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#503 – AI Crisis in Math: Navier-Stokes, Riemann Hypothesis & Complexity Theory

$#503 – AI Crisis in Math: Navier-Stokes, Riemann Hypothesis & Complexity Theory$

#503 – AI Crisis in Math: Navier-Stokes, Riemann Hypothesis & Complexity Theory

Lex Fridman Podcast vor 2 Wochen

0:00

3:42:40

Ankur Moitra, Steven Brunton and Alex Kontorovich are three
mathematicians who can speak to this incredible moment in the
history of mathematics, when AI solved some of its hardest
problems: Navier-Stokes, the quasi-Riemann hypothesis, the unique
games conjecture and hundreds of other problems. Ankur Moitra is
a mathematician at MIT (visiting the Institute for Advanced Study
in Princeton) working in theoretical computer science, who can
speak to the unique games conjecture, complexity theory and the
mathematics of how AI learns. Steven Brunton is a mathematician
and fluid dynamics expert at UW, who can speak to Navier-Stokes,
turbulence and machine learning for fluid dynamics. Alex
Kontorovich is a mathematician at Rutgers specializing in number
theory, who can speak to the Riemann hypothesis, Lean and
machine-checked proofs.

Thank you for listening Check out our sponsors:
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See below for timestamps, transcript, and to give feedback,
submit questions, contact Lex, etc.

Transcript:

https://lexfridman.com/math-ai-crisis-transcript

CONTACT LEX:

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EPISODE LINKS:

Ankur’s Website: https://people.csail.mit.edu/moitra/

Alex’s X: https://x.com/AlexKontorovich

Alex’s Website: https://sites.math.rutgers.edu/~alexk/

Steven’s X: https://x.com/eigensteve

Steven’s YouTube: https://youtube.com/@Eigensteve

Steven’s Website: https://eigensteve.com

Lean: https://lean-lang.org/

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OUTLINE:

(00:00) – Introduction

(01:58) – Sponsors, Comments, and Reflections

(09:53) – Crisis moment in mathematics

(18:10) – Will AI “solve” mathematics?

(34:21) – Can AI create new math?

(1:13:53) – Riemann hypothesis

(1:37:45) – Navier-Stokes

(2:03:42) – How nature computes

(2:12:35) – Unique Games Conjecture and complexity theory

(2:27:28) – How mathematicians think

(2:41:05) – Is math invented or discovered?

(2:47:13) – Can AI solve P vs NP?

(2:57:28) – Why LLMs work so well

(3:11:54) – Problems AI can’t solve yet

(3:16:23) – Grigori Perelman

(3:25:41) – Advice for young people