How Much Math Is Knowable?

In this lecture, Scott Aaronson from the Department of Computer Science at the University of Texas, Austin explores the fundamental question of which mathematical truths are knowable by finite beings bounded by time, space, and physical laws. Delve into a fascinating journey beginning with Gödel's Incompleteness Theorem and Turing's discovery of uncomputability before examining the remarkable Busy Beaver function, which grows faster than any computable function. Learn about Aaronson and Yedidia's work showing that BB(745) is independent of set theory axioms, while recent collaborative research has determined that BB(5) equals 47,176,870. Consider whether BB(6) will ever be known by humans or AI systems. Explore the P!=NP conjecture and its implications for machine intelligence limitations, discover how quantum computers might expand mathematical knowability boundaries, and contemplate hypothetical models beyond quantum computing that could further extend these boundaries through exotic scenarios like black hole exploration, closed timelike curves, or holographic universe projections. This Harvard CMSA Yip Lecture, supported by Dr. Shing-Yiu Yip, runs for 1 hour and 7 minutes.