Infinity, Paradoxes, Gödel Incompleteness & the Mathematical Multiverse | Lex Fridman Podcast #488

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

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*EPISODE LINKS:*
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Joel's Website: https://jdh.hamkins.org
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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:*
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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