TL;DR
OpenAI says a previously unreleased internal model, running as a swarm of roughly 10,000 agents, produced a solution to part of the Navier-Stokes existence and smoothness problem in 88 hours. The company is not claiming the associated $1 million Millennium Prize, and the work has not been independently verified. Within hours a mathematician working on the same problem alleged that details of his progress reached OpenAI shortly before it began. Both halves of that matter, and only one is about mathematics.
The run
The equations describe fluid motion and are central to turbulence, a phenomenon still poorly understood. Key aspects have lacked a proof for ninety years. OpenAI began training the model in late August, found it unusually strong at mathematics, and — after hearing that two Millennium problems had reportedly fallen elsewhere — pointed thousands of agents at what remained.
The resource figures are the part worth dwelling on. Reaching the result consumed 130 billion output tokens and nearly three million messages exchanged between agents, which at the company’s own published rates works out at roughly £7.3 million ($10 million) of inference. It resolved two of the four statements the prize requires. OpenAI framed the release as a progress report on model capability rather than a claim on the prize.
The dispute
Tristan Buckmaster, a New York University mathematics professor, said that he — working alongside Anthropic’s Levent Alpöge — had been pursuing the same problem using OpenAI’s Codex tool, and that he learned on 3 September that word of their progress had reached OpenAI. His contention is that the company only turned to these equations afterwards. He published emails and went public before reading the full proof, saying the alternative was letting an announcement stand that he knew to be untrue.
OpenAI called the parallel work remarkable, said it had seen none of it before public release, and stated that it touched no user data. It conceded it could not entirely exclude that anonymised traces of their tool use had helped improve its models, while maintaining the two proofs differ substantially.
Looking forward
Verification will take months, and the Clay Mathematics Institute has accepted nothing. For UK professionals the durable lesson is the second story rather than the first: this is a live dispute about whether using a vendor’s tool exposes your research direction to that vendor. Anyone doing competitive R&D on a commercial AI platform now has a concrete case to point at when negotiating terms.