NYU professor challenges OpenAI’s claimed breakthrough on a Millennium Prize problem

One of the biggest open questions in mathematics has suddenly become a flashpoint in the debate over how far AI companies can go with user data and research.

NYU mathematics professor Tristan Buckmaster is publicly challenging OpenAI’s headline‑grabbing claim that an internal AI model helped crack a famous Millennium Prize problem in just 88 hours. He says the company’s system may have quietly leaned on his own unpublished work—stored on OpenAI’s servers through its coding tools—without credit or consent.

What is the Navier–Stokes problem and why it matters

At the center of the controversy is the Navier–Stokes equation, a set of formulas that describe how fluids move. They’re based on Newton’s second law of motion and are used in everything from weather modeling to aerodynamics and oceanography.

The Clay Mathematics Institute named the Navier–Stokes existence and smoothness problem as one of the seven Millennium Prize Problems. Solving it—proving that solutions always exist and behave nicely in three dimensions, or that they sometimes don’t—comes with a $1 million prize and huge prestige in the math world.

Buckmaster says this problem has been his “North Star” for his entire career, guiding his research path even when the final solution stayed out of reach.

OpenAI’s 88-hour ‘breakthrough’

According to Buckmaster’s account, OpenAI recently announced that an internal system, powered by thousands of AI agents working in parallel, had solved the Navier–Stokes problem in just 88 hours. Alongside that, the system also reportedly produced a key result for a related fluid equation called the Euler equation.

OpenAI described this Euler result as the “seed” they fed into their swarm of AI agents to reach the Navier–Stokes solution. In other words, the Euler breakthrough was presented as the crucial stepping stone that unlocked the bigger Millennium Prize result.

How Buckmaster’s research fits into the story

Buckmaster says that while he had not yet solved the full Navier–Stokes problem, he and a collaborator had made major progress on the Euler equations—one step below Navier–Stokes in complexity. He believed they were perhaps a month away from finishing their work.

Some of that research was public, but some was still unpublished. Crucially, Buckmaster says he had been using OpenAI’s coding assistant, Codex, to work on the project. That meant his drafts and papers were stored on OpenAI’s servers as part of his normal workflow.

When rumors began circulating that another AI company, Anthropic, had solved a Navier–Stokes problem (a rumor that later turned out to be false), Buckmaster says this spurred OpenAI to invest heavily—spending millions of dollars—to attack the same problem using AI agents.

The allegation: AI powered by scraped, private research

Here’s where Buckmaster’s concerns become serious. He claims that the Euler result OpenAI later released is “near identical” to his own unpublished result, and also very similar to the partial result he had already made public.

In his telling, OpenAI’s internal tools had access to his private work through Codex. That raises a sharp question: did OpenAI’s system, or its engineers, directly or indirectly use his unpublished research as the seed that enabled the AI swarm to reach the Navier–Stokes solution?

Buckmaster says OpenAI initially contacted him suggesting they shouldn’t “compete” and instead offered resources to help him complete his work. A meeting was scheduled. Then, shortly before that meeting, he received a message saying OpenAI was about to do something “really stupid” and that they needed to talk. On the follow‑up call, he says the story shifted.

Conflicting timelines and changing explanations

According to Buckmaster, an OpenAI scientist first claimed they had simply taken the Navier–Stokes problem, put it into a prompt, and hit enter—implying a kind of instant, magical solution. Within minutes, he says, they admitted that wasn’t true.

He also alleges that OpenAI kept changing critical details about when they started working on the problem and what data their models were trained on. At different points, he says, they gave different cutoff dates for the training data (first April, then July) and different descriptions of how many attempts they made before getting the result.

Buckmaster points to one especially suspicious detail: he claims OpenAI’s team made no real progress on the Euler problem until, in a single day, they suddenly produced the key Euler result that mirrors his own work. That result, OpenAI has said, was then used as the seed to unlock the Navier–Stokes solution.

OpenAI’s response: ‘categorically impossible’

OpenAI, for its part, strongly denies that Buckmaster’s private prompts or files played any role. In a statement shared publicly, the company said: “We can say categorically it is impossible for Dr. Buckmaster’s Codex prompts to have influenced the system in any way including training.”

Buckmaster doesn’t accept that explanation. He says the company has already changed its story several times and accuses them of lying about how many problems they tried, how many attempts were made, and how they built on “previous work” inside their own files.

At this stage, the core dispute is factual and technical: did OpenAI’s systems, directly or indirectly, use Buckmaster’s unpublished research? Without full transparency into logs, training data, and internal workflows, it’s difficult for outsiders to verify either side’s claims.

The bigger issue: 720 AI-generated math papers and users’ ‘life work’

Beyond his own case, Buckmaster says OpenAI has generated roughly 720 mathematical papers with its internal AI system. Some of these clearly showcase AI’s growing power in pure math. But he argues that a subset of these papers appear to resolve problems that human mathematicians—who are also OpenAI customers—have been working on for years and were close to publishing themselves.

That raises a broader ethical and practical concern: if you use an AI coding or writing assistant to draft your research, are you effectively handing your life’s work to a company that might then let its models or agents compete against you?

The analogy he and others draw is simple: if you’re writing a book in Google Docs, you don’t expect Google to turn around and publish a similar book based on your drafts. Many researchers treating AI tools as private assistants may not realize how their data can be stored, processed, or potentially repurposed.

This fits into a wider pattern of tension between AI companies and academia, where issues like data scraping, attribution, and verification of AI-generated proofs are becoming hot topics. For more background on how AI is reshaping research workflows, you can look at recent coverage of AI in academia and AI-checked proofs.

Will this end up in court?

When asked directly if he plans to sue, Buckmaster didn’t commit either way. He laughed and noted that it would be “me versus a trillion‑dollar company,” hinting at the scale of the challenge. But he also acknowledged that this is his life’s work—and that the stakes go beyond a single $1 million prize.

Legal action would likely hinge on complex questions: what exactly do terms of service allow AI companies to do with user prompts and uploaded files? How traceable is influence from private data inside large AI systems? And what counts as copying versus independent discovery when the outputs are mathematical proofs?

These are the kinds of questions that could define how researchers, writers, and developers choose which AI tools to trust—and how they use them.

What this means for AI, research, and trust

Regardless of how this specific dispute is resolved, it highlights a deeper tension at the heart of modern AI: these models are powerful collaborators, but they’re owned and controlled by private companies whose incentives may not always align with individual users.

For mathematicians and academics, the case is a warning signal. Using proprietary AI tools for sensitive or unpublished work may carry risks that aren’t fully understood yet. At the same time, AI models are clearly becoming capable of tackling serious research problems—something we’ve also seen in discussions around systems like OpenAI’s Astra and its push toward more general intelligence, covered in more depth in our piece on how close Astra might be to AGI.

As AI systems move from assisting with emails and code snippets into generating original theorems and proofs, the rules for credit, ownership, and fair use will need to evolve quickly. Buckmaster’s story is likely one of the first big public battles over these questions—but it almost certainly won’t be the last.