It sounds like he's talking about the incompleteness theorem, that there are statements that are true but we can never find a proof. That's closely related to

It sounds like he's talking about the incompleteness theorem, that there are statements that are true but we can never find a proof. That's closely related to the halting problem and the idea of computability. There are some programs that will run forever without halting, but we have no method for identifying all of them. ("true and not provable" matches "runs forever without halting, but we can't prove it")