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

Lex Fridman Podcast

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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.
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

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: <a href="https://lexfridman.com/sponsors/ep472-sc">https://lexfridman.com/sponsors/ep472-sc</a> 
See below for timestamps, transcript, and to give feedback, submit questions, contact Lex, etc.
Transcript: 
<a href="https://lexfridman.com/terence-tao-transcript">https://lexfridman.com/terence-tao-transcript</a>
CONTACT LEX: 
Feedback – give feedback to Lex: <a href="https://lexfridman.com/survey">https://lexfridman.com/survey</a> 
AMA – submit questions, videos or call-in: <a href="https://lexfridman.com/ama">https://lexfridman.com/ama</a> 
Hiring – join our team: <a href="https://lexfridman.com/hiring">https://lexfridman.com/hiring</a> 
Other – other ways to get in touch: <a href="https://lexfridman.com/contact">https://lexfridman.com/contact</a>
EPISODE LINKS: 
Terence’s Blog: <a href="https://terrytao.wordpress.com/">https://terrytao.wordpress.com/</a> 
Terence’s YouTube: <a href="https://www.youtube.com/@TerenceTao27">https://www.youtube.com/@TerenceTao27</a> 
Terence’s Books: <a href="https://amzn.to/43H9Aiq">https://amzn.to/43H9Aiq</a>
SPONSORS: 
To support this podcast, check out our sponsors & get discounts: 
Notion: Note-taking and team collaboration. 
Go to <a href="https://lexfridman.com/s/notion-ep472-sc">https://notion.com/lex</a> 
Shopify: Sell stuff online. 
Go to <a href="https://lexfridman.com/s/shopify-ep472-sc">https://shopify.com/lex</a> 
NetSuite: Business management software. 
Go to <a href="https://lexfridman.com/s/netsuite-ep472-sc">http://netsuite.com/lex</a> 
LMNT: Zero-sugar electrolyte drink mix. 
Go to <a href="https://lexfridman.com/s/lmnt-ep472-sc">https://drinkLMNT.com/lex</a> 
AG1: All-in-one daily nutrition drink. 
Go to <a href="https://lexfridman.com/s/ag1-ep472-sc">https://drinkag1.com/lex</a>
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: <a href="https://lexfridman.com/podcast">https://lexfridman.com/podcast</a> 
– Apple Podcasts: <a href="https://apple.co/2lwqZIr">https://apple.co/2lwqZIr</a> 
– Spotify: <a href="https://spoti.fi/2nEwCF8">https://spoti.fi/2nEwCF8</a> 
– RSS: <a href="https://lexfridman.com/feed/podcast/">https://lexfridman.com/feed/podcast/</a> 
– Podcast Playlist: <a href="https://www.youtube.com/playlist?list=PLrAXtmErZgOdP_8GztsuKi9nrraNbKKp4">https://www.youtube.com/playlist?list=PLrAXtmErZgOdP_8GztsuKi9nrraNbKKp4</a> 
– Clips Channel: <a href="https://www.youtube.com/lexclips">https://www.youtube.com/lexclips</a>

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

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