Major breakthrough made on famous Millennium maths problem — SkimNews
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- Tristan Buckmaster (NYU) and Levent Alpöge (Harvard) claimed three results toward solving the Navier-Stokes equations, developed with 'a great deal of help' from LLMs supplied by Anthropic and OpenAI.
- Two of the three results were published alongside Lean formalisation — code that rigorously checks the math for logical flaws — while a third awaits a finished formalisation.
- The findings cover the Boussinesq approximation and Euler equations, close cousins of Navier-Stokes, but have not yet been generalised to the full Navier-Stokes problem.
- Buckmaster called the achievement a 'Deep Blue-Kasparov moment,' framing AI as a rapidly emerging amplifier of human mathematical effort rather than the headline result itself.
- David Silvester (University of Manchester) said the Euler equations paper shows spontaneous 'blow-ups' or turbulence can appear, and that the current work alone may already be enough to claim the $1 million Millennium Prize.
- Terence Tao (UCLA) wrote that 'there does not seem to be anything in principle preventing the methods from extending all the way to Navier-Stokes,' and said he would not be surprised if a full extension came from pouring enormous compute and AI assistance into the task.
Why it matters: If the Clay Mathematics Institute agrees with Silvester, Buckmaster and Alpöge could collect the $1 million Millennium Prize — and Tao, a Fields Medalist, sees no in-principle barrier to extending the methods to a full Navier-Stokes solution with more AI and compute. The practical payoff is essentially nil: computer fluid models already work well enough to make wind tunnels obsolete. The story's real weight is symbolic — a two-centuries-old problem suddenly looks tractable when human intuition is paired with LLM speed.
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