NYU mathematician posts three AI-aided fluid blowup results

NYU mathematician Tristan Buckmaster and Anthropic mathematician Levent Alpöge posted three AI-aided results today: finite-time blowup with smooth forcing for incompressible porous media, Boussinesq, and 3D incompressible Euler. Buckmaster’s statement says the Lean formalizations for those three are done. They are not releasing a hypo-dissipative Navier-Stokes writeup yet — Lean unfinished. They do not claim the Clay Millennium Prize (unforced Navier-Stokes).

What the tech did: Buckmaster says they used Anthropic’s Claude and OpenAI’s Codex (GPT-5.6 Sol, later Astra for writeup/audit only) to push the Córdoba–Martínez-Zoroa forced-blowup program from rough forcing to smooth forcing and to Euler. He calls the Euler writeup “AI slop” and says outside pressure forced an early public post. Fields Medalist Terence Tao publicly called the Euler/Boussinesq line a remarkable achievement in a Mastodon post.

The OpenAI fight: Buckmaster alleges that after rumors of an Anthropic-linked breakthrough reached OpenAI, scientist Sébastien Bubeck joined Sunday calls in which OpenAI said an internal model had a ~100-page proof of forced Navier-Stokes (Fefferman options c/d — smooth forcing). He says OpenAI eventually agreed the first prompt came after word of his work reached the lab, that a full team and heavy compute were involved (not “very little human input”), and that two proposals followed: coordinated announcements, or Buckmaster alone writing up OpenAI’s Navier-Stokes result while dropping Alpöge — twice citing Alpöge’s Anthropic job as “annoying.” Buckmaster says he declined and was asked why he would “ruin [his] career.” He states he has not seen OpenAI’s proof and is not accusing Codex of training on his sessions — only that training questions went unanswered.

Denial: Bubeck posted that the allegations are “false and inflammatory,” said he followed academic norms, and promised more tomorrow. OpenAI and Anthropic had no formal institutional claim on the Buckmaster–Alpöge collaboration, per the statement.

Who it hits: Frontier labs racing Millennium-adjacent math; mathematicians putting drafts into commercial coding agents; anyone treating “model solved X” announcements as provenance-free.

What’s next: OpenAI’s fuller reply and any released forced-Navier-Stokes formalization; whether Lean certificates for the three public papers hold under outside check; any lab policy on user-session access for research scoops.

— Lark Pemberton