It appears now that there are many random truths in any given formal system. This is extremely unfortunate in many ways. With random truths, even if we were able to construct an automatic proof generator to generate all proofs from the axioms, we would never be able to construct a list of all truths in any given formal system.
This means that these random truths must be divinely inspired or the result of a long meditation. Presumably Buddha would have known of all the random truths in the Universe.
Godel's Theorem is an extremely important result which really really sucks. Here's why:
Godel's Theorem talks about what is 'random truths', the problem is most of science, math, and even stats (uses set theory) use formal systems. Therefore there are true statements which cannot be proven. Since our understanding of the universe hinges on Physics which hinges on formal logic systems, there are true things in the universe which we cannot prove.