[nonethewiser]

>likewise we have true statements that we can’t prove

Yes, and "can't" as in it is absolutely impossible. Not that we simple haven't been able to due to information or tech constraints.

Which is an interesting implication. That there are (or may be) things that are true which cannot be proved. I guess it kinda defies an instinct I have that at least in theory, everything that is true is provable.