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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 Don't miss a video! Subscribe NOW: https://www.youtube.com/worldsciencefestival?sub_confirmation=1 ABOUT WORLD SCIENCE FESTIVAL: The World Science Festival (WSF) is a multimedia organization bringing the most transformative ideas in science to global audiences. Through long- and short-form videos spanning physics, cosmology, quantum mechanics, biology, neuroscience, consciousness, medicine, space exploration, the dilemma of free will, artificial intelligence, engineering, robotics, and beyond. WSF gathers world-renowned scientists, artists, and thinkers for dynamic discussions, debates, lectures, performances, films, and immersive live experiences. Founded in 2008 and headquartered in New York City, the World Science Festival is a production of the World Science Foundation, a 501(c)(3) nonprofit organization. Our mission is to cultivate a public informed by science, inspired by its wonder, convinced of its value, and prepared to engage with its implications for the future. With live events reaching millions worldwide and hundreds of millions of digital views, WSF continues to expand its global impact through festivals, educational initiatives like World Science U, and digital content that explores the near and far future of our world. FOLLOW WORLD SCIENCE FESTIVAL: Website: https://worldsciencefestival.com/ Instagram: https://www.instagram.com/worldscifest/ TikTok: https://www.tiktok.com/@worldscifest X(Twitter): https://twitter.com/worldscifest Facebook: https://www.facebook.com/worldsciencefestival LinkedIn: https://www.linkedin.com/company/world-science-festival 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 https://youtu.be/PQYFRuZ5phs

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