A potential breakthrough in one of the most famous unsolved problems in mathematics has emerged, centered on the Navier-Stokes equations. These equations describe how fluids, such as water or air, move at a large scale, and they are crucial for fields ranging from weather prediction to engineering. On September 8, 2026, Tristan Buckmaster, a professor at New York University, shared on Mastodon that he and Levent Alpöge, a mathematician working at Anthropic, had made three important discoveries related to these equations. Their findings involve complex mathematical phenomena called "finite-time blowup" in different fluid dynamics models, such as incompressible porous media, Boussinesq, and incompressible Euler in 3D. These results were published online and have sparked interest among mathematicians, including Terence Tao, a renowned Fields Medalist, who praised the work as a significant achievement. While the findings are closely related to the Navier-Stokes equations, they do not yet formally solve the problem itself, which is one of the seven Millennium Prize Problems, each carrying a $1 million reward for a correct solution. Buckmaster explained that his research was inspired by earlier work by Diego Córdoba and Luis Martínez-Zoroa, whose contributions he believes are also worthy of the Fields Medal. The research also highlights the growing role of generative AI in mathematical discovery. Buckmaster and Alpöge used AI tools like Anthropic's Claude and OpenAI's Codex to assist in their work. He noted that some of the initial proofs generated by AI were difficult to understand and required weeks of refinement. The final proofs were verified using Lean, a software that checks each step of a mathematical proof for correctness. The situation took an unexpected turn when Buckmaster learned that OpenAI, a major competitor of Anthropic, had allegedly developed a proof related to the Navier-Stokes equations. He claimed that an internal OpenAI model had generated a nearly 100-page proof, which he has not seen personally. He noted that the approach used by OpenAI was similar to the one he and Alpöge had been exploring for nearly a year. Buckmaster suggested that the prompt used by OpenAI might have been sent shortly after details of their work became known to the company. He raised concerns about whether OpenAI’s model had been trained on data from their Codex sessions, where they had been submitting drafts for months. OpenAI responded by offering computational support and suggesting that they either publish their result the day after Buckmaster’s or allow him to write the article on Navier-Stokes alone, crediting OpenAI’s model. Buckmaster also mentioned that Sébastien Bubeck, a computer scientist at OpenAI, had insisted twice that Alpöge be removed from the list of authors, citing that Alpöge works for Anthropic, a direct competitor. Buckmaster said he threatened to make the situation public, and Bubeck reportedly replied, "Why would you ruin your career?" Buckmaster responded, "If you don't want me to be nice, I don't have to be." He emphasized that he has not seen OpenAI's proof and is unsure if his data were used in the training of the AI model. He stated that he "accuses no one of anything" but wants to report what he heard and what was proposed. He noted that if OpenAI's model has indeed made progress on the Navier-Stokes problem, it would be a significant achievement and should be stated clearly and respectfully. At this time, the proof attributed to OpenAI has neither been published nor verified.