Lex Fridman Podcast
Lex Fridman
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
DEC 31, 2025-1 MIN
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
DEC 31, 2025-1 MIN
Description
<p>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.<br />
Thank you for listening ❤ Check out our sponsors: <a href="https://lexfridman.com/sponsors/ep488-sc">https://lexfridman.com/sponsors/ep488-sc</a><br />
See below for timestamps, transcript, and to give feedback, submit questions, contact Lex, etc.</p>
<p><b>Transcript:</b><br />
<a href="https://lexfridman.com/joel-david-hamkins-transcript">https://lexfridman.com/joel-david-hamkins-transcript</a></p>
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<b>Feedback</b> – give feedback to Lex: <a href="https://lexfridman.com/survey">https://lexfridman.com/survey</a><br />
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<b>Other</b> – other ways to get in touch: <a href="https://lexfridman.com/contact">https://lexfridman.com/contact</a></p>
<p><b>EPISODE LINKS:</b><br />
Joel’s X: <a href="https://x.com/JDHamkins">https://x.com/JDHamkins</a><br />
Joel’s Website: <a href="https://jdh.hamkins.org">https://jdh.hamkins.org</a><br />
Joel’s Substack: <a href="https://www.infinitelymore.xyz">https://www.infinitelymore.xyz</a><br />
Joel’s MathOverflow: <a href="https://mathoverflow.net/users/1946/joel-david-hamkins">https://mathoverflow.net/users/1946/joel-david-hamkins</a><br />
Joel’s Papers: <a href="https://jdh.hamkins.org/publications">https://jdh.hamkins.org/publications</a><br />
Joel’s Books:<br />
Lectures on the Philosophy of Mathematics: <a href="https://amzn.to/3MThaAt">https://amzn.to/3MThaAt</a><br />
Proof and the Art of Mathematics: <a href="https://amzn.to/3YACc9A">https://amzn.to/3YACc9A</a></p>
<p><b>SPONSORS:</b><br />
To support this podcast, check out our sponsors & get discounts:<br />
<b>Perplexity:</b> AI-powered answer engine.<br />
Go to <a href="https://lexfridman.com/s/perplexity-ep488-sc">https://www.perplexity.ai/</a><br />
<b>Fin:</b> AI agent for customer service.<br />
Go to <a href="https://lexfridman.com/s/fin-ep488-sc">https://fin.ai/lex</a><br />
<b>Miro:</b> Online collaborative whiteboard platform.<br />
Go to <a href="https://lexfridman.com/s/miro-ep488-sc">https://miro.com/</a><br />
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Go to <a href="https://lexfridman.com/s/chevron-ep488-sc">https://chevron.com/power</a><br />
<b>Shopify:</b> Sell stuff online.<br />
Go to <a href="https://lexfridman.com/s/shopify-ep488-sc">https://shopify.com/lex</a><br />
<b>LMNT:</b> Zero-sugar electrolyte drink mix.<br />
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<b>MasterClass:</b> Online classes from world-class experts.<br />
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<p><b>OUTLINE:</b><br />
(00:00) – Introduction<br />
(01:58) – Sponsors, Comments, and Reflections<br />
(15:40) – Infinity & paradoxes<br />
(1:02:50) – Russell’s paradox<br />
(1:15:57) – Gödel’s incompleteness theorems<br />
(1:33:28) – Truth vs proof<br />
(1:44:52) – The Halting Problem<br />
(2:00:45) – Does infinity exist?<br />
(2:18:19) – MathOverflow<br />
(2:22:12) – The Continuum Hypothesis<br />
(2:31:58) – Hardest problems in mathematics<br />
(2:41:25) – Mathematical multiverse<br />
(3:00:18) – Surreal numbers<br />
(3:10:55) – Conway’s Game of Life<br />
(3:13:11) – Computability theory<br />
(3:23:04) – P vs NP<br />
(3:26:21) – Greatest mathematicians in history<br />
(3:40:05) – Infinite chess<br />
(3:58:24) – Most beautiful idea in mathematics</p>