x.com/basedjensen/status/2097200251312701479
1 correction found
both labs have actually solved Navier-Stokes independently
Buckmaster and Alpöge did not publicly announce a Navier–Stokes solution. Their released results were for related equations including 3D Euler, which experts describe as major progress toward Navier–Stokes, not a completed solution.
Full reasoning
This overstates what the Buckmaster/Alpöge side had actually achieved publicly as of September 8, 2026.
Terence Tao's writeup of their work says they had not yet achieved Navier–Stokes: he writes that Buckmaster and Alpöge "do not quite achieve these goals yet" and specifies that their demonstrated blowup results were for three simpler model equations — incompressible porous medium, 2D Boussinesq, and 3D incompressible Euler — while their method has a "high likelihood of also extending to Navier-Stokes as well." In other words, Tao describes their work as a breakthrough toward Navier–Stokes, not a solution of Navier–Stokes itself.
Scientific American reports the same distinction. It says Buckmaster and Alpöge "made significant progress toward the problem" and that on August 15 they proved blowup for the Euler equations, calling that result "a key step toward solving the Navier-Stokes problem." That directly contradicts the claim that both labs had already solved Navier–Stokes independently.
So, based on the public record available that day, only OpenAI was being reported as claiming a Navier–Stokes proof. Buckmaster and Alpöge had publicly released important related results, but not a solved Navier–Stokes proof.
2 sources
- Finite time blowup with smooth forcing term for the incompressible porous medium, Boussinesq, and incompressible Euler equations | What's new
Terence Tao writes that Buckmaster and Alpöge "do not quite achieve these goals yet" and says they demonstrated blowup for three simpler model equations: incompressible porous medium, Boussinesq, and three-dimensional incompressible Euler.
- AI may have just solved a million-dollar math problem. The field will never be the same | Scientific American
Scientific American reports that Buckmaster and Alpöge "made significant progress toward the problem" and proved blowup for the Euler equations, calling that finding "a key step toward solving the Navier-Stokes problem."