OpenAI announced today that its AI agents have solved one of the Millennium Prize Problems, which rank among the most significant unsolved questions in mathematics. But the achievement has been overshadowed by allegations that the company drew on AI-assisted research by NYU mathematician Tristan Buckmaster and Anthropic employee Levent Alpöge without properly acknowledging them. The episode highlights how frontier AI companies with exclusive models and massive budgets are reshaping mathematics, potentially leaving human mathematicians with fewer meaningful problems to tackle.
The mathematical question OpenAI claims to have answered is the Navier–Stokes existence and smoothness problem, one of seven Millennium Prize Problems designated by the Clay Mathematics Institute in 2000. Only one other Millennium Prize Problem had been solved before today, and solutions carry a million-dollar award. OpenAI's proof demonstrates that the full Navier–Stokes equations, which describe how fluids like water and air move over time, can break down under certain conditions and predict impossible scenarios such as infinite fluid velocity. The company obtained its proof using an internal model that far surpasses the Astra model released just last week, running approximately 10,000 agents simultaneously at a cost of millions of dollars. OpenAI says it won't claim the prize money. Meanwhile, Buckmaster posted a proof on Monday showing that a simplified version of the equations can break down, representing major progress on the Millennium Problem after nearly a year of work with Alpöge using publicly available models from OpenAI and Anthropic.
According to Buckmaster's account posted alongside his proof, OpenAI employees gave him two options: either he and Alpöge could publish their work with OpenAI releasing its solution the next day, or he could collaborate with OpenAI on a paper that excluded Alpöge because of his affiliation with Anthropic, OpenAI's primary competitor. Buckmaster also wrote that he inquired whether the agents had accessed transcripts of his work with Alpöge done through OpenAI models, which employees denied, and whether OpenAI models had been trained on those transcripts, to which they gave no answer. In a press briefing, Mark Chen, OpenAI's chief research officer, again denied that any agents or employees accessed Buckmaster and Alpöge's transcripts, though Sébastien Bubeck, a member of OpenAI's technical staff, acknowledged the team was inspired to pursue the problem after hearing rumors about Buckmaster and Alpöge's efforts. Both the Buckmaster/Alpöge and OpenAI proofs rely on an approach developed by mathematicians Diego Córdoba and Luis Martínez-Zoroa, which Javier Gómez-Serrano, a Brown University mathematics professor, described as one of several promising avenues for the Navier-Stokes problem.
The report explains that if OpenAI's models did leverage Buckmaster and Alpöge's research, it would suggest that human "research taste"—the capacity to identify promising research questions and directions—played a crucial role in the agents' success, since experts have long viewed this skill as a major obstacle for AI in science and mathematics. However, the broader implications are troubling for the field. While Buckmaster and Alpöge's nearly year-long collaboration with publicly available models demonstrates the potential of human-AI partnership, they couldn't reach a complete solution, whereas OpenAI brute-forced an answer in days using an internal model and resources—running thousands of concurrent agents at multi-million-dollar expense—that few mathematicians can access. Gómez-Serrano notes that "very few mathematicians will have resources of that scale." UCLA mathematician Terence Tao wrote that when AI agents solve problems without full transparency into the solution process, it can become "a net negative for the progress of mathematics as a whole," because humans working through problems uncover new approaches and ideas that inspire peers and spawn entire subfields—benefits that vanish when private companies keep agents' missteps hidden from view.
The report concludes that mathematics is rapidly becoming the domain of frontier AI companies with powerful internal-only models, substantial financial resources, and limited collaborative ethos. If OpenAI and Anthropic continue pursuing increasingly impressive mathematical achievements, there may not be any open problems remaining for human mathematicians outside these companies to work on, which would fundamentally transform the field. Researchers are becoming depressed as the trajectory becomes clearer: the progress that matters most may soon require compute budgets and proprietary tools beyond academic reach, while the messy, incomplete human work that traditionally advances mathematical understanding gets replaced by opaque agent breakthroughs. The controversy underscores that this shift is already underway, and it remains uncertain what else will disappear as mathematics moves behind corporate walls. The stakes extend beyond any single prize or proof—when the tools required to make meaningful contributions become exclusive corporate assets, the collaborative culture that has defined mathematics for centuries may not survive the transition.