The Incomplete Axism in Mathematics

Around the 1930s, Gertel proved that actually any sort of intelligible axiom system that you might have attains the modest goal of formalizing arithmetic on the natural numbers is necessarily incomplete. That statement can be coded as some sort of statement about number theory but not in a particularly natural way. And so it was a question that kind of was left from Gertel's time whether there's some other natural mathematical statement which is undecidable based on the axiom system we were working with.