About This Video

What is the nature of mathematics? Mathematics is an a priori discipline, meaning its proofs arise from first principles. The early 19th-century logician Kurt Gödel wrestled with this notion in forming his landmark ideas known as the incompleteness theorems. Philosopher Rebecca Newberger Goldstein explains how Gödel demonstrated that in any formal system, such as mathematics, there will arise some true propositions that cannot be proven within the system—a paradox that still inspires philosophers, mathematicians, and scientists today.

Image courtesy of the Kurt Gödel Papers, The Shelby White and Leon Levy Archives Center, Institute for Advanced Study, Princeton, NJ, USA, on deposit at Princeton University; Recorded June 2010; Posted October 2010