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.
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Transcript:
<a href="https://lexfridman.com/joel-david-hamkins-transcript">https://lexfridman.com/joel-david-hamkins-transcript</a>
CONTACT LEX:
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EPISODE LINKS:
Joel&#8217;s X: <a href="https://x.com/JDHamkins">https://x.com/JDHamkins</a>
Joel&#8217;s Website: <a href="https://jdh.hamkins.org">https://jdh.hamkins.org</a>
Joel&#8217;s Substack: <a href="https://www.infinitelymore.xyz">https://www.infinitelymore.xyz</a>
Joel&#8217;s MathOverflow: <a href="https://mathoverflow.net/users/1946/joel-david-hamkins">https://mathoverflow.net/users/1946/joel-david-hamkins</a>
Joel&#8217;s Papers: <a href="https://jdh.hamkins.org/publications">https://jdh.hamkins.org/publications</a>
Joel&#8217;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) &#8211; Introduction
(01:58) &#8211; Sponsors, Comments, and Reflections
(15:40) &#8211; Infinity & paradoxes
(1:02:50) &#8211; Russell&#8217;s paradox
(1:15:57) &#8211; Gödel&#8217;s incompleteness theorems
(1:33:28) &#8211; Truth vs proof
(1:44:52) &#8211; The Halting Problem
(2:00:45) &#8211; Does infinity exist?
(2:18:19) &#8211; MathOverflow
(2:22:12) &#8211; The Continuum Hypothesis
(2:31:58) &#8211; Hardest problems in mathematics
(2:41:25) &#8211; Mathematical multiverse
(3:00:18) &#8211; Surreal numbers
(3:10:55) &#8211; Conway&#8217;s Game of Life
(3:13:11) &#8211; Computability theory
(3:23:04) &#8211; P vs NP
(3:26:21) &#8211; Greatest mathematicians in history
(3:40:05) &#8211; Infinite chess
(3:58:24) &#8211; 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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