The Limits of Proof

Explore the foundations and limitations of mathematical proofs in this 56-minute lecture by Paul Beame from the University of Washington. Delve into formal proofs, examining the contributions of influential figures like Gottlob Fraga, David Hilbert, Bertrand Russell, and Alfred North Whitehead. Investigate propositional logic, Boolean formulas, and various proof systems including textbook proofs, truth tables, and inference systems. Analyze advanced topics such as resolution proofs, DPLC, CDCL, and random formulas. Examine proof complexity, polynomial calculus, optimization techniques, and cutting planes. Discover higher degree proof systems, positive selling sets, sum of squares proofs, extension complexity, and dynamic systems. Gain insights into the limits and capabilities of general proof systems in this comprehensive exploration of mathematical reasoning.