In 1931 Kurt Gödel published his now-famous "incompleteness theorems," which showed the limitations of axiomatic systems of mathematics. Specifically, Gödel showed: (1) there are true statements about numbers that humans will never be able to prove, and (2) a mathematical system that is internally consistent (i.e. doesn't generate contradictions) cannot prove its own consistency. These results have been widely cited not just in mathematics but also philosophy and computer science, as they completely revolutionized our understanding of knowledge itself. It this episode Bob gives an intuitive explanation of what Gödel precisely did and how he did it.