Has a machine just solved one of the most famous open problems in mathematics? Brian Greene speaks with Tristan Buckmaster, professor of mathematics at NYU’s Courant Institute, about the Navier-Stokes equations, the Clay Institute’s million dollar Millennium Prize, and the role artificial intelligence played in the progress toward an answer.
Buckmaster explains what the Euler and Navier-Stokes equations describe and why mathematicians have long asked whether their solutions can reach infinite velocity, a result that would mean the equations break down as a model of the physical world. He traces the path from early computer-assisted proofs through his own collaboration with Google DeepMind, and describes proofs produced by AI that he calls the worst mathematics he has ever seen while confirming they were correct. Brian presses him on what it means to hold a proof that no human can read, and whether AI systems are beginning to develop a language of their own. Buckmaster closes on what all of this means for the future of mathematics, for students entering the field, and for the questions in fluid dynamics that remain wide open, including why nobody can yet explain lift from first principles.
This program is part of the Rethinking Reality series, supported by the John Templeton Foundation.
Participant: Tristan Buckmaster
Moderator: Brian Greene
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CHAPTERS:
00:00 Can AI Really Be Creative?
06:00 How AI Is Changing Mathematics
12:07 Understanding the Navier-Stokes Equations
15:53 Why Fluid Equations Can Break Down
18:16 The Millennium Prize Problem
21:41 The History of the Navier-Stokes Problem
24:45 The “Nightmare” Solutions
27:46 How Simulations Led to Mathematical Proofs
30:10 Computer-Assisted Mathematical Proofs
35:00 Why the Millennium Problem Remained Unsolved
42:03 Using Neural Networks to Search for Singularities
43:22 Why DeepMind Couldn’t Solve the Core Problem
47:31 How LLMs Approach Mathematical Proofs
56:08 How AI Agents Help Solve Math Problems
59:14 AI-Generated Proofs and Verifying Their Accuracy
1:02:37 When AI Starts Creating Its Own Language
1:05:13 AI’s Progress Toward Solving the Euler Problem
1:08:54 The Anthropic–OpenAI Competition
1:16:20 Has AI Solved the Millennium Prize Problem?
1:19:19 How the OpenAI and Buckmaster Work Connect
1:21:23 AI Compresses Years of Mathematical Progress
1:23:35 How AI Could Change Mathematics
1:25:21 The Future of Mathematicians
1:27:00 The Next Big Questions in Fluid Dynamics
1:28:09 What AI Beyond Human Intellect Could Mean
The Moment AI Changed Mathematics Forever | World Science Festival
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