Does solving "P=NP?" require filling every hole ever left in math?

Clearly P=NP as the universe is predeterministic, science remember? But wouldn’t proving that require math we haven’t invented because it’s useless?

It seems to me (though I might be completely wrong of course) that most P=NP problems are just unexpected combinations of functions. Why are we trying to prove that P=NP??? Will it help AI?