OpenAI has reported that one of its artificial intelligence systems identified solutions related to the blow-up question for the Navier–Stokes equations in a matter of days, according to a New Scientist report.
What is the issue and why it matters
The Navier–Stokes equations describe the viscous motion of Newtonian fluids. The Clay Mathematics Institute designated the Navier–Stokes problem as one of seven Millennium Prize Problems in the 2000s and attached a $1 million prize to a correct resolution. The central question posed by the Clay Institute asks whether the equations always produce well-defined solutions or whether there exist situations where solutions break down and yield mathematically meaningless results — a phenomenon mathematicians call a blow-up. Although the equations were formulated nearly two centuries ago, key questions remain open.
What OpenAI did
OpenAI says it began by applying a set of AI agents to a variant of the Euler equations, which is considered a step toward the Navier–Stokes problem. According to the company, 1,000 AI agents worked on the Euler case and found blow-up instances in about 50 hours. The team then deployed 10,000 agents to extend those blow-ups to cases relevant for the full Navier–Stokes problem, and OpenAI reports that this extension took 11 hours.
Model, performance and cost
At a press briefing, OpenAI said reproducing the same work for a third party would cost roughly $15 million. The company did not disclose the exact model used, but claimed the system outperformed the publicly known GPT-6 Astra model.
Related announcements and disputes
OpenAI’s announcement arrived hours after Tristan Buckmaster of New York University and Levent Alpöge of Anthropic announced they had solved three problems described as steps toward a Navier–Stokes solution, and said they had received substantial help from large language models (LLMs), including models from Anthropic and OpenAI.
After reports circulated that OpenAI had solved the Navier–Stokes puzzle, Tristan Buckmaster released a statement indicating concern about how OpenAI contacted him to clarify the situation, suggesting their approach was unusual and lacked transparency. Buckmaster said OpenAI began looking for a solution only after learning about his and Alpöge’s work. At the press briefing, OpenAI denied using Buckmaster and Alpöge’s proofs or prompts and said its Euler proof differs from theirs.
Next steps: independent verification and prize adjudication
The claims will need rigorous independent verification by the mathematical community. Martin Bridson, president of the Clay Mathematics Institute, told New Scientist by email that the institute is deliberately not rushing the evaluation process and will ensure the review is fully rigorous and thorough before considering the $1 million prize.
Summary
OpenAI reports that AI agents found blow-up solutions connected to the Navier–Stokes problem in short timeframes — days overall, with particular stages completed in hours. The company’s assertions and methods remain subject to scrutiny by the research community, disputes about the provenance of ideas have emerged, and any formal recognition or prize award will await exhaustive independent assessment.
