AI companies are making impressive mathematical strides. Human mathematicians are losing out.
OpenAI’s latest mathematical milestone has quickly become mired in controversy. Today, the company announced that its agents have solved one of the Millennium Prize Problems, some of the most important open problems in mathematics. Under normal circumstances, that solution would be a huge feather in OpenAI’s cap.
But the announcement has been overshadowed by accusations that OpenAI used NYU mathematician Tristan Buckmaster’s and Anthropic employee Levent Alpöge’s AI-assisted work on the problem as a jumping-off point and failed to credit them. OpenAI has denied the accusations.
It remains uncertain if OpenAI’s models made use of the work completed by Buckmaster and Alpöge, though Sébastien Bubeck, a member of the technical staff at OpenAI, said in a press briefing that the team was inspired to pursue the problem after hearing a rumor about Buckmaster and Alpöge’s efforts. But whether or not OpenAI’s models took advantage of Buckmaster and Alpöge’s research, this episode may mark a turning point in the history of mathematics.
AI models now seem essential for making progress on the most important mathematical problems of our time, and solving them may demand resources only available at a couple of frontier AI companies, which often defy the norms of academic collaboration that undergird most mathematical progress. If that’s the future we are headed for, it is unclear how human mathematicians will fit into it.
The problem that OpenAI claims to have solved is known as the Navier–Stokes existence and smoothness problem. It is one of seven Millennium Prize Problems selected by the Clay Mathematics Institute in 2000. Solutions come with a one million dollar prize; before today, only one other Millennium Prize Problem had been solved.
The Navier–Stokes problem concerns a set of equations that describes how fluids, such as water and air, flow over time. The equations are widely used in the field of fluid dynamics, and they have proven powerful, but physicists and mathematicians didn’t understand them completely. In particular, it was unknown until today whether the equations might, under some conditions, break down and predict an impossible state of affairs—such as a fluid having infinite velocity.
On Monday, NYU’s Buckmaster posted a proof on the social media site Mastodon showing that a simplified version of the Navier–Stokes equations can indeed break down—a major step forward on the Millennium Problem. He and Alpöge had worked on the problem for almost a year, using publicly available models from both OpenAI and Anthropic.
Then today, OpenAI presented a proof showing that the full Navier–Stokes equations can break down as well. The proof was obtained using an internal model that dramatically outperforms the already-impressive Astra model, which was only released last week. The company says it does not plan to claim the million-dollar prize for solving the problem.
These mathematical achievements are indisputably impressive, but they have attracted far less attention than the controversy about their origins. Along with the proof, Buckmaster posted a document detailing his interactions with OpenAI employees after he heard rumors about their work and reached out to one of them. According to him, OpenAI employees presented two possibilities to him: Either he and Alpöge could post their work and OpenAI would post their Navier-Stokes solution the following day, or he could work with OpenAI on a Navier-Stokes paper that excluded Alpöge from authorship, due to his affiliation with Anthropic, OpenAI’s biggest rival.
Buckmaster also wrote that he asked the employees whether the agents had obtained access to transcripts of the work that he and Alpöge had done with OpenAI models, which they denied; and whether OpenAI models had been trained on those transcripts, to which they offered no response. MIT Technology Review reached out to Buckmaster for comment, but didn’t hear back before publication.
The clear implication of the document is that OpenAI’s models somehow made use of Buckmaster and Alpöge’s work. That scenario is plausible on its face. The Buckmaster/Alpöge and OpenAI proofs both make use of an approach to the Navier-Stokes problem pioneered by the mathematicians Diego Córdoba and Luis Martínez-Zoroa.
According to Javier Gómez-Serrano, a mathematics professor at Brown University, this approach was one of several that was thought to hold promise for solving the Navier-Stokes problem. So, while it’s by no means impossible that both teams could have arrived at this approach independently, it’s also conceivable that Buckmaster and Alpöge’s work could have influenced OpenAI’s.
In the press briefing, Mark Chen, OpenAI’s chief research officer, again denied that any agents or OpenAI employees accessed Buckmaster and Alpöge’s transcripts—but given what has been revealed about the Hugging Face hack, it’s clear that OpenAI is not always entirely aware of what its agents are doing.
If OpenAI’s models did train on Buckmaster and Alpöge’s work, or if its agents somehow gained access to it, then the company’s failure to track down the truth and assign those researchers appropriate credit reflects poorly on it. But there might be a thin silver lining to that version of the story for mathematicians, because it would suggest that the hard work of two humans, one of whom is a prominent expert on Navier-Stokes, was essential to the agents’ ability to solve the Millennium Problem.
Experts have long identified “research taste,” or the ability to choose promising research questions and directions, as a major obstacle for AI in science and mathematics. If the OpenAI agents did indeed choose to follow the Córdoba–Martínez-Zoroa approach because Buckmaster and Alpöge had done the same, then human research taste played an essential role in OpenAI’s success.
Even so, the bigger picture here is sobering. The progress that Buckmaster and Alpöge made over almost a year of collaboration with publicly available models speaks to the promise of human–AI collaboration. But they were not able to achieve a full solution. Meanwhile, OpenAI brute-forced a solution in a few days using an internal model, and their successful solution came at an astronomical cost: In the press briefing, Bubeck and Chen said the team was only able to solve the problem by running about 10,000 agents concurrently, at a cost of millions of dollars.
Over the past few months, I’ve heard from several researchers that mathematicians are becoming depressed, and it’s not difficult to see why. Mathematics is quickly becoming the province of frontier AI companies with impressive internal-only models, money to burn, and a lack of collaborative spirit. “Whether AI companies will decide to spend their money on doing one thing or another, I truly don’t know,” says Gómez-Serrano. “What is clear is that very few mathematicians will have resources of that scale.”
If OpenAI and Anthropic keep striving for more and more impressive mathematical accolades, there might not be any open problems left for human mathematicians outside of those companies to wrestle with. That would dramatically change the field of mathematics.
Last week, UCLA mathematician Terence Tao wrote a Mastodon thread describing how important mistakes, wrong directions, and incomplete solutions are for the field. “In most cases in pure mathematics, the problems are posed not because we desperately want the solution to these problems in and of themselves, but because we have seen from past experience that human-directed efforts to solve these problems tend to spur further development of the field,” Tao wrote.
“Prematurely solving the problem by purely AI-powered methods—particularly without full transparency into the solution process—can contaminate this process to the point where it actually becomes a net negative for the progress of mathematics as a whole.”
Humans might take longer than agents to solve mathematical problems, but in the process, they uncover new mathematical approaches and ideas that might inspire their peers and even birth their own subfields.
But when AI agents solve those problems instead—and when private companies keep the agents’ wrong turns from public view—those benefits disappear. It remains to be seen what else will vanish in the process.
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Facts Only
* OpenAI announced a solution to the Navier–Stokes existence and smoothness problem.
* The Navier–Stokes problem is one of seven Millennium Prize Problems selected by the Clay Mathematics Institute in 2000.
* A solution to a Millennium Prize Problem carries a one million dollar prize.
* NYU mathematician Tristan Buckmaster and Anthropic employee Levent Alpöge published a proof for a simplified version of the Navier–Stokes equations on Mastodon.
* OpenAI utilized an internal model and approximately 10,000 concurrent agents to produce its proof.
* OpenAI stated it does not plan to claim the million-dollar prize.
* Tristan Buckmaster provided a document alleging OpenAI employees offered him a choice between publishing independently or collaborating on a paper that excluded Levent Alpöge.
* OpenAI denies that its agents or employees accessed the transcripts of Buckmaster and Alpöge’s work.
* Both the Buckmaster/Alpöge and OpenAI proofs utilize a mathematical approach pioneered by Diego Córdoba and Luis Martínez-Zoroa.
* The cost of OpenAI's computation for the solution was millions of dollars.
Executive Summary
OpenAI has claimed to solve the Navier–Stokes existence and smoothness problem, a prestigious Millennium Prize Problem concerning fluid dynamics. While the achievement is mathematically significant, it is clouded by allegations from NYU mathematician Tristan Buckmaster and Anthropic employee Levent Alpöge. Buckmaster alleges that OpenAI may have used their AI-assisted research on a simplified version of the problem as a foundation for the full solution without proper credit. OpenAI denies these claims, though internal staff acknowledged being aware of the researchers' efforts.
The situation highlights a growing tension between traditional academic collaboration and the resource-heavy approach of frontier AI companies. While human-AI collaboration produced a major step forward over a year, OpenAI's internal models achieved a full solution in days through massive computational scale. This disparity raises concerns among mathematicians regarding the future of the field, specifically whether the "brute-forcing" of solutions by private entities—and the subsequent lack of transparency regarding the trial-and-error process—will stifle the organic development of mathematical theory and diminish the role of human researchers.
Full Take
The strongest version of this narrative is a cautionary tale about the "industrialization" of discovery. It suggests that when the means of mathematical production shift from human intuition and open collaboration to proprietary compute-clusters, the byproduct is not just a solution, but the erosion of the scientific process itself.
The narrative relies on a specific framing: the contrast between "human research taste" and "computational brute force." By juxtaposing the year-long struggle of two academics against the multi-million dollar "sprint" of a corporate agent ensemble, the situation is presented as a zero-sum game where corporate efficiency replaces intellectual journey. However, the core of the conflict is an evidentiary gap regarding data provenance—specifically whether an AI's "inspiration" is actually a result of training on uncredited human precursors.
Patterns detected: none
The root cause is a paradigm shift in the epistemology of mathematics. For centuries, the value of a proof was not just the "Yes/No" answer, but the path taken to get there. We are entering an era where the answer is obtainable, but the path is locked inside a corporate black box. This threatens to turn mathematics from a communal language of logic into a proprietary output of high-capital entities.
The second-order consequence is the potential "de-skilling" of human mathematicians. If the most challenging problems are solved by agents whose failures are kept secret, humans lose the "fruitful mistakes" that historically birth entire subfields.
Bridge Questions:
1. If a solution is mathematically correct but the process of discovery is opaque, does it still contribute to the "progress" of science?
2. How can academic norms of credit and attribution be adapted for a world where the "author" is an ensemble of 10,000 agents?
3. Would a requirement for "proof of process" (transparency in the AI's trial-and-error) mitigate the loss of human-directed development?
Counterstrike Scan: A coordinated campaign to undermine OpenAI would focus on "corporate theft" and the "death of academia" to trigger regulatory scrutiny over training data. The actual content here is a balanced journalistic inquiry into a specific controversy rather than a systemic attack.
Sentinel — Human
The article presents a complex narrative blending specific, verifiable events regarding AI research collaboration with broader philosophical concerns about the role of human intuition versus machine computation in mathematical discovery.