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$What Did AI Prove About Navier-Stokes? · Lex Fridman Podcast$

Lex Fridman Podcast

#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…

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Notes

Would Alex Kontorovich Call AI in Mathematics a Crisis? at 9:53

Alex Kontorovich does not know whether he would call the moment in AI and mathematics a crisis. A lot of opportunity sits in the crisis. Full answer
Does Ankur Moitra Feel More Intellectually Lonely? at 11:13

Ankur Moitra says he might feel more intellectually lonely than before. He feels very excited. Full answer
Why Does Steven Brunton Stay Hopeful About AI? at 14:52

Steven Brunton says most of his feelings are hopeful. Full answer
Did AI Solve the Riemann Hypothesis? at 19:40

No. Alex Kontorovich says the Riemann hypothesis is not solved. Full answer
Why Is the Doorman Fallacy Useful for Math and AI? at 27:48

Ankur Moitra treats the doorman fallacy as a good way to think about mathematics in the age of AI. Full answer
Are Machines Already Finding Physical Laws? at 35:46

Steven Brunton says that search is already happening for physical laws. Full answer
Why Is AI Math More Than a Convex Hull? at 41:52

Alex Kontorovich says AI math is more than a convex hull because known moves, chained together, reach much further than that label allows. Full answer
Is the quasi-Riemann Hypothesis Proof a New Idea? at 44:09

Alex Kontorovich says the quasi Riemann Hypothesis case is not a genuinely new idea. It is a beautiful combination of things that were already very well known. Full answer
How Are Research Papers Changing Because of AI? at 55:10

Steven Brunton says an academic contribution in engineering and applied science is already shifting, and with AI a small reusable piece is worth more than one… Full answer
Why Do Journals Need New Models for AI Proofs? at 1:00:38

Ankur Moitra wants new models that ease the load on journals and conferences, including a shared effort to verify AI proofs, while the older publishing models… Full answer
What Is the Riemann Hypothesis? at 1:14:33

Alex Kontorovich says the Riemann hypothesis predicts that every wave behind the prime numbers has exactly the same amplitude. Full answer
How Long Is Fermat's Last Theorem in Lean? at 1:18:20

Alex Kontorovich says the Lean formalization of Fermat's Last Theorem is 13 million lines. He was sure that formalization was at least three years away. Full answer
Can AI Formalize a Proof a Human Already Wrote? at 1:25:20

Alex Kontorovich says autoformalization is basically solved, and not in the way he wants. Full answer
What Did AI Prove About the quasi-Riemann Hypothesis? at 1:32:40

Alex Kontorovich says the proof gives an infinite vertical strip with no zeros whose real part lies between seven-eighths and one. Full answer
Why Is a Fluid So Hard to Solve? at 1:39:25

Steven Brunton says force equals mass times acceleration is simple to write down, yet a fluid becomes very complicated to solve in any practical sense. Full answer
What Is the Basic Building Block of a Fluid? at 1:48:12

Steven Brunton says the basic building block of a fluid is a velocity field, together with the pressures that force it to move. Full answer
What Did AI Prove About Navier-Stokes? at 1:50:20

Steven Brunton says the proven result is the forced version on the Clay website, one of four versions, not every Navier-Stokes problem. Full answer
Why Is Turbulence So Hard? at 1:59:01

Steven Brunton says turbulence is a complex fluid roiling, mixing, and moving, and it is hard because it is multi-scale. Full answer
What Did Kamal Jain Say About Laptops and Markets? at 2:05:09

Ankur Moitra cites Kamal Jain for the line he likes: if my laptop can't find it, then neither can the market. Full answer
Did AI Prove the Unique Games Conjecture? at 2:12:40

Ankur Moitra says a headlining result in the OpenAI drop is that the unique games conjecture is true. Full answer
How Many Authors Does a Math Paper Have? at 2:28:56

Alex Kontorovich says almost every math paper written until the 20th century had one author. He thinks the median in mathematics is now two. Full answer
How Do AI Swarms Act Like the Game of Life? at 3:07:42

Lex Fridman says a single large LLM that does a lot of reasoning and can interact with tools is already a dynamical process, and multi-agent swarms built from… Full answer
What Should Pure Math PhD Students Learn? at 3:26:10

Alex Kontorovich says PhD students in pure mathematics should do what mathematicians have always done: learn the most difficult, most abstract mathematics… Full answer
Why Learn Linear Algebra If a Computer Does It Better? at 3:28:53

Steven Brunton says you should still learn linear algebra even if a computer can do linear algebra better than you, because the point is to build intuition… Full answer
Why Does Ankur Moitra Say to Pretend You Already Won? at 3:34:46

Ankur Moitra says the best way to live a rich and fulfilling life is to pretend you have already won, then figure out what you would do. Full answer
What Matters When AI Commodifies Intelligence? at 3:40:40

Lex Fridman believes that as AI commodifies intelligence, people will treat intelligence and the puzzles they solve as a cherry on top, or a cherry to the… Full answer

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