OpenAI claims an AI proof of Navier–Stokes; a credit fight erupts
An unreleased model beat GPT-6 Astra to the Millennium result — now a rival mathematician asks whether OpenAI’s Codex trained on his private sessions.
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The claim: finite-time blow-up, formalized in Lean
OpenAI says an internal model “significantly more capable than GPT-6 Astra” proved that smooth 3D Navier–Stokes flow can develop a singularity in finite time (statements C and D), in about 88 hours of work, with GPT-6 Astra doing the Lean verification. The writeup, the Lean formalization, and a GitHub repo are public — the model that produced it is not.
Did Codex train on your sessions? Nobody answered
Tristan Buckmaster (NYU) and Anthropic’s Levent Alpöge say they spent nearly a year on the same line of attack inside Codex. Buckmaster says he asked whether OpenAI’s model had been trained on their Codex sessions and got no clear answer; OpenAI’s Sébastien Bubeck denies using their prompts or proofs. If you build inside Codex, that ambiguity is the part worth watching.
The credit fight turned personal
Buckmaster alleges OpenAI only attempted the problem after rumors of Anthropic’s imminent solution, then pushed to strip Alpöge’s name off the papers over his Anthropic ties — and quotes a researcher pressing him, “Why would you ruin your career?” OpenAI says it deliberately offered a concurrent release and has “nothing but congratulations” for the pair.
Tao: stop strip-mining math for marketing
Terence Tao warned that racing AI to crack open problems yields “answers without insight” and could “destroy the ecosystem” that trains the next generation of mathematicians. The builder takeaway: a proof or a benchmark win is not the same thing as a capability you can deploy.
What is actually usable today
The one shippable signal in all of this: GPT-6 Astra — which you can call right now — formally verified a Millennium-Prize-grade proof in Lean in roughly 17 hours. If you work in formal methods, that is a concrete endorsement of Astra as a Lean proof assistant.