In 1931, "he proved for any computable axiomatic system that is powerful enough to describe the arithmetic of the natural numbers (e.g., the Peano axioms or Zermelo–Fraenkel set theory with the axiom of choice), that:
- If the system is consistent, it cannot be complete.
- The consistency of the axioms cannot be proved within the system."
This is known as "Godel's Second Incompleteness Theorem". It implies:
- Infinite nature of any knowledge
Worked together with Einstein at Princeton Institute for the Advanced Studies.