Infinity, Paradoxes, Gödel Incompleteness & the Mathematical Multiverse | Lex Fridman Podcast

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:
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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/j...
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:
0:00 - Introduction
2:17 - Infinity & paradoxes
49:27 - Russell's paradox
1:02:35 - Gödel's incompleteness theorems
1:20:06 - Truth vs proof
1:31:30 - The Halting Problem
1:47:23 - Does infinity exist?
2:04:57 - MathOverflow
2:08:49 - The Continuum Hypothesis
2:18:36 - Hardest problems in mathematics
2:28:03 - Mathematical multiverse
2:46:55 - Surreal numbers
2:57:33 - Conway's Game of Life
2:59:49 - Computability theory
3:09:41 - P vs NP
3:12:58 - Greatest mathematicians in history
3:26:43 - Infinite chess
3:45:01 - Most beautiful idea in mathematics

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