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.
This program can be watched here, and on our YouTube channel, starting at 7PM on Friday, October 2.
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