Mathematician Kurt Gödel in 1931 published his two famous “incompleteness theorems,” which showed the principled limits on the knowledge we could generate from formal axiomatic systems. Loosely speaking, Gödel showed that there exist true statements about numbers that we will never be able to prove are true. His results have been cited not just in mathematics but also computer science and philosophy. In this episode, Bob details more precisely just what Gödel demonstrated, and gives an intuitive explanation of how Gödel did it.