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Dr. Joel Hamkins on Lex Fridman: How Cantor broke math

Cantor's diagonal proof showed uncountable infinities exist, outpacing counting itself; Hamkins uses Hilbert's Hotel to illustrate where infinite sets differ.

Lex FridmanhostJoel David Hamkinsguest
Dec 31, 20253h 52mWatch on YouTube ↗

CHAPTERS

  1. 0:00 – 2:17

    Introduction

  2. 2:17 – 49:27

    Infinity & paradoxes

  3. 49:27 – 1:02:35

    Russell's paradox

  4. 1:02:35 – 1:20:06

    Gödel's incompleteness theorems

  5. 1:20:06 – 1:31:30

    Truth vs proof

  6. 1:31:30 – 1:47:23

    The Halting Problem

  7. 1:47:23 – 2:04:57

    Does infinity exist?

  8. 2:04:57 – 2:08:49

    MathOverflow

  9. 2:08:49 – 2:18:36

    The Continuum Hypothesis

  10. 2:18:36 – 2:28:03

    Hardest problems in mathematics

  11. 2:28:03 – 2:46:55

    Mathematical multiverse

  12. 2:46:55 – 2:57:33

    Surreal numbers

  13. 2:57:33 – 2:59:49

    Conway's Game of Life

  14. 2:59:49 – 3:09:41

    Computability theory

  15. 3:09:41 – 3:12:58

    P vs NP

  16. 3:12:58 – 3:26:43

    Greatest mathematicians in history

  17. 3:26:43 – 3:45:01

    Infinite chess

  18. 3:45:01 – 3:52:17

    Most beautiful idea in mathematics

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