[xamuel]

You need to be a bit more specific: no matter what kind of true, computable axiom-set you're using (this has nothing to do with 'how much mathematics generally speaking develops'), there will be objectively true mathematical statements that can't be proven by that axiom-set.

>a disconnect between what's knowable and what's provable

"what's provable [from a given axiom-set]" is a concrete, technical, unambiguously defined set of things. "what's knowable" is a vague philosophical set of things. Goedel's Incompleteness Theorem is a technical result about the former, and it's a common mistake to assume it says anything about the latter, except very tangentially.

For those who are interested in the misty area where the two things do overlap, I will shamelessly plug this 2-page paper of mine, "Mathematical shortcomings in a simulated universe": https://philpapers.org/archive/ALEMSI.pdf

[guerrilla]

I think they meant what is true, which is also concrete, technical and unambiguously defined in this setting. But you are very correct to make the distinction between truth and knowledge. Pointing out that many philosophers have believed that knowledge is justified true belief might elucidate the relationship a bit.