Infinity, Paradoxes, Gödel Incompleteness & the Mathematical Multiverse - Lex Fridman Podcast
This is a 31 December 2025 published video, host Lex Fridman talks with Joel David Hamkins, a mathematician and philosopher specializing in set theory, the foundations of mathematics, and the nature of infinity, and he’s the 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.
https://youtu.be/14OPT6CcsH4
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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