Buckmaster and Alpöge post three AI-assisted fluid blowup proofs, dispute OpenAI's approach

NYU's Tristan Buckmaster and Anthropic's Levent Alpöge released three Lean-verified preprints proving finite-time blowup with smooth forcing for the incompressible porous medium equation, the 2D Boussinesq system, and 3D Euler — real results, drafted largely by Claude and Codex under human direction, with Buckmaster calling the first model output the worst mathematical writing he had ever read. He also disclosed a 6 September call where OpenAI staff described an internal model's roughly 100-page forced Navier-Stokes blowup proof, proposed a coordinated announcement, and twice pushed to drop Alpöge from authorship over the Anthropic affiliation; he declined, and says he has not seen the proof and makes no accusation about training data. Machine-generated proofs have reached the edge of a Millennium Prize problem, and the credit and provenance norms around them are being negotiated in public rather than settled.

Source: unite.ai ↗

I did not get an answer.

Tristan Buckmaster, on whether OpenAI's model was trained on their shared Codex sessions

Why this matters

→ Machine-generated proofs reach a Clay Millennium Prize problem's edge.
→ AI authorship and institutional credit norms are being contested publicly.
→ OpenAI reportedly pressured the lead author to exclude his Anthropic collaborator.

Proof wars

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