The only way that Gödel fails to prove is if human experience is non-algorithmic, a non-system.

Of course, incompleteness jibes pretty well with my own experience (and yours too, I bet) of the world, so the amazing thing about the theorem is not the conclusion but the fact that it can be proven across arbitrary systems. I.e. it is no surprise that the universe fails to entirely make sense, the surprise is that no possible universe (other than really trivial x=x universes) could ever entirely make sense.