#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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https://lexfridman.com/joel-david-hamkins-transcript (https://lexfridman.com/joel-david-hamkins-transcript)

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EPISODE LINKS:

Joel’s X: https://x.com/JDHamkins (https://x.com/JDHamkins)

Joel’s Website: https://jdh.hamkins.org (https://jdh.hamkins.org)

Joel’s Substack: https://www.infinitelymore.xyz (https://www.infinitelymore.xyz)

Joel’s MathOverflow: https://mathoverflow.net/users/1946/joel-david-hamkins (https://mathoverflow.net/users/1946/joel-david-hamkins)

Joel’s Papers: https://jdh.hamkins.org/publications (https://jdh.hamkins.org/publications)

Joel’s Books:

Lectures on the Philosophy of Mathematics: https://amzn.to/3MThaAt (https://amzn.to/3MThaAt)

Proof and the Art of Mathematics: https://amzn.to/3YACc9A (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