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The most careful summary written by anybody outside mathematics, and the only widely shared one that carries Buckmaster's own disclaimer rather than dropping it.
Andrew Akbashev
1. The authors - Alpöge and Buckmaster - showed how to achieve a blowup with smooth forcing for 2D Boussinesq equation. Then they also worked it out for 3D incompressible Euler equations. These are Navier-Stokes but without viscosity.
Now, Tarrence Tao says that this approach may likely be extended to actual Navier-Stokes.
BUT there's a big drama behind it:
- OpenAI had learned about their progress before it was published and pushed their AI to quickly come up with a similar solution.
- However, OpenAI's solution was based on the same smooth-forcing approach that Buckmaster/Alpöge had quietly been developing. Buckmaster said that he does not know if their data was used, so he is “not accusing anyone of anything.”
- However, Sébastien Bubeck (a research lead at OpenAI) didn’t want to see Alpöge as the author because Alpöge works at Anthropic.
Bubeck from OpenAI called these allegations “false and inflammatory”. As of now, there are no further comments.
Andrew Akbashev's post on X, curated on eChai
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