Mathematicians Accuse OpenAI of Using Private Work Without Proof

OpenAI is facing fresh scrutiny from mathematicians who say the company has not adequately explained whether its systems were trained on private research conversations, after the firm celebrated major new results in mathematics. The latest criticism centers on claims that OpenAI’s output may have been influenced by unpublished work or user interactions, raising questions about credit, consent, and transparency in high-stakes AI research.

The dispute matters because OpenAI has now publicly claimed progress on elite mathematical problems while researchers say the company has offered only partial answers about what data may have helped produce those results. That has intensified concerns that AI labs could gain an advantage from material academics shared in confidence, then race ahead of the people who developed the ideas in the first place.

Mathematician Andreas Thom has become the latest researcher to challenge OpenAI’s handling of data provenance. In public posts, Thom said his own exchanges with ChatGPT left him wondering whether the company had used those conversations, directly or indirectly, in training models that later demonstrated unexpected command of his field.

His concerns arrived just days after another academic, Tristan Buckmaster of New York University, raised a similar alarm about whether his work with OpenAI’s Codex system may have influenced the company’s mathematical output. Together, the complaints have turned what might have been a celebration of progress into a broader argument about the ethics of AI-assisted discovery.

What OpenAI said it achieved — and why mathematicians reacted so strongly

OpenAI recently announced what it described as a set of notable mathematical breakthroughs, including work touching one of the field’s prestigious Millennium Prize problems. If verified by outside experts, that would represent a major milestone, because Millennium Prize problems are among the most famous unsolved questions in mathematics.

One of the company’s headline results involved non-sofic groups, a highly technical area of abstract algebra. These are infinite mathematical objects that resist approximation by finite systems, making them especially difficult to study. OpenAI later acknowledged that the result drew heavily on prior contributions from Thom and mathematician Gábor Kun.

The reaction from mathematicians was not simply about whether OpenAI had solved a hard problem. It was also about how the company described the path to the result, who received credit, and whether recent unpublished or semi-private work may have informed the model’s performance.

That tension is amplified by the fact that, in mathematics, priority matters. A field built on proof, attribution, and careful recordkeeping is particularly sensitive to the possibility that a private interaction with an AI system could be folded into a model and later surface as a competitor’s advantage.

How did Andreas Thom say OpenAI may have benefited from his work?

Thom said he began re-examining his own interactions with OpenAI after Buckmaster publicly questioned whether AI tools had absorbed ideas from his own use of Codex. Thom then connected those concerns to OpenAI’s non-sofic groups announcement, especially after seeing what he called the company’s unusually deep grasp of techniques he and colleagues had explored.

According to Thom, the methods OpenAI appeared to understand were not the most obvious or promising paths available at the time. That observation led him to ask whether his conversations with ChatGPT were included in training data or otherwise reachable by the model’s reasoning system.

He said he contacted OpenAI researchers Sébastien Bubeck and Mark Sellke seeking clarification. The response, in his view, failed to answer the core question: whether his exchanges were merely unavailable to the system in real time, or whether they had already entered the company’s broader training pipeline.

Thom said the reply did not settle whether his chats were used in training and argued that OpenAI had not provided enough explanation or evidence to rule that out.

In Thom’s telling, that omission is not just a technicality. If a user’s research discussion can be de-identified and then folded into model training, the intellectual content may remain valuable even if the person’s name disappears from the record.

Why the training-data dispute is so difficult to resolve

At the heart of the controversy is a basic asymmetry: OpenAI knows what data went into its models, while outside researchers generally do not. Thom argued that mathematicians are not in a position to reconstruct the company’s training pipeline or determine whether their own ideas were absorbed along the way.

He said the burden should fall on OpenAI to prove what was not used, rather than on individual researchers to prove that their material was. In his view, meaningful transparency would require disclosure of the relevant datasets and a clearer explanation of how the company handles user interactions across different product settings and terms of service.

The problem is not limited to one conversation or one field. As AI systems become more capable, the boundary between a user’s query and a model’s training corpus becomes increasingly hard for outsiders to see. That leaves academics, startups and professional users with few tools to determine whether their input may later help an AI system outperform them.

Thom argued that if OpenAI denies using such data, it should be prepared to demonstrate that with documentation. Without that, he said, the company’s assurances remain too vague to be reassuring.

What OpenAI has said before about user data

OpenAI’s own public language around one of its recent achievements has added fuel to the backlash. In announcing a solution related to the Navier-Stokes equations, the company said its researchers and agents did not see any of the outside researchers’ work before it was publicly released and that no specific user data was accessed to solve the problem.

But the same statement stopped short of eliminating every possible data pathway. OpenAI said it could not rule out that de-identified data derived from product usage may have helped improve its models, even if that connection was described as unlikely.

That distinction has become central to the dispute. To mathematicians like Thom, de-identification may remove a personal label, but it does not erase the underlying idea, proof strategy or problem-solving insight. In fields where originality is the currency, the content itself may be more important than the source name attached to it.

Critics argue that this kind of wording allows a company to deny direct access to user material while leaving open the possibility that the same material shaped the model in indirect ways. Supporters of strong AI development, meanwhile, may see the language as an attempt to acknowledge uncertainty without overstating certainty about complex training pipelines.

Why mathematicians are worried about a chilling effect

The controversy has broader implications for how research is conducted. Several mathematicians say they fear that if AI companies can monitor public hints of a breakthrough and then rapidly deploy powerful models against the same problem, researchers may become more guarded about sharing early ideas.

That could push mathematics toward a more secretive culture, especially in areas where progress is already slow and fragile. In a discipline where a single key idea can take years to develop, the prospect of a well-funded technology company arriving late to the conversation but leaving first with the result could alter behavior across the field.

There is also a reputational issue for OpenAI. A company that presents itself as a leader in advanced reasoning has little room for error when it comes to crediting prior work and explaining how its systems were built. Even if the company’s mathematical results ultimately hold up, the perception of opacity can still erode trust.

That is especially true because the episode touches on one of the oldest norms in science: the obligation to be clear about where ideas came from. In a space where artificial intelligence increasingly intersects with original research, those norms are becoming harder to preserve — and more important to defend.

OpenAI’s mathematics push, explained

OpenAI’s recent mathematical claims did not emerge in a vacuum. The company has been investing heavily in models that can reason through complex symbolic problems, and mathematics has become a test case for whether large language models can do more than generate fluent text.

Success in this area would matter for several reasons:

• It would signal that AI systems can contribute to formal reasoning, not just language tasks.
• It could accelerate discovery in fields that rely on proof, abstraction and pattern recognition.
• It would strengthen the case for using frontier AI in scientific research.
• It could also raise the stakes for data sourcing, attribution and academic norms.

But the same qualities that make mathematical breakthroughs exciting also make them controversial. In any research field, a machine’s ability to reproduce or surpass human insight is only part of the story. The other part is how the machine was trained, what it learned from, and whether the people who supplied the original ideas had any say in the process.

Timeline of the dispute

The recent row developed quickly, but it is rooted in a longer tension between AI development and academic authorship. The sequence below shows how the conflict escalated.

What exactly is non-sofic groups research?

Non-sofic groups are a topic in abstract mathematics dealing with infinite structures that cannot be closely approximated by finite ones. The subject is notoriously technical, but for researchers in the field it is one of those areas where a breakthrough can carry outsized weight because progress is so hard to make.

OpenAI’s work in this area stood out not just because the problem is difficult, but because it seemed to engage with specialized techniques that human researchers had been developing over time. That is one reason the company’s announcement drew attention well beyond the immediate result.

When a system displays a refined understanding of a niche area, observers naturally ask how it got there. Did it infer the solution from public literature alone? Did it see private discussions? Or did it extract useful patterns from de-identified interactions hidden somewhere in a massive training set?

Those questions are not easy to answer externally, which is exactly why they are now at the center of the backlash.

Why attribution matters in mathematics

Attribution matters in mathematics because a proof is not only a conclusion; it is also a record of intellectual labor. Giving credit for a method, lemma or strategy can shape careers, establish priority and preserve the history of an idea’s development.

When a company presents a result without fully acknowledging the recent contributions that helped make it possible, mathematicians may view that as more than an oversight. They may see it as a breach of the discipline’s basic norms.

Thom said it would be ethically indefensible if private, nonpublic research supplied by users helped improve models that were then used to outpace those same users in publication, especially without consent, disclosure or credit.

What happens next?

OpenAI has not immediately responded to the latest request for comment, leaving the company’s position on these specific concerns unresolved in public. That silence may not last, but for now it leaves mathematicians and other users to debate the issue without a definitive explanation from the firm.

There are several possible outcomes. The company could provide more detail about its data policies and how it handles user content. It could stand by its existing statements and argue that the allegations misunderstand its systems. Or the controversy could fade without a full accounting, as often happens when disputes over model training run into the practical limits of outside verification.

Even if OpenAI eventually proves its case, the episode may have already changed expectations. Researchers now appear more alert to the possibility that interactions with AI systems are not merely ephemeral exchanges but potential inputs to future models.

That realization could make people think twice before discussing unfinished ideas with an AI tool, especially in fields where the difference between a promising path and a published result can be measured in months — or days.

Why this story matters beyond one company

The fight over OpenAI’s math data is really about the rules of the next research economy. As AI systems become collaborators, search tools and possible competitors, the definition of “training data” becomes more politically and scientifically significant.

If researchers cannot tell whether their private exchanges are feeding future models, trust in AI tools may weaken. If companies cannot explain their data practices in a way outsiders can verify, suspicion will grow even when the underlying model performance is impressive.

For now, the debate is being fought in one of the world’s most exacting disciplines. But its implications stretch far beyond mathematics, touching every industry that relies on confidential expertise, unpublished work and the promise that a conversation with an AI system is not automatically destined to become someone else’s competitive edge.

In that sense, the current dispute is about more than a single theorem or one set of model outputs. It is about whether the AI industry can prove that its most celebrated advances are built not only on power and scale, but also on transparency, consent and fair attribution.

And that is why mathematicians are demanding something OpenAI has not yet fully supplied: a clear accounting of where the ideas came from.