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

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Published on June 14, 2025 8:15:34 PM ● Video Link: https://www.youtube.com/watch?v=HUkBz-cdB-k

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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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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

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