There is a theory that many famous unproved conjectures are true but unprovable with the traditional methods you hold dear. Of course Godel showed there are tru

There is a theory that many famous unproved conjectures are true but unprovable with the traditional methods you hold dear. Of course Godel showed there are true unprovable theorems. But those are weird paradoxical self referencing things. That can sort of be proved if you use a different system of axioms. But it's possible there are unprovable true theorems that aren't like that. Freeman Dyson created an example of one. He conjectured that no power of 5, it's base 10 representation reversed, is a power of 2. This is almost certainly true. There is no particular correlation with powers of numbers and their base 10 representation. They are basically random except for the last digit. There is no pattern to it. And because the base 10 representations get longer and longer, it gets increasingly unlikely there exists a counterexample. You can calculate the probability and it's very low. The thing is that statement is very likely to be unprovable. If it's true, it's not true for any particular reason. Nothing at all says a counterexample can't exist. It just happens to be increasingly unlikely to happen. A mathematical coincidence. You can prove some famous conjectures using probabilistic arguments. For instance Goldbach's conjecture that every even number is the sum of 2 primes. Because primes are distributed basically randomly, as numbers get bigger, it gets more and more likely there are two primes that add to get that number. There are an awful lot of prime numbers after all. But again, there's not any reason to suspect there's a mathematical reason a counterexample can't exist. It's just unlikely. This is really hard to formalize. Obviously prime numbers are deterministic, not random. Obviously base 10 representations aren't really random. It'd be more precise to say that they aren't correlated with the particular properties we are interested in. But even that is pretty hard to pin down precisely. Mathematicians strongly disrespect anything that isn't a rigorous proof. But if you do that you might miss out on a lot of interesting things. And there is absolutely no guarantee that the universe will always give us that!