{"id":6378,"date":"2025-12-31T16:24:33","date_gmt":"2025-12-31T21:24:33","guid":{"rendered":"https:\/\/lexfridman.com\/?p=6378"},"modified":"2025-12-31T16:24:33","modified_gmt":"2025-12-31T21:24:33","slug":"joel-david-hamkins","status":"publish","type":"post","link":"https:\/\/lexfridman.com\/joel-david-hamkins\/","title":{"rendered":"#488 \u2013 Infinity, Paradoxes that Broke Mathematics, G\u00f6del Incompleteness &#038; the Multiverse &#8211; Joel David Hamkins"},"content":{"rendered":"<div class=\"powerpress_player\" id=\"powerpress_player_4235\"><audio class=\"wp-audio-shortcode\" id=\"audio-6378-1\" preload=\"none\" style=\"width: 100%;\" controls=\"controls\"><source type=\"audio\/mpeg\" src=\"https:\/\/media.blubrry.com\/takeituneasy\/ins.blubrry.com\/takeituneasy\/lex_ai_joel_david_hamkins.mp3?_=1\" \/><a href=\"https:\/\/media.blubrry.com\/takeituneasy\/ins.blubrry.com\/takeituneasy\/lex_ai_joel_david_hamkins.mp3\">https:\/\/media.blubrry.com\/takeituneasy\/ins.blubrry.com\/takeituneasy\/lex_ai_joel_david_hamkins.mp3<\/a><\/audio><\/div><p class=\"powerpress_links powerpress_links_mp3\" style=\"margin-bottom: 1px !important;\">Podcast: <a href=\"https:\/\/media.blubrry.com\/takeituneasy\/ins.blubrry.com\/takeituneasy\/lex_ai_joel_david_hamkins.mp3\" class=\"powerpress_link_pinw\" target=\"_blank\" title=\"Play in new window\" onclick=\"return powerpress_pinw('https:\/\/lexfridman.com\/?powerpress_pinw=6378-podcast');\" rel=\"nofollow\">Play in new window<\/a> | <a href=\"https:\/\/media.blubrry.com\/takeituneasy\/ins.blubrry.com\/takeituneasy\/lex_ai_joel_david_hamkins.mp3\" class=\"powerpress_link_d\" title=\"Download\" rel=\"nofollow\" download=\"lex_ai_joel_david_hamkins.mp3\">Download<\/a><\/p><p class=\"powerpress_links powerpress_subscribe_links\">Subscribe: <a href=\"https:\/\/open.spotify.com\/show\/2MAi0BvDc6GTFvKFPXnkCL\" class=\"powerpress_link_subscribe powerpress_link_subscribe_spotify\" target=\"_blank\" title=\"Subscribe on Spotify\" rel=\"nofollow\">Spotify<\/a> | <a href=\"https:\/\/tunein.com\/podcasts\/Technology-Podcasts\/Artificial-Intelligence-p1153019\/\" class=\"powerpress_link_subscribe powerpress_link_subscribe_tunein\" target=\"_blank\" title=\"Subscribe on TuneIn\" rel=\"nofollow\">TuneIn<\/a> | <a href=\"https:\/\/lexfridman.com\/feed\/podcast\/\" class=\"powerpress_link_subscribe powerpress_link_subscribe_rss\" target=\"_blank\" title=\"Subscribe via RSS\" rel=\"nofollow\">RSS<\/a><\/p><p>Joel David Hamkins is a mathematician and philosopher specializing in set theory, the foundations of mathematics, and the nature of infinity, and he&#8217;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 \/>\nThank you for listening \u2764 Check out our sponsors: <a href=\"https:\/\/lexfridman.com\/sponsors\/ep488-sc\">https:\/\/lexfridman.com\/sponsors\/ep488-sc<\/a><br \/>\nSee below for timestamps, transcript, and to give feedback, submit questions, contact Lex, etc.<\/p>\n<p><b>Transcript:<\/b><br \/>\n<a href=\"https:\/\/lexfridman.com\/joel-david-hamkins-transcript\">https:\/\/lexfridman.com\/joel-david-hamkins-transcript<\/a><\/p>\n<p><b>CONTACT LEX:<\/b><br \/>\n<b>Feedback<\/b> &#8211; give feedback to Lex: <a href=\"https:\/\/lexfridman.com\/survey\">https:\/\/lexfridman.com\/survey<\/a><br \/>\n<b>AMA<\/b> &#8211; submit questions, videos or call-in: <a href=\"https:\/\/lexfridman.com\/ama\">https:\/\/lexfridman.com\/ama<\/a><br \/>\n<b>Hiring<\/b> &#8211; join our team: <a href=\"https:\/\/lexfridman.com\/hiring\">https:\/\/lexfridman.com\/hiring<\/a><br \/>\n<b>Other<\/b> &#8211; other ways to get in touch: <a href=\"https:\/\/lexfridman.com\/contact\">https:\/\/lexfridman.com\/contact<\/a><\/p>\n<p><b>EPISODE LINKS:<\/b><br \/>\nJoel&#8217;s X: <a href=\"https:\/\/x.com\/JDHamkins\">https:\/\/x.com\/JDHamkins<\/a><br \/>\nJoel&#8217;s Website: <a href=\"https:\/\/jdh.hamkins.org\">https:\/\/jdh.hamkins.org<\/a><br \/>\nJoel&#8217;s Substack: <a href=\"https:\/\/www.infinitelymore.xyz\">https:\/\/www.infinitelymore.xyz<\/a><br \/>\nJoel&#8217;s MathOverflow: <a href=\"https:\/\/mathoverflow.net\/users\/1946\/joel-david-hamkins\">https:\/\/mathoverflow.net\/users\/1946\/joel-david-hamkins<\/a><br \/>\nJoel&#8217;s Papers: <a href=\"https:\/\/jdh.hamkins.org\/publications\">https:\/\/jdh.hamkins.org\/publications<\/a><br \/>\nJoel&#8217;s Books:<br \/>\nLectures on the Philosophy of Mathematics: <a href=\"https:\/\/amzn.to\/3MThaAt\">https:\/\/amzn.to\/3MThaAt<\/a><br \/>\nProof and the Art of Mathematics: <a href=\"https:\/\/amzn.to\/3YACc9A\">https:\/\/amzn.to\/3YACc9A<\/a><\/p>\n<p><b>SPONSORS:<\/b><br \/>\nTo support this podcast, check out our sponsors &amp; get discounts:<br \/>\n<b>Perplexity:<\/b> AI-powered answer engine.<br \/>\nGo to <a href=\"https:\/\/lexfridman.com\/s\/perplexity-ep488-sc\">https:\/\/www.perplexity.ai\/<\/a><br \/>\n<b>Fin:<\/b> AI agent for customer service.<br \/>\nGo to <a href=\"https:\/\/lexfridman.com\/s\/fin-ep488-sc\">https:\/\/fin.ai\/lex<\/a><br \/>\n<b>Miro:<\/b> Online collaborative whiteboard platform.<br \/>\nGo to <a href=\"https:\/\/lexfridman.com\/s\/miro-ep488-sc\">https:\/\/miro.com\/<\/a><br \/>\n<b>CodeRabbit:<\/b> AI-powered code reviews.<br \/>\nGo to <a href=\"https:\/\/lexfridman.com\/s\/coderabbit-ep488-sc\">https:\/\/coderabbit.ai\/lex<\/a><br \/>\n<b>Chevron:<\/b> Reliable energy for data centers.<br \/>\nGo to <a href=\"https:\/\/lexfridman.com\/s\/chevron-ep488-sc\">https:\/\/chevron.com\/power<\/a><br \/>\n<b>Shopify:<\/b> Sell stuff online.<br \/>\nGo to <a href=\"https:\/\/lexfridman.com\/s\/shopify-ep488-sc\">https:\/\/shopify.com\/lex<\/a><br \/>\n<b>LMNT:<\/b> Zero-sugar electrolyte drink mix.<br \/>\nGo to <a href=\"https:\/\/lexfridman.com\/s\/lmnt-ep488-sc\">https:\/\/drinkLMNT.com\/lex<\/a><br \/>\n<b>MasterClass:<\/b> Online classes from world-class experts.<br \/>\nGo to <a href=\"https:\/\/lexfridman.com\/s\/masterclass-ep488-sc\">https:\/\/masterclass.com\/lexpod<\/a><\/p>\n<p><b>OUTLINE:<\/b><br \/>\n(00:00) &#8211; Introduction<br \/>\n(01:58) &#8211; Sponsors, Comments, and Reflections<br \/>\n(15:40) &#8211; Infinity &amp; paradoxes<br \/>\n(1:02:50) &#8211; Russell&#8217;s paradox<br \/>\n(1:15:57) &#8211; G\u00f6del&#8217;s incompleteness theorems<br \/>\n(1:33:28) &#8211; Truth vs proof<br \/>\n(1:44:52) &#8211; The Halting Problem<br \/>\n(2:00:45) &#8211; Does infinity exist?<br \/>\n(2:18:19) &#8211; MathOverflow<br \/>\n(2:22:12) &#8211; The Continuum Hypothesis<br \/>\n(2:31:58) &#8211; Hardest problems in mathematics<br \/>\n(2:41:25) &#8211; Mathematical multiverse<br \/>\n(3:00:18) &#8211; Surreal numbers<br \/>\n(3:10:55) &#8211; Conway&#8217;s Game of Life<br \/>\n(3:13:11) &#8211; Computability theory<br \/>\n(3:23:04) &#8211; P vs NP<br \/>\n(3:26:21) &#8211; Greatest mathematicians in history<br \/>\n(3:40:05) &#8211; Infinite chess<br \/>\n(3:58:24) &#8211; Most beautiful idea in mathematics<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Joel David Hamkins is a mathematician and philosopher specializing in set theory, the foundations of mathematics, and the nature of infinity, and he&#8217;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 \u2764 Check out our sponsors: https:\/\/lexfridman.com\/sponsors\/ep488-sc See below for timestamps, transcript, and to give feedback, submit questions, contact Lex, etc. Transcript: https:\/\/lexfridman.com\/joel-david-hamkins-transcript CONTACT LEX: Feedback &#8211; give feedback to Lex: https:\/\/lexfridman.com\/survey AMA &#8211; submit questions, videos<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[3392],"tags":[],"class_list":["post-6378","post","type-post","status-publish","format-standard","hentry","category-ai"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>#488 \u2013 Infinity, Paradoxes that Broke Mathematics, G\u00f6del Incompleteness &amp; the Multiverse - Joel David Hamkins | Lex Fridman Podcast<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/lexfridman.com\/joel-david-hamkins\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"#488 \u2013 Infinity, Paradoxes that Broke Mathematics, G\u00f6del Incompleteness &amp; the Multiverse - Joel David Hamkins | Lex Fridman Podcast\" \/>\n<meta property=\"og:description\" content=\"Joel David Hamkins is a mathematician and philosopher specializing in set theory, the foundations of mathematics, and the nature of infinity, and he&#8217;s the #1 highest-rated user on MathOverflow. 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Thank you for listening \u2764 Check out our sponsors: https:\/\/lexfridman.com\/sponsors\/ep488-sc See below for timestamps, transcript, and to give feedback, submit questions, contact Lex, etc. Transcript: https:\/\/lexfridman.com\/joel-david-hamkins-transcript CONTACT LEX: Feedback &#8211; give feedback to Lex: https:\/\/lexfridman.com\/survey AMA &#8211; submit questions, videos\" \/>\n<meta property=\"og:url\" content=\"https:\/\/lexfridman.com\/joel-david-hamkins\/\" \/>\n<meta property=\"og:site_name\" content=\"Lex Fridman\" \/>\n<meta property=\"article:author\" content=\"https:\/\/www.facebook.com\/lexfridman\" \/>\n<meta property=\"article:published_time\" content=\"2025-12-31T21:24:33+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/lexfridman.com\/wordpress\/wp-content\/uploads\/2025\/12\/thumb_joel_david_hamkins.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1280\" \/>\n\t<meta property=\"og:image:height\" content=\"720\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Lex Fridman\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@lexfridman\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Lex Fridman\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/lexfridman.com\\\/joel-david-hamkins\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/lexfridman.com\\\/joel-david-hamkins\\\/\"},\"author\":{\"name\":\"Lex Fridman\",\"@id\":\"https:\\\/\\\/lexfridman.com\\\/#\\\/schema\\\/person\\\/8bc69a469063031599412b1a93e75b9f\"},\"headline\":\"#488 \u2013 Infinity, Paradoxes that Broke Mathematics, G\u00f6del Incompleteness &#038; the Multiverse &#8211; Joel David Hamkins\",\"datePublished\":\"2025-12-31T21:24:33+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/lexfridman.com\\\/joel-david-hamkins\\\/\"},\"wordCount\":391,\"articleSection\":[\"ai\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/lexfridman.com\\\/joel-david-hamkins\\\/\",\"url\":\"https:\\\/\\\/lexfridman.com\\\/joel-david-hamkins\\\/\",\"name\":\"#488 \u2013 Infinity, Paradoxes that Broke Mathematics, G\u00f6del Incompleteness & the Multiverse - Joel David Hamkins | Lex Fridman Podcast\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/lexfridman.com\\\/#website\"},\"datePublished\":\"2025-12-31T21:24:33+00:00\",\"author\":{\"@id\":\"https:\\\/\\\/lexfridman.com\\\/#\\\/schema\\\/person\\\/8bc69a469063031599412b1a93e75b9f\"},\"breadcrumb\":{\"@id\":\"https:\\\/\\\/lexfridman.com\\\/joel-david-hamkins\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/lexfridman.com\\\/joel-david-hamkins\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/lexfridman.com\\\/joel-david-hamkins\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/lexfridman.com\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"#488 \u2013 Infinity, Paradoxes that Broke Mathematics, G\u00f6del Incompleteness &#038; the Multiverse &#8211; Joel David Hamkins\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/lexfridman.com\\\/#website\",\"url\":\"https:\\\/\\\/lexfridman.com\\\/\",\"name\":\"Lex Fridman\",\"description\":\"Research Scientist at MIT. 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