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

Joel David Hamkins is a mathematician and philosopher specializing in set theory, the foundations of mathematics, and the nature of infinity, and he’s the #1 highest-rated user on MathOverflow. He is also the author of several books, including Proof and the Art of Mathematics and Lectures on the Philosophy of Mathematics. And he has a great blog called Infinitely More. https://lexfridman.com/sponsors/ep488-sc Transcript: https://lexfridman.com/joel-david-hamkins-transcript CONTACT LEX: Feedback – give feedback to Lex: https://lexfridman.com/survey AMA – submit questions, videos or call-in: https://lexfridman.com/ama Hiring – join our team: https://lexfridman.com/hiring Other – other ways to get in touch: https://lexfridman.com/contact EPISODE LINKS: https://x.com/JDHamkins https://jdh.hamkins.org https://www.infinitelymore.xyz https://mathoverflow.net/users/1946/joel-david-hamkins https://jdh.hamkins.org/publications https://amzn.to/3MThaAt https://amzn.to/3YACc9A SPONSORS: Perplexity: AI-powered answer engine. https://www.perplexity.ai/ Fin: AI agent for customer service. https://fin.ai/lex Miro: Online collaborative whiteboard platform. https://miro.com/ CodeRabbit: AI-powered code reviews. https://coderabbit.ai/lex Chevron: Reliable energy for data centers. https://chevron.com/power Shopify: Sell stuff online. https://shopify.com/lex LMNT: Zero-sugar electrolyte drink mix. https://drinkLMNT.com/lex MasterClass: Online classes from world-class experts. https://masterclass.com/lexpod OUTLINE: (00:00) – Introduction (01:58) – Sponsors, Comments, and Reflections (15:40) – Infinity & paradoxes (1:02:50) – Russell’s paradox (1:15:57) – Gödel’s incompleteness theorems (1:33:28) – Truth vs proof (1:44:52) – The Halting Problem (2:00:45) – Does infinity exist? (2:18:19) – MathOverflow (2:22:12) – The Continuum Hypothesis (2:31:58) – Hardest problems in mathematics (2:41:25) – Mathematical multiverse (3:00:18) – Surreal numbers (3:10:55) – Conway’s Game of Life (3:13:11) – Computability theory (3:23:04) – P vs NP (3:26:21) – Greatest mathematicians in history (3:40:05) – Infinite chess (3:58:24) – Most beautiful idea in mathematics

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