OpenAI’s distributed AI agents make headway on Navier-Stokes problem
Developing story first seen 2 hours ago
A dispute has emerged over OpenAI's claim to have made progress on the Navier–Stokes existence and smoothness problem, one of the Clay Mathematics Institute's six unsolved Millennium Prize problems. New York University mathematics professor Tristan Buckmaster has said he and Levent Alpöge, a mathematician at rival firm Anthropic, had themselves been working towards a solution using OpenAI's Codex tool, and that OpenAI only began its own work on the problem after "information about our progress" reached the company on 3 September, hours before OpenAI published its result.
OpenAI says it used a new, unreleased internal AI model and around 10,000 AI agents working in parallel, taking roughly 88 hours, exchanging nearly three million messages and generating 130 billion output tokens, at an estimated cost of about $10m (£7.3m) based on its own pricing. The effort resolved two of the four statements required for a full proof, and OpenAI describes the result as a milestone demonstrating rapid AI progress, stressing it has not been independently verified, is not accepted by the Clay Mathematics Institute, and is not being submitted for the $1m prize. Buckmaster said he had not yet reviewed OpenAI's full proof but felt compelled to make the timeline public.
- Rival mathematician disputes OpenAI's account of who solved what first
- NYU professor says OpenAI got his team's progress before publishing
- OpenAI's result still unverified, not claiming the $1m prize
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OpenAI's proof of Navier-Stokes progress, achieved using thousands of parallel AI agents, is not the first controversy of this kind, but it has raised questions about how AI labs handle and credit shared research.
The Navier-Stokes existence and smoothness problem is one of seven originally listed Millennium Prize problems set by the Clay Mathematics Institute, each carrying a $1m reward for a full solution. It concerns whether certain equations describing fluid flow always have smooth, well-behaved solutions, and it has remained unsolved since being named in 2000. OpenAI says its AI agents made partial progress on the problem, though it stresses the work has not been checked by outside mathematicians or accepted by the institute.
The dispute centres on how that progress came about. Tristan Buckmaster, a mathematician at New York University, says he and Levent Alpöge, who works at OpenAI's rival Anthropic, had already been pursuing a solution using OpenAI's own Codex tool, and that OpenAI began its published effort only after learning of their work shortly beforehand. This matters because it touches on questions of credit and transparency in a field where AI companies are racing to demonstrate that their systems can produce genuine mathematical breakthroughs.
Both sides, in good faith
The strongest fair case each way — we don't pick a winner.
The case for
Those sympathetic to OpenAI's position would argue that publishing a partial, clearly-caveated result is itself good scientific practice: the company explicitly says the work is unverified, not accepted by the Clay Institute and not being submitted for the prize money, so it is offering a transparent progress report rather than claiming a solved Millennium Problem. They would add that using thousands of parallel AI agents to resolve two of four required statements is a legitimate and notable demonstration of how automated systems can accelerate research mathematics, regardless of who first identified the problem as promising, and that ideas and open problems are not owned by whoever mentions them first – independent verification, not priority disputes, is what should ultimately settle the mathematics.
The case against
Those sympathetic to Buckmaster's account would argue that timing and attribution matter enormously in research, and that if OpenAI only began its own effort after learning of Buckmaster and Alpöge's progress hours before publishing, it raises serious questions about whether credit is being fairly assigned to the mathematicians who identified the problem's tractability in the first place. They would emphasise that going public with the timeline, even without having reviewed OpenAI's full proof, is a reasonable act of scholarly transparency meant to protect proper credit in a field where reputational stakes and precedence are taken seriously, especially given the commercial rivalry between the two AI labs involved.
Full account
OpenAI has said that a large, coordinated fleet of its artificial intelligence agents made substantial progress on one of mathematics' most stubborn unsolved problems, the Navier-Stokes existence and smoothness question, which has resisted a complete proof for around ninety years. The company set out roughly ten thousand AI agents, powered by an as-yet unreleased internal model, to work on the problem, and reported that within some 88 hours it had produced a resolution to two of the four statements demanded by the Clay Mathematics Institute's Millennium Prize criteria for that problem. OpenAI described the outcome as a marker of how quickly its systems are advancing, while stopping short of calling it a complete or verified solution.
The Navier-Stokes equations describe how fluids and gases move, and they sit at the centre of efforts to understand turbulence, a phenomenon that remains only partially explained by physics and mathematics. According to OpenAI, the effort began at the end of August when it started training a new model that showed unusual aptitude for mathematics, and it was spurred into targeting the Millennium Prize problems specifically after hearing, on 1 September, unconfirmed reports that two of the seven prize problems had already been cracked elsewhere. The scale of the undertaking was considerable: the agents are said to have exchanged close to three million messages and generated some 130 billion output tokens tackling this single problem, an effort OpenAI estimated would have cost in the region of $10m had it been billed at standard rates for its most capable models.
OpenAI has been careful to frame the result as partial and preliminary rather than a finished proof. It has not sought to claim the associated $1m Millennium Prize, and the work has not yet been independently verified or endorsed by the Clay Mathematics Institute, which administers the prize and would need to confirm any solution before it could be considered resolved. Since the prize scheme was established in 2000, only one of its seven original problems had previously been solved, underlining how significant a genuine breakthrough on Navier-Stokes would be, even as OpenAI's own language keeps expectations in check by presenting the announcement chiefly as evidence of its models' improving mathematical capability.
The announcement has also become entangled in a dispute over credit and conduct. Mathematician Tristan Buckmaster of New York University, working with Levent Alpöge, a researcher at rival lab Anthropic acting in a personal capacity, say they had independently been pursuing their own solution using a mix of AI tools, including Anthropic's Claude alongside OpenAI's Codex and an OpenAI frontier model known as Astra. Buckmaster has suggested OpenAI may have accelerated its own push after learning that his team, which included an Anthropic-affiliated researcher, was closing in on an answer, and has said he pressed OpenAI on whether its model had been trained on or had accessed the draft work he and Alpöge had stored in Codex sessions, receiving what he described as an evasive response. He has also said OpenAI mathematician Sebastien Bubeck presented him with two options for how credit might be apportioned, either publishing a partial account of his own team's work a day ahead of OpenAI's announcement, or writing it up solo while acknowledging OpenAI's model as a tool used along the way.
Where outlets differ
The BBC-style account concentrates on the mechanics and scale of the achievement — the number of agents, the 88-hour timeframe, the token and cost figures — and only gestures at the credit dispute in its closing lines, without detail.
The other report leads with the credit and conduct controversy as the central story, giving much fuller background on the Millennium Prize Problems, naming Buckmaster and Alpöge, detailing their independent work with Claude and OpenAI tools, and quoting Buckmaster's allegations about OpenAI's conduct and Bubeck's proposed credit-sharing options at length.
Only the second source explains that Alpöge is an Anthropic employee working in a personal capacity, a detail that sharpens the rivalry angle largely absent from the first account.
The first source includes direct OpenAI quotes disclaiming any Millennium Prize claim; the second does not reproduce that language and instead foregrounds OpenAI's alleged handling of the dispute.
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Originally published by BBC Technology as “OpenAI says it cracked 90-year-old maths problem in 88 hours”.