>So the question really is if there are non self-referential unprovable statements, and the answer seems to be yes Some mathematicians believe that many popula

>So the question really is if there are non self-referential unprovable statements, and the answer seems to be yes Some mathematicians believe that many popular conjectures are true but unprovable. Like Goldbach's conjecture, Riemann's hypothesis, or perhaps even the collatz conjecture. We know these things are probably true. If the prime numbers are distributed randomly, there are probabilistic proofs that show the probability of goldbach's conjecture approaches 1, and there is a similar argument for Riemann's hypothesis. However it's just a "mathematical coincidence", there is no reason there can't be a counterexample at 10^500+1, it's just really improbable, so it's impossible to prove.