Companion · #488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse

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. Thank you for listening ❤ Check out our sponsors: <a href="https://lexfridman.com/sponsors/ep488-sc">https://lexfridman.com/sponsors/ep488-sc</a> See below for timestamps, transcript, and to give feedback, submit questions, contact Lex, etc. Transcript: <a href="https://lexfridman.com/joel-david-hamkins-transcript">https://lexfridman.com/joel-david-hamkins-transcript</a> CONTACT LEX: Feedback – give feedback to Lex: <a href="https://lexfridman.com/survey">https://lexfridman.com/survey</a> AMA – submit questions, videos or call-in: <a href="https://lexfridman.com/ama">https://lexfridman.com/ama</a> Hiring – join our team: <a href="https://lexfridman.com/hiring">https://lexfridman.com/hiring</a> Other – other ways to get in touch: <a href="https://lexfridman.com/contact">https://lexfridman.com/contact</a> EPISODE LINKS: Joel’s X: <a href="https://x.com/JDHamkins">https://x.com/JDHamkins</a> Joel’s Website: <a href="https://jdh.hamkins.org">https://jdh.hamkins.org</a> Joel’s Substack: <a href="https://www.infinitelymore.xyz">https://www.infinitelymore.xyz</a> Joel’s MathOverflow: <a href="https://mathoverflow.net/users/1946/joel-david-hamkins">https://mathoverflow.net/users/1946/joel-david-hamkins</a> Joel’s Papers: <a href="https://jdh.hamkins.org/publications">https://jdh.hamkins.org/publications</a> Joel’s Books: Lectures on the Philosophy of Mathematics: <a href="https://amzn.to/3MThaAt">https://amzn.to/3MThaAt</a> Proof and the Art of Mathematics: <a href="https://amzn.to/3YACc9A">https://amzn.to/3YACc9A</a> SPONSORS: To support this podcast, check out our sponsors & get discounts: Perplexity: AI-powered answer engine. Go to <a href="https://lexfridman.com/s/perplexity-ep488-sc">https://www.perplexity.ai/</a> Fin: AI agent for customer service. Go to <a href="https://lexfridman.com/s/fin-ep488-sc">https://fin.ai/lex</a> Miro: Online collaborative whiteboard platform. Go to <a href="https://lexfridman.com/s/miro-ep488-sc">https://miro.com/</a> CodeRabbit: AI-powered code reviews. Go to <a href="https://lexfridman.com/s/coderabbit-ep488-sc">https://coderabbit.ai/lex</a> Chevron: Reliable energy for data centers. Go to <a href="https://lexfridman.com/s/chevron-ep488-sc">https://chevron.com/power</a> Shopify: Sell stuff online. Go to <a href="https://lexfridman.com/s/shopify-ep488-sc">https://shopify.com/lex</a> LMNT: Zero-sugar electrolyte drink mix. Go to <a href="https://lexfridman.com/s/lmnt-ep488-sc">https://drinkLMNT.com/lex</a> MasterClass: Online classes from world-class experts. Go to <a href="https://lexfridman.com/s/masterclass-ep488-sc">https://masterclass.com/lexpod</a> 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

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

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