A better way to say it is that math is a formal system - It is a set of symbols and rules for transforming those symbols. It is often mistakenly believed that i

A better way to say it is that math is a formal system - It is a set of symbols and rules for transforming those symbols. It is often mistakenly believed that it is the one and only universal system. But not long ago we used Roman numerals and did not even have calculus. (How Archimedes did his work I can't imagine.) What we consider modern formal mathematics is only one possible system and there is no reason to think that a completely different one would not do the same job just as well. You use the terms "verification" and validity." These terms are used in symbolic systems to describe formulas that are well-formed (follow all the rules of their formal system) or equivalent to another formula (derivation) or a legitimate combination of multiple formulas (proofs.) Unfortunately, no matter how much you "prove" a pure mathematical theorem, it will never mean a darn thing about our observable universe. That is a job only science can do.