RANDOMNESS AND GÖDEL'S THEOREM

Complexity, non-predictability and randomness not only occur in quantum mechanics and non-linear dynamics, they also occur in pure mathematics and shed new light on the limitations of the axiomatic method. In particular, we discuss a Diophantine equation exhibiting randomness, and how it yields a proof of Gödel’s incompleteness theorem. Our view of the physical world has certainly changed radically during the past hundred years, as unpredictability, randomness and complexity have replaced the comfortable world of classical physics. Amazingly enough, the same thing has occurred in the world of pure mathematics,