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I think you could effectively argue that mathematics is a branch of philosophy.

You can construct proofs for mathematics, but not for the existence or refutation of a divine creator.

I think you have a narrow view of philosophy. Very little modern philosophy has anything to do with that kind of question.

Nope, you're projecting and using a strawman. That's not the point. :)

True, but with math you also eventually get down to axioms that can't be proven.

I don't think we know if we can know everything or not. That seems like _the_ question to answer.