[crystal_revenge]

> understand theorems for which we comprehend

I don't know what your distinction between "understand" and "comprehend" but my point was not about these words, but about being "useful" and being "understandable".

I'm saying there's no relationship between a mathematical statement being useful and it being understandable.

If it is true that "understanding is a prerequisite for usefulness" (where "understanding" means that a statement can be proven in a way that is intelligible to humans) was a property of mathematical expressions, then this fact would certainly be useful (we could exclude any statements that no human understand from the world of useful mathematical expression). But, by that definition, we would need to understand that statement, so you would need to be able to prove that "understanding is a prerequisite for usefulness" in a human intelligible way.

Now what I just wrote is in itself not a proof that we can't know, but proving the above statement would involve expressing the claim in a mathematically verifiable way that was also understandable by humans, which does imply something remarkable about human cognition (something that would be intelligible no less!)