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

2025-06-14 Science & Technology
1.6m
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Lex Fridman
Lex Fridman
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Description

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. Thank you for listening ❤ Check out our sponsors: https://lexfridman.com/sponsors/ep472-sb See below for timestamps, transcript, and to give feedback, submit questions, contact Lex, etc. *Transcript:* https://lexfridman.com/terence-tao-transcript *CONTACT LEX:* *Feedback* - give feedback to Lex: https://lexfridman.com/survey *AMA* - submit questions, videos or call-in: https://lexfridman.com/ama *Hiring* - join our team: https://lexfridman.com/hiring *Other* - other ways to get in touch: https://lexfridman.com/contact *EPISODE LINKS:* Terence's Blog: https://terrytao.wordpress.com/ Terence's YouTube: https://www.youtube.com/@TerenceTao27 Terence's Books: https://amzn.to/43H9Aiq *SPONSORS:* To support this podcast, check out our sponsors & get discounts: *Notion:* Note-taking and team collaboration. Go to https://lexfridman.com/s/notion-ep472-sb *Shopify:* Sell stuff online. Go to https://lexfridman.com/s/shopify-ep472-sb *NetSuite:* Business management software. Go to https://lexfridman.com/s/netsuite-ep472-sb *LMNT:* Zero-sugar electrolyte drink mix. Go to https://lexfridman.com/s/lmnt-ep472-sb *AG1:* All-in-one daily nutrition drink. Go to https://lexfridman.com/s/ag1-ep472-sb *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 *PODCAST LINKS:* - Podcast Website: https://lexfridman.com/podcast - Apple Podcasts: https://apple.co/2lwqZIr - Spotify: https://spoti.fi/2nEwCF8 - RSS: https://lexfridman.com/feed/podcast/ - Podcast Playlist: https://www.youtube.com/playlist?list=PLrAXtmErZgOdP_8GztsuKi9nrraNbKKp4 - Clips Channel: https://www.youtube.com/lexclips *SOCIAL LINKS:* - X: https://x.com/lexfridman - Instagram: https://instagram.com/lexfridman - TikTok: https://tiktok.com/@lexfridman - LinkedIn: https://linkedin.com/in/lexfridman - Facebook: https://facebook.com/lexfridman - Patreon: https://patreon.com/lexfridman - Telegram: https://t.me/lexfridman - Reddit: https://reddit.com/r/lexfridman

Top Comments (10)

@pi5549 2025-06-15

Love how the interview is 3h14m

2.9k 40 replies
@TacsBrazilianGhost 2025-06-15

Terrence is a sweet enough man to explain things in a way that makes me believe I understand what he is saying.

1.1k 3 replies
@3mergent 2025-06-15

I thought my speed was set to 1.25x until Lex spoke 😅 Fascinating interview.

918 32 replies
@hellomon 2025-06-20

Terence, or "Terry", starting attended my high school in Adelaide Australia when he was 7 or 8 years old I think. He was in my older sister's class and he was the sweetest kid. I would see him often quietly eating his lunch, and of course he existed in a world of his own – he wasn't like the other 7 year old kids, nor was he one of the 15 year old kids who he was sharing classes with. He was the little genius. He would sometimes be in the local newspaper, and his Dad would talk about how at the age of 3 he was reading maths books. I vividly remember what always struck me about Terry was his humility. He never walked around as the gifted kid. He never made anyone feel as though he was above them, and it warms my heart to see him here - exactly as he was when he was 7. Good for you Terry. You really were the gifted kid, but not because you were given the talents, but because you gifted the world. We were all rooting for you and look at the contributions you have gone on to make. Best episode ever.

866 23 replies
@RobotProctor 2025-06-15

Missed opportunity to have a podcast last 3:14:15 first 5 digits of pi

839 17 replies
@xyphenius9942 2025-06-16

This is INCREDIBLE. How did u get him on for 3hrs?!?!? He does an interview like once every few years. This is by far the most comprehensive interview ever. Love.

806 14 replies
@Dorinaaah 2025-06-17

This is what we need to praise in our society, not socialites and pseudo artists but scientists and people that leave long lasting contributions in our society.

423 16 replies
@lexfridman 2025-06-14

Thank you for listening ❤ Check out our sponsors: https://lexfridman.com/sponsors/ep472-sa See below for timestamps, transcript, and to give feedback, submit questions, contact Lex, etc. 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 *Transcript:* https://lexfridman.com/terence-tao-transcript *CONTACT LEX:* *Feedback* - give feedback to Lex: https://lexfridman.com/survey *AMA* - submit questions, videos or call-in: https://lexfridman.com/ama *Hiring* - join our team: https://lexfridman.com/hiring *Other* - other ways to get in touch: https://lexfridman.com/contact *EPISODE LINKS:* Terence's Blog: https://terrytao.wordpress.com/ Terence's YouTube: https://www.youtube.com/@TerenceTao27 Terence's Books: https://amzn.to/43H9Aiq *SPONSORS:* To support this podcast, check out our sponsors & get discounts: *Notion:* Note-taking and team collaboration. Go to https://lexfridman.com/s/notion-ep472-sa *Shopify:* Sell stuff online. Go to https://lexfridman.com/s/shopify-ep472-sa *NetSuite:* Business management software. Go to https://lexfridman.com/s/netsuite-ep472-sa *LMNT:* Zero-sugar electrolyte drink mix. Go to https://lexfridman.com/s/lmnt-ep472-sa *AG1:* All-in-one daily nutrition drink. Go to https://lexfridman.com/s/ag1-ep472-sa

348 31 replies
@andreihandru 2025-06-15

Holy moly, this guy is living in another plane of existence.

310 4 replies
@andycai9866 2025-07-08

Huge fan of professor Tao. When I was an undergrad at UCLA, I remember Professor Tao bringing donuts for everyone in the engineering study hall on a rainy day. Super friendly and approachable, and what a kind soul

154 2 replies

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