#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
12/31/20250 min
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:
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
Clips
Transcript
8 sentencesLex Fridman· Host0:00
The following is a conversation with Joel David Hamkins, a mathematician and philosopher specializing in set theory, the foundation of mathematics, and the nature of infinity. He is the number one highest rated user on MathOverflow, which I think is a legendary accomplishment. MathOverflow, by the way, is like Stack Overflow, but for research mathematicians. He is also the author of several books, including Proof in The Art of Mathematics and Lectures on the Philosophy of Mathematics, and he has a great blog, infinitelymore.xyz. This is a super technical and super fun conversation about the foundation of modern mathematics and some mind-bending ideas about infinity, nature of reality, truth, and the mathematical paradoxes that challenged some of the greatest minds of the 20th century. I have been hiding from the world a bit, reading, thinking, writing, soul-searching, as we all do every once in a while. But mostly, just deeply focused on work and preparing mentally for some challenging travel I plan to, uh, take on in the new year. Through all of it, a recurring thought comes to me: how damn lucky I am to be alive and to get to experience