Tao Flags Major Break Toward Navier-Stokes Blowup, Formalized in Lean via Autoformalization Agents
peterjliu · x · 2026-09-08
Terence Tao's blog highlights new work by Alpöge and Buckmaster, building on Córdoba and Martínez-Zoroa, toward the global regularity problem for incompressible 3D Navier-Stokes — one of the seven $1M Millennium Prize problems.
Key points:
- It is now widely expected that smooth initial data and smooth forcing can be constructed to produce finite-time singularities, possibly even without forcing
- The authors haven't fully achieved this yet, but the breakthrough makes completing it look "very feasible in the near future"
- Finite-time blowup is demonstrated for three simpler model equations: the incompressible porous medium equation, the 2D Boussinesq equation, and the 3D incompressible Euler equations, with the method likely extending to Navier-Stokes
- The arguments have been formalized in Lean, feasible in the modern era of autoformalization agents
If completed, this would be a landmark result — and a flagship case of AI-assisted mathematics.
Related event: Tao Hails AI-Assisted Fluid Blowup Breakthrough, Formalized in Lean(9 posts)→
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