Lex Fridman Podcast
#472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
15 Jun 2025
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-sc 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://notion.com/lex Shopify: Sell stuff online. Go to https://shopify.com/lex NetSuite: Business management software. Go to http://netsuite.com/lex LMNT: Zero-sugar electrolyte drink mix. Go to https://drinkLMNT.com/lex AG1: All-in-one daily nutrition drink. Go to https://drinkag1.com/lex 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 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
Full Episode
The following is a conversation with Terence Tao, widely considered to be one of the greatest mathematicians in history, often referred to as the Mozart of math. He won the Fields Medal and the Breakthrough Prize in Mathematics, and has contributed groundbreaking work to a truly astonishing range of fields in mathematics and physics.
This was a huge honor for me, for many reasons, including the humility and kindness that Terry showed to me throughout all our interactions. It means the world. And now a quick few second mention of each sponsor. Check them out in the description or at lexfriedman.com slash sponsors. It's the best way to support this podcast.
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I enjoy their stuff. Maybe you will too. To get in touch with me for whatever reason, go to lexfreeman.com slash contact. All right, let's go. This episode is brought to you by Notion, a note-taking and team collaboration tool.
I use Notion for everything, for personal notes, for planning these podcasts, for collaborating with other folks, and for super boosting all of those things with AI because Notion does a great job of integrating AI into the whole thing.
You know, what's fascinating is the mechanisms of human memory before we had widely adopted technologies and tools for writing and recording stuff, certainly before the computer. So you can look at medieval monks, for example, that would use the now well-studied memory techniques, like the memory palace, the spatial memory techniques to memorize entire books.
That is certainly the effect of technology started by Google search and moving to all the other things like notion that we're offloading more and more and more of the task of memorization to the computers, which I think is probably a positive thing because it frees more of our brain to do deep reasoning, whether that's deep dive focused specialization or the journalist type of thinking versus memorizing facts.
Although I do think that there's a kind of background model that's formed when you memorize a lot of things. And from there, from inspiration, arises discovery. So I don't know. It could be a great cost to offloading most of our memorization to the machines. But it is the way of the world. Try Notion AI for free when you go to notion.com slash lex. That's all lowercase.
Notion.com slash lex to try the power of Notion AI today. This episode is also brought to you by Shopify, a platform designed for anyone to sell anywhere with a great looking online store. Our future, friends, has a lot of robots in it. Looking into that distant future, you have Amazon warehouses with millions of robots that move packages around.
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