Breaking

OpenAI Reportedly Produced a Navier–Stokes Proof; Verification Is Pending

September 8, 2026 at 08:29 EDT

Foundation Models
Research & Papers

OpenAI is under scrutiny after NYU mathematician Tristan Buckmaster said an internal OpenAI model produced a roughly 100-page proof of finite-time blow-up for a forced version of the Navier–Stokes equations. The alleged proof has not been published or independently checked, and OpenAI researcher Sebastien Bubeck has rejected the allegations against him.

September 8, 2026 · OpenAI

A reported proof, not a verified solution

Tristan Buckmaster says an internal OpenAI model produced a roughly 100-page proof related to forced Navier–Stokes blow-up. The proof has not been published or independently checked.

The numbers in view

~100

claimed proof pages

1 year

reported collaboration

$1M

Clay prize

related systems

Three adjacent equations made public

Each block represents one related fluid system. This is not a Navier–Stokes proof.

IPM

Boussinesq

3D Euler

3 systems

The public work is adjacent to the target

The reported internal result concerns Navier–Stokes, while the released formalizations concern related equations with different assumptions.

The central distinction

A reported internal result is not a verified Millennium solution

NOT PUBLIC

The alleged proof has not been released for examination.

NOT INDEPENDENTLY CHECKED

A model-generated argument still requires mathematical verification.

DATA QUESTION OPEN

The account of access to or training on private Codex drafts remains disputed.

From research to dispute

PRIVATE WORK

A year-long collaboration develops a narrow mathematical route.

→

Why researchers care

AI can help search difficult proof spaces.
Lean artifacts can expose formal derivation steps.

What remains open

No Navier–Stokes proof is public.
The authorship and Codex-data accounts remain disputed.

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