Incomplete Mathematics?

``The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (essentially, a computer program) is capable of proving all facts about the natural numbers. For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem shows that if such a system is also capable of proving certain basic facts about the natural numbers, then one particular arithmetic truth the system cannot prove is the consistency of the system itself.''

Taken from Wikipedia.

Kurt Gödel proved in 1931 that Hilbert's - second problem - had a negative answer. The question: Is there a proof that arithmetic is consistent – free of any internal contradictions.

Gödel found that no set of axioms is complete for number theory. Valid questions about numbers go unanswered with any set of axioms.

My question: Is Nature incomplete?

I believe Nature is complete. Definitely more so than all our models of it so far. Nevertheless one could envision an Autopoietic Universe, building itself all the time. Then the question has no content, because the Universe has never finished making itself; almost like asking which is the biggest number?