Terence Tao on Solving the Toughest Problems in Math, Physics & the Future of AI 🤖 | Lex Fridman Podcast #472
Join Lex Fridman as he talks with Terence Tao, a legendary mathematician, about his groundbreaking work on the hardest problems in mathematics, physics, and what’s next for AI innovation.

Lex Fridman
1.5M views • Jun 14, 2025

About this video
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.
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*LMNT:* Zero-sugar electrolyte drink mix.
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*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
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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
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Video Information
Views
1.5M
Likes
21.2K
Duration
03:14:34
Published
Jun 14, 2025
User Reviews
4.7
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