as I understand them, Gödel's incompleteness theorems prove that in mathematics (and every axiomatic logic system), there exist true statements which, while true, cannot be proven
OP got me wondering, do the theorems provide any insight into the nature or trends of these statements? is it that at least one must always exist? can they form their own branches and systems in the same manner as say, geometry? Is it highly/arbitrarily likely that a large/infinite amount of unique structures exist? perhaps, based on their unprovability, we'll never know for sure.
