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:
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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:
(00:00) - Introduction
(00:36) - Sponsors, Comments, and Reflections
(09:49) - First hard problem
(15:16) - Navier–Stokes singularity
(35:25) - Game of life
(42:00) - Infinity
(47:07) - Math vs Physics
(53:26) - Nature of reality
(1:16:08) - Theory of everything
(1:22:09) - General relativity
(1:25:37) - Solving difficult problems
(1:29:00) - AI-assisted theorem proving
(1:41:50) - Lean programming language
(1:51:50) - DeepMind's AlphaProof
(1:56:45) - Human mathematicians vs AI
(2:06:37) - AI winning the Fields Medal
(2:13:47) - Grigori Perelman
(2:26:29) - Twin Prime Conjecture
(2:43:04) - Collatz conjecture
(2:49:50) - P = NP
(2:52:43) - Fields Medal
(3:00:18) - Andrew Wiles and Fermat's Last Theorem
(3:04:15) - Productivity
(3:06:54) - Advice for young people
(3:15:17) - The greatest mathematician of all time

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#472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI