boundary can be fuzzy) is not like that. In pure mathematics, physical plausibility is a bonus, not a requirement.

So, definitely a tool, in so far as it's employed by physics and other natural sciences.

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"A witty saying proves nothing" Voltaire.
"All your bias are belong to us" Ara Pacis.