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

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

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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