OpenAI has announced the solution to one of the Millennium Prize Problems—the Navier-Stokes existence and smoothness problem—using an internal AI system and approximately 10 thousand autonomous agents working for 88 hours. The company spent millions of dollars in computing resources on this and verified the result using the Lean language. This is the first time an AI has claimed to solve one of the seven million-dollar prize problems from the Clay Mathematics Institute.
However, a sharp dispute over authorship arose immediately after the announcement. Mathematicians Tristan Buckmaster of New York University and Levent Alpöge of Anthropic had achieved significant progress a month earlier in related aspects of the problem, actively using AI tools, including OpenAI's Codex. Buckmaster stated in a public announcement that OpenAI could have gained access to their drafts through chats or model training, although the company categorically denies this, asserting that user data was not used.
The situation was complicated by an OpenAI proposal for a joint publication in which it was proposed to exclude Alpöge from the authors because of his work at a competing company. Buckmaster refused, and the negotiations became tense. This is not just a personal conflict: it exposes systemic issues that arise when commercial labs with vast resources enter a race for fundamental results, building on the work of independent researchers.
Technically, OpenAI's approach—scaling multiple agents to search for a singularity in the three-dimensional Navier-Stokes equations—differs from a traditional human proof. Previously, progress relied on the work of Diego Córdoba and Luis Martínez-Zoroa, which Buckmaster and Alpöge developed using AI. OpenAI, however, threw unprecedented computing power at the task, allowing them to "blow up" the problem in days rather than years.
The methodology raises questions about reproducibility and generalization. Although the result is formalized in Lean, independent community verification is still to come. It is unclear how well the approach scales to other Millennium Prize Problems or whether it requires specific prompts unavailable to ordinary researchers. A comparison with previous AI successes in mathematics, such as solving Erdős problems, shows that the scale here is different: not a single heuristic, but a massive attack by agents.
In the landscape, this event contrasts with the work of Anthropic and other labs, where AI is used as a tool to augment human intelligence rather than replace it. OpenAI emphasizes that it will not claim the prize, but the announcement itself changes the dynamics: now, large companies can "close" open problems faster than academic groups, calling into question traditional mechanisms of priority and citation.
The implications for the field are significant. Mathematicians, including Fields Medalists, have already expressed concern about the misalignment of goals: companies chase public victories, while science values gradual, collaborative progress. This could lead to researchers hiding intermediate results or avoiding the use of commercial AI tools.
Open questions include whether the proof will be accepted by the Clay Mathematics Institute, exactly how to distribute credit between humans and AI agents, and whether such a race will lead to the fragmentation of the community. New protocols are needed to track contributions in AI-assisted research.
Ultimately, this case shows that accelerating mathematical discoveries with AI requires a simultaneous revision of authorship and ethics norms; otherwise, trust within the community will be at risk.
