OpenAI announced on Tuesday that an internal AI model produced a proof claiming the three-dimensional Navier–Stokes equations can develop a finite-time singularity. The company described the model as "significantly more capable than GPT‑6 Astra."
According to OpenAI, the effort began on Sept. 1 after their researchers heard rumors that solutions had appeared for two Millennium Prize problems. They redirected the new internal model to work on the remaining open problems. OpenAI says roughly 10,000 concurrent agents were engaged on the Navier–Stokes effort and that the result was reached in about 88 hours.
Company executives told reporters they devoted enormous computing resources to the task and estimated the cost of reaching the solution at "millions of dollars."
Questions about originality and external work
The announcement prompted immediate scrutiny from researchers working on related fluid‑dynamics questions. Tristan Buckmaster, a mathematician at New York University, and Levent Alpöge, a researcher at Anthropic, had been working on closely related material. Buckmaster has publicly questioned whether OpenAI pursued a research direction it learned about from their work and raised concerns about the potential role of private Codex material.
OpenAI has denied that its researchers or its agents saw Buckmaster and Alpöge's work before the pair released it publicly. The company further asserted that "no people or AI systems searched through user data to solve this problem," a statement reiterated by OpenAI Chief Research Officer Mark Chen on a call with reporters. Chen added he was "a little disappointed with the allegations."
OpenAI's position on the Millennium Prize and wider significance
OpenAI said it does not intend to claim the $1 million Millennium Prize, framing the result instead as evidence of how rapidly its frontier models are advancing. The company presented the outcome as a demonstration of scaling and capability rather than an attempt to secure the prize.
The controversy highlights a core trust issue for AI-assisted science: whether researchers can safely and ethically use powerful, proprietary tools to explore problems where outside researchers may have unpublished or in‑progress work. It also raises questions about provenance, reproducibility, and transparency when vast computational resources produce fast-moving mathematical claims.
This is a developing story; further details may emerge as researchers and institutions respond.
