Infinity, Paradoxes, Gödel Incompleteness & the Mathematical Multiverse | Lex Fridman Podcast #488

Yep I’m understanding all of this 🙃

What a joy to be alive. Happy New Year for all infinities

Happy New Year everyone. So glad Lex is sticking to maths, science, tech these days.

This is awesome Lex. I know it's much less popular to have someone talk at length about something so involved but for the people who watch and are interested in this topic area its a brilliant resource and refreshing to go in depth on a topic, rather than keeping it pop sci.

The remark Lex made about professor Hamkins' status as a user of mathoverflow really is no joke: I have lost the count of how many times his answers have been useful for my own curiosity and self-study. The level of detail and clarity is beyond belief, such a gem of a contributor

I was telling my husband how pondering infinity is slowly making me go insane and then this pops up not long after to make it worse 😅 send thoughts and prayers to my husband cause he’s about to be annoyed af for the next few years, as there’s no way I’m shutting up about this

Thank you for listening ❤ Check out our sponsors: https://lexfridman.com/sponsors/ep488-sa See below for timestamps, transcript, and to give feedback, submit questions, contact Lex, etc. 0:00 - Introduction 2:17 - Infinity & paradoxes 49:27 - Russell's paradox 1:02:35 - Gödel's incompleteness theorems 1:20:06 - Truth vs proof 1:31:30 - The Halting Problem 1:47:23 - Does infinity exist? 2:04:57 - MathOverflow 2:08:49 - The Continuum Hypothesis 2:18:36 - Hardest problems in mathematics 2:28:03 - Mathematical multiverse 2:46:55 - Surreal numbers 2:57:33 - Conway's Game of Life 2:59:49 - Computability theory 3:09:41 - P vs NP 3:12:58 - Greatest mathematicians in history 3:26:43 - Infinite chess 3:45:01 - Most beautiful idea in mathematics *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:* Joel's X: https://x.com/JDHamkins Joel's Website: https://jdh.hamkins.org Joel's Substack: https://www.infinitelymore.xyz Joel's MathOverflow: https://mathoverflow.net/users/1946/joel-david-hamkins Joel's Papers: https://jdh.hamkins.org/publications Joel's Books: Lectures on the Philosophy of Mathematics: https://amzn.to/3MThaAt Proof and the Art of Mathematics: https://amzn.to/3YACc9A *SPONSORS:* To support this podcast, check out our sponsors & get discounts: *Perplexity:* AI-powered answer engine. Go to https://lexfridman.com/s/perplexity-ep488-sa *Fin:* AI agent for customer service. Go to https://lexfridman.com/s/fin-ep488-sa *Miro:* Online collaborative whiteboard platform. Go to https://lexfridman.com/s/miro-ep488-sa *CodeRabbit:* AI-powered code reviews. Go to https://lexfridman.com/s/coderabbit-ep488-sa *Chevron:* Reliable energy for data centers. Go to https://lexfridman.com/s/chevron-ep488-sa *Shopify:* Sell stuff online. Go to https://lexfridman.com/s/shopify-ep488-sa *LMNT:* Zero-sugar electrolyte drink mix. Go to https://lexfridman.com/s/lmnt-ep488-sa *MasterClass:* Online classes from world-class experts. Go to https://lexfridman.com/s/masterclass-ep488-sa

This is one of the best interviews ever... I love the emphasis on construction to demystify all notions of abstract existences

Bachelor in Math here, how does an infinitely countable set of countable infinites violate Euclid's Principle? The principle is that THE whole is greater than the parts. Without a proof and an identity for a "whole," how can one conclude that there is no "whole" above the aforementioned part?

If you've ever grappled with rebelion against mathenatical rigor, this is a MUST WATCH.