Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472

Lex FridmanSat, June 14, 2025 8:15pmURL:
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Terence Tao is widely considered to be one of the greatest mathematicians in history. He won the Fields Medal and the Breakthrough Prize in Mathematics, and has contributed to a wide range of fields from fluid dynamics with Navier-Stokes equations to mathematical physics & quantum mechanics, prime numbers & analytics number theory, harmonic analysis, compressed sensing, random matrix theory, combinatorics, and progress on many of the hardest problems in the history of mathematics.
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*Transcript:*
https://lexfridman.com/terence-tao-transcript

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*EPISODE LINKS:*
Terence’s Blog: https://terrytao.wordpress.com/
Terence’s YouTube: https://www.youtube.com/@TerenceTao27
Terence’s Books: https://amzn.to/43H9Aiq

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*OUTLINE:*
0:00 – Introduction
0:49 – First hard problem
6:16 – Navier–Stokes singularity
26:26 – Game of life
33:01 – Infinity
38:07 – Math vs Physics
44:26 – Nature of reality
1:07:09 – Theory of everything
1:13:10 – General relativity
1:16:37 – Solving difficult problems
1:20:01 – AI-assisted theorem proving
1:32:51 – Lean programming language
1:42:51 – DeepMind’s AlphaProof
1:47:45 – Human mathematicians vs AI
1:57:37 – AI winning the Fields Medal
2:04:47 – Grigori Perelman
2:17:30 – Twin Prime Conjecture
2:34:04 – Collatz conjecture
2:40:50 – P = NP
2:43:43 – Fields Medal
2:51:18 – Andrew Wiles and Fermat’s Last Theorem
2:55:16 – Productivity
2:57:55 – Advice for young people
3:06:17 – The greatest mathematician of all time