PennApps XXIII Workshop: Introduction to Proof Theory and Computability

What is a proof, and can every mathematical statement be proved? Within this presentation, we will introduce the idea of a proof as a mathematical object, working up from languages to ultimately understand the limits of math and computation. Topics covered include the Compactness Theorem, Decidability theorem, Gödel’s Incompleteness Theorem, and Halting Problem Reductions.