There are deep mathematical results about our limits to understand things simply because we communicate through finite series of symbols from finite dictionaries. Basically what we can express and prove is infinite but discrete, but there is much larger infinities than that that will be beyond our grasps forever. Things like theorems that are true but can not be proven to be true, or properties on individuals real numbers that exist but can not be expressed.
And there is no reason to believe the universe doesn't have the same kind of thing: it remains to be shown whether or not you can describe or understand the universe with a finite set of symbols.