On September 8, OpenAI announced that an internal model had generated a proof related to the Navier-Stokes equations, one of the seven Millennium Prize problems established by the Clay Mathematics Institute. These problems are among the most challenging unsolved questions in mathematics, with a $1 million prize offered for each solution. Only one of these problems, the Poincaré conjecture, has been solved so far. OpenAI’s proof, if verified, would be a major breakthrough. The model used approximately 10,000 agents in parallel to produce a 165-page proof, which was also verified using Lean, a formal language that ensures each logical step is sound. The company estimated that the computational cost was in the millions of dollars, involving billions of tokens processed. The model used in this project was described as significantly more advanced than GPT-6 Astra, the latest version of OpenAI’s GPT series. OpenAI emphasized that the work was conducted in a secure, isolated environment. The proof suggests that, under Navier-Stokes dynamics, a fluid could develop a singularity in finite time, forming a vortex—a whirlpool that spirals inward and elongates like a strand of spaghetti. This would represent a dramatic change in the behavior of fluids, with profound implications for physics and engineering. Despite the technical details, the proof has not yet been validated by the broader mathematical community. While the use of Lean confirms the internal logic of the reasoning, the result still needs to be reviewed and accepted by experts before it can be considered a definitive solution. The Clay Mathematics Institute requires that any solution to a Millennium Prize problem be published in a peer-reviewed journal and gain general acceptance from the global mathematical community before the prize can be awarded. The announcement has sparked controversy, particularly over allegations of plagiarism. On the same day as OpenAI’s announcement, mathematician Tristan Buckmaster from New York University and Levent Alpöge, a researcher at Anthropic (a competitor of OpenAI), revealed their own work on similar equations. They used AI tools like OpenAI’s Codex and Anthropic’s Claude, and their findings have received praise from notable mathematicians, including Terence Tao, a Fields Medalist. Buckmaster suggested that OpenAI may have learned about their method before the public release and reused it in their own proof. He also claimed that OpenAI might have used his drafts stored in Codex to train their model. Sébastien Bubeck, who leads OpenAI’s mathematics team, denied these claims, calling them "false and incendiary." OpenAI stated that their proof differs from Buckmaster and Alpöge’s work, particularly in the specific results proven, such as the distinction between forced and non-forced Euler equations. Sam Altman, OpenAI’s CEO, noted that the company had initially believed the other team had solved the problem and proposed that they should be allowed to claim the prize first. However, this offer was not accepted, and no communication occurred between the teams. OpenAI emphasized that neither the researchers nor the AI agents had access to the other team’s work before publication. However, the company admitted that while it is unlikely, it cannot rule out that de-identified data from users of their products may have contributed to improving their models. Tristan Buckmaster criticized OpenAI’s admission, arguing that the company used training data from a period after the discovery of their results, raising ethical concerns about using client data to gain an advantage over competitors. Despite the controversy, OpenAI’s proof remains unverified, and the Clay Institute’s rules require a solution to first appear in a peer-reviewed journal, gain general acceptance, and wait at least two years after publication before the prize can be awarded. The situation remains unresolved, with the mathematical community yet to reach a consensus on the validity of the claims.