#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

In this episode of the Lex Fridman Podcast, Lex interviews Joel David Hamkins, a mathematician and philosopher specializing in set theory and the nature of infinity. They delve into Cantor's work on infinity, the development of set theory, and the implications of Gödel's incompleteness theorems. Hamkins explains complex concepts like Hilbert's Hotel, the uncountability of real numbers, and the axiom of choice, often using relatable analogies. They further discuss the philosophical implications of these mathematical ideas, including the nature of mathematical truth, the existence of mathematical objects, structuralism, and the set-theoretic multiverse. The conversation also touches on infinite chess, the surreal number system, and the role of AI in mathematical research, with Hamkins sharing personal anecdotes and insights from his career.