{"id":211,"date":"2026-01-01T05:24:33","date_gmt":"2025-12-31T21:24:33","guid":{"rendered":"https:\/\/connectword.dpdns.org\/?p=211"},"modified":"2026-01-01T05:24:33","modified_gmt":"2025-12-31T21:24:33","slug":"488-infinity-paradoxes-that-broke-mathematics-godel-incompleteness-the-multiverse-joel-david-hamkins","status":"publish","type":"post","link":"https:\/\/connectword.dpdns.org\/?p=211","title":{"rendered":"#488 \u2013 Infinity, Paradoxes that Broke Mathematics, G\u00f6del Incompleteness & the Multiverse \u2013 Joel David Hamkins"},"content":{"rendered":"

Joel David Hamkins is a mathematician and philosopher specializing in set theory, the foundations of mathematics, and the nature of infinity, and he\u2019s 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.
\nThank you for listening \u2764 Check out our sponsors: https:\/\/lexfridman.com\/sponsors\/ep488-sc<\/a>
\nSee below for timestamps, transcript, and to give feedback, submit questions, contact Lex, etc.<\/p>\n

Transcript:<\/b>
\nhttps:\/\/lexfridman.com\/joel-david-hamkins-transcript<\/a><\/p>\n

CONTACT LEX:<\/b>
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\nOther<\/b> \u2013 other ways to get in touch: https:\/\/lexfridman.com\/contact<\/a><\/p>\n

EPISODE LINKS:<\/b>
\nJoel\u2019s X: https:\/\/x.com\/JDHamkins<\/a>
\nJoel\u2019s Website: https:\/\/jdh.hamkins.org<\/a>
\nJoel\u2019s Substack: https:\/\/www.infinitelymore.xyz<\/a>
\nJoel\u2019s MathOverflow: https:\/\/mathoverflow.net\/users\/1946\/joel-david-hamkins<\/a>
\nJoel\u2019s Papers: https:\/\/jdh.hamkins.org\/publications<\/a>
\nJoel\u2019s Books:
\nLectures on the Philosophy of Mathematics: https:\/\/amzn.to\/3MThaAt<\/a>
\nProof and the Art of Mathematics: https:\/\/amzn.to\/3YACc9A<\/a><\/p>\n

SPONSORS:<\/b>
\nTo support this podcast, check out our sponsors & get discounts:
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OUTLINE:<\/b>
\n(00:00) \u2013 Introduction
\n(01:58) \u2013 Sponsors, Comments, and Reflections
\n(15:40) \u2013 Infinity & paradoxes
\n(1:02:50) \u2013 Russell\u2019s paradox
\n(1:15:57) \u2013 G\u00f6del\u2019s incompleteness theorems
\n(1:33:28) \u2013 Truth vs proof
\n(1:44:52) \u2013 The Halting Problem
\n(2:00:45) \u2013 Does infinity exist?
\n(2:18:19) \u2013 MathOverflow
\n(2:22:12) \u2013 The Continuum Hypothesis
\n(2:31:58) \u2013 Hardest problems in mathematics
\n(2:41:25) \u2013 Mathematical multiverse
\n(3:00:18) \u2013 Surreal numbers
\n(3:10:55) \u2013 Conway\u2019s Game of Life
\n(3:13:11) \u2013 Computability theory
\n(3:23:04) \u2013 P vs NP
\n(3:26:21) \u2013 Greatest mathematicians in history
\n(3:40:05) \u2013 Infinite chess
\n(3:58:24) \u2013 Most beautiful idea in mathematics<\/p>","protected":false},"excerpt":{"rendered":"

Joel David Hamkins is a mathem…<\/p>\n","protected":false},"author":1,"featured_media":212,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-211","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/connectword.dpdns.org\/index.php?rest_route=\/wp\/v2\/posts\/211","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/connectword.dpdns.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/connectword.dpdns.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/connectword.dpdns.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/connectword.dpdns.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=211"}],"version-history":[{"count":0,"href":"https:\/\/connectword.dpdns.org\/index.php?rest_route=\/wp\/v2\/posts\/211\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/connectword.dpdns.org\/index.php?rest_route=\/wp\/v2\/media\/212"}],"wp:attachment":[{"href":"https:\/\/connectword.dpdns.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=211"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/connectword.dpdns.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=211"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/connectword.dpdns.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=211"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}