#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
December 31, 2025
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Show notes
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:
() – Introduction
() – Sponsors, Comments, and Reflections
() – Infinity & paradoxes
() – Russell’s paradox
() – Gödel’s incompleteness theorems
() – Truth vs proof
() – The Halting Problem
() – Does infinity exist?
() – MathOverflow
() – The Continuum Hypothesis
() – Hardest problems in mathematics
() – Mathematical multiverse
() – Surreal numbers
() – Conway’s Game of Life
() – Computability theory
() – P vs NP
() – Great