AI Summary
5 min readWhen AI "Solved" a Million-Dollar Math Problem—And Why Mathematicians Aren't Celebrating
In 2000, the Clay Mathematics Institute offered $1 million for a proof of the Navier-Stokes existence and smoothness problem—a question about whether the equations describing fluid flow can ever break down and produce infinite velocities. For 25 years, no human mathematician had claimed the prize. Then OpenAI announced they had done it, not with a human researcher, but with a swarm of 10,000 coordinating AI agents working over 88 hours, exchanging 2.7 million messages, and costing an estimated $15 million in computing resources.
The result? The equations do blow up. But the proof is so convoluted that mathematicians may need years just to understand what the AI actually did—and whether it solved the problem anyone actually cared about.
What the Navier-Stokes Equations Actually Say
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What you'll learn
- 1 (00:00) **Episode Opening & AI News Update** - Hada and Michael introduce the Navier-Stokes problem and the bombshell that OpenAI solved it using AI agents.
- 2 (06:02) **Future Update: OpenAI Releases 700+ Manuscripts** - Hada and Michael reveal that between recording and release, OpenAI has released hundreds more mathematical manuscripts, including work on the Riemann hypothesis.
- 3 (08:31) **The Core Problem: F=MA for Fluids** - Hada begins her expert explanation of the Navier-Stokes equations, starting with the fundamental challenge of applying Newton's laws to a fluid.
- 4 (10:51) **When the Continuum Approximation Breaks Down** - Hada explains the limits of the continuum approximation, using the examples of air at sea level and a re-entry vehicle.
- 5 (13:48) **Cauchy's Contribution: The Stress Tensor** - Hada introduces the French mathematician Cauchy and his approach to describing all the forces acting on a "blob" of fluid.
- 6 (20:42) **Navier and Stokes: The Newtonian Simplification** - Hada explains how Navier and Stokes simplified Cauchy's equation by focusing only on Newtonian fluids with constant viscosity.
- 7 (27:18) **The "Beast in the Bay": The Feedback Loop** - Hada breaks down the most dangerous term in the Navier-Stokes equation, comparing it to a microphone and speaker feedback loop.
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Show Notes
OpenAI claims a swarm of AI agents has solved the Navier-Stokes problem, one of the hardest unsolved questions in mathematics, with a $1 million prize attached. Then it released more than 700 more mathematical manuscripts, including claims touching the Riemann hypothesis, faster than anyone can check them. Mathematicians are not happy, and the reason goes far beyond the money.
In this episode of The Rest of Science, mathematician and fluid dynamicist Hannah Fry takes Michael Stevens through the equations that describe everything that flows, from the blood in your veins to a rocket leaving the atmosphere. Then she tells him why this story has turned the vocation of mathematics upside down.
Ten thousand AI agents. Millions of messages. One tiny term in the equation that nobody wanted to look at, until it unlocked the problem. But did AI really solve a million dollar problem? Why are some mathematicians accusing the models of stealing their work? And how might a proof that is completely correct be the least satisfying result in the history of maths?
Along the way, Hannah un-mixes a glass of dye with nothing but corn syrup and patience, and the pair ask what happens to curiosity when the answers arrive faster than the understanding.
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