OpenAI’s claimed solution to $1 million math problem faces scrutiny

A math problem that has remained unresolved for roughly 90 years was announced Tuesday night, September 8, as solved by AI giant OpenAI. But the academic community is not happy about it. “We’re sharing a solution to the Navier-Stokes Millennium Prize Problem, one of the deepest problems at the frontier of mathematics. The proof was produced by a group of agents, using an OpenAI next-generation model significantly more capable than GPT-6 Astra. The problem concerns whether the description of smooth three-dimensional fluid motion, modeled by the Navier-Stokes equations, can break down,” an OpenAI statement said. ALSO READ: Education experts on how abacus could change the way children learn maths In simple terms, the Navier-Stokes equations are used to describe how fluids such as water and air move. The unresolved question is whether those equations can always produce smooth, predictable solutions in three dimensions or whether the mathematics can eventually break down. The equations date to the nineteenth-century work of Claude-Louis Navier and George Gabriel Stokes. According to OpenAI, the model represents a step-function improvement on many benchmarks, and its training is ongoing. “Our internal model group arrived at the Navier-Stokes solution in 88 hours, using around 10,000 coordinating AI agents.” ALSO READ: We can’t build our education system on fabricated results OpenAI reposted the announcement with a quote congratulating Levent Alpöge and Tristan Buckmaster on their mathematical work. “We congratulate Levent Alpöge and Tristan Buckmaster on their remarkable mathematical work. “We (the researchers and the agents) did not see any of their work through any means until they released it publicly. In particular, no specific user data was accessed in order to solve this problem.” So, you might wonder, what is the problem? OpenAI continued: “While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models.” “However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs. unforced).” That technicality claimed by OpenAI is facing scrutiny because, just this July, the tech giant announced it was giving 10,000 scientists, mathematicians and engineers free access to its frontier models, with plans to expand that to 100,000 by 2027 through what it calls ChatGPT for Academic Researchers. Simply put, OpenAI has claimed to have solved one of the deepest problems in mathematics, which carries a $1 million prize from the Clay Mathematics Institute for whoever is able to solve it. The problem is that two human mathematicians, Tristan Buckmaster and Levent Alpöge, were recently working on a very similar breakthrough in fluid dynamics and had been extensively using AI chatbots such as GPT to assist their research. Levent Alpöge had something to say: “we cannot rule out that de-identified data derived from their usage of our products helped improve our models.” “I mean, props to them for straight coming clean.” Alpöge went on to say that the proof appears to be closer to another Euler blowup proof the researchers had worked on, referring to the mathematical work on whether certain fluid equations can develop singularities, or points where the equations stop behaving smoothly. He said he would have been open to collaborating with OpenAI researchers and did not place much importance on authorship at that stage. “I actually woulda been pumped to collaborate on this, there are a lot of people at oai I like,” he wrote. “I also like the idea of the labs cooperating, and even better on scientific progress. It’s a shame!” But he said the situation appeared to have become settled before that could happen. “On hearing the loud convo in the hallway, especially the part where a millennium prize was offered if I’d just be removed from the paper, it was kinda clear the die had been cast and things were locked.” For Alpöge, the situation was “pretty wacky, unstrategic, and unnecessary,” particularly because, from his perspective, much of the work had been informal experimentation rather than a formal institutional effort. The dispute now sits at the intersection of AI research, academic credit and questions over how much influence publicly available research, conversations and user interactions may have on the development of frontier AI models.

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OpenAI’s claimed solution to $1 million math problem faces scrutiny