According to the latest research, the final proof that if there is a universal grammar of numbers in which all facets of their behaviour can be expressed, it lies beyond our ken has been discovered. Somehow, though, I doubt "Peano's rules have been debunked by Gödel's incompleteness theorems and boolean relation theory," would've gotten me very far when I brought home a D in math, back in the day.

Update: Link fixed!