I am begging everyone to stop pretending that "understanding" and "finding true propositions" are not strongly correlated, in fact nearly the same thing.
I heard many smart people saying this over and over, all summer long in Europe - but this is actually not very clever. It is one of those things that sounds very deep and clever until you think about it for > 2min.
Also, let's please agree to stop pretending that LLMs are not quite efficient at providing understanding. They are not some kind of oracle/black boxes, as anyone who has ever tried to one knows very well. Look at Terry Tao's blogpost on unpacking the Jacobian conj counterexample, for example.