OpenAI has announced a solution to one of the seven Millennium Prize problems – the existence and smoothness of solutions to the Navier-Stokes equations.
A custom multi-agent system composed of approximately 10,000 parallel AI agents was able to construct analytical proofs and complete formalizations in Lean, showing that the three-dimensional motion of an incompressible fluid can form a singularity at a finite point in time under the influence of smooth external forces.
It took agents approximately 88 hours to resolve the issue, and verification took another 17 hours after that. This result demonstrates a huge leap in the capabilities of OpenAI’s promising model, significantly surpassing the level of GPT-6 Astra on the mathematical benchmark. At the same time, the creators emphasized that they were not applying for an official Clay Prize, but were sharing this achievement to demonstrate the rapid progress of artificial intelligence and the need for responsible methods to manage its capabilities.
Tristan Buckmaster, a mathematician at New York University, accused OpenAI collaborator Sébastien Boubeck of trying to impose strict conditions on joint publication, including demanding that co-author Levent Alpöge’s name be removed from Anthropic and requiring public confirmation of artificial intelligence research results. His refusal was followed by threats and severe pressure, according to Buckmaster.
In addition, the scientific community is concerned about the source of the data: Although OpenAI categorically denies using the sessions of others in Codex when training models, the company cannot completely eliminate the leakage or indirect influence of anonymous information.
Against this background, the financial aspects of the experiment are also impressive: according to reports in the specialized press, a week’s work of ten thousand agents costs about $22.5 million at Astra rates, which makes pursuing the Clay Institute award economically pointless.
