Please explain.
Mathematics began when it was noticed that by defining a few simple terms and assuming the truth of a few elementary propositions, other, often much more complicated propositions could be proved to hold (this is part of the compressive power of mathematics). What Chaitin points out (he's not the first, by the way) is that we've come to learn that there are infinitely mathematical propositions whose proofs cannot be made any simpler than the propositions themselves, and so such propositions exceed the limits of rational proof as understood in traditional mathematics.