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

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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Transcript:
https://lexfridman.com/joel-david-hamkins-transcript

CONTACT LEX:
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EPISODE LINKS:
Joel’s X: https://x.com/JDHamkins
Joel’s Website: https://jdh.hamkins.org
Joel’s Substack: https://www.infinitelymore.xyz
Joel’s MathOverflow: https://mathoverflow.net/users/1946/joel-david-hamkins
Joel’s Papers: https://jdh.hamkins.org/publications
Joel’s Books:
Lectures on the Philosophy of Mathematics: https://amzn.to/3MThaAt
Proof and the Art of Mathematics: https://amzn.to/3YACc9A

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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