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

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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. 
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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> 
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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: 
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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

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

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