The mathematician Andreas Thom is demanding that OpenAI provide conclusive proof that its models did not benefit from his private research interactions, marking the second major ethics dispute to engulf the company in as many weeks. In a series of posts on Mastodon, the Dresden-based mathematician accused OpenAI of “dishonest” behavior and a lack of transparency about whether conversations he and his colleagues had with ChatGPT were silently absorbed into the training data powering its mathematical discoveries. His challenge follows a separate confrontation over OpenAI’s celebrated Navier-Stokes solution, and it threatens to cast a shadow over some of the most impressive results the AI industry has ever produced.
Why Andreas Thom Is Demanding That OpenAI Prove It Did Not Use His Work
The controversy centers on one of ten mathematical advances OpenAI announced with great fanfare last month. Among those results was a breakthrough involving non-sofic groups, an esoteric but deeply important area of infinite mathematics that happens to be Thom’s specialty. OpenAI explicitly acknowledged that its result built heavily on previous work by Thom and fellow mathematician Gábor Kun, yet the company initially failed to credit their most recent contributions. The omission drew sharp criticism within mathematical circles, and OpenAI quietly amended its writeup to correct the record.
For Thom, however, the credit issue was only the beginning. As he reflected on the nature of the OpenAI result, he became increasingly troubled by what he described as the company’s “detailed command of our techniques.” The methods OpenAI’s models used were neither the most obvious nor the most promising routes to a solution at the time, he said. That raised a disturbing possibility: Had his own private conversations with ChatGPT, conducted before the company’s triumphant announcement, somehow leaked into the system and shaped the very result OpenAI was now claiming as its own?
What Are Non-Sofic Groups?
Non-sofic groups are, roughly speaking, infinite mathematical structures that cannot be approximated by finite ones. They sit at a crossroads of group theory, connecting abstract algebra to computer science, operator algebras, and even questions about the fundamental nature of computation. The concept was introduced by Mikhail Gromov in 1999, and for decades mathematicians have sought to determine whether every group is sofic, or whether genuine non-sofic examples exist. A concrete advance on this question carries significance far beyond abstract mathematics, touching on deep open problems in areas as diverse as quantum information and graph theory.
This is why the OpenAI result mattered so much to the mathematical community, and why the circumstances surrounding it have proven so combustible. This was not a marginal footnote in an obscure journal; it was a potentially landmark contribution to a problem that has resisted the world’s best minds for a quarter of a century.
Thom’s Suspicion: Did ChatGPT Conversations Shape the Result?
Thom did not arrive at his suspicions casually. In his Mastodon posts, he explained that he had spent considerable time interacting with ChatGPT in his professional capacity, discussing technical details of his research with the chatbot. Those interactions occurred before OpenAI announced its mathematics results, and Thom’s area of expertise aligned almost precisely with the result OpenAI chose to showcase.
What troubled him most was the strategic reasoning embedded in OpenAI’s solution. The techniques it employed were not the kind of approach a researcher would typically try first, nor were they the most naturally suggested by the existing literature. They were, in Thom’s words, distinctive, the kind of methodological choices that suggest familiarity with a particular line of thinking. That familiarity, he argued, could plausibly have come from his own prior conversations with the AI system.
Determined to get an answer, Thom wrote directly to two OpenAI researchers: Sébastien Bubeck, who has been at the forefront of the company’s mathematics initiatives, and Mark Sellke, who is also a statistician at Harvard. His question was pointed: Were his interactions with ChatGPT part of the training data, or accessible to the reasoning process, in a way that could have contributed to the non-sofic groups result?
The Unsatisfying Answer: Direct Access Versus Training Data
The response Thom received did little to ease his concerns. He said the answer addressed only whether his conversations could be accessed directly by the model, essentially, whether ChatGPT could retrieve his specific messages on demand. It did not, in his view, properly address whether his conversations had been absorbed into the vast pools of training data that OpenAI uses to improve its models behind the scenes.
“No such qualification, explanation, or evidence was given,” Thom wrote. “I take this as dishonesty to say the least.”
That distinction matters enormously. Direct access to a user’s conversation would be a clear and obvious violation of trust, and OpenAI presumably knows better than to build such a pipeline. Training data absorption is far murkier. When a user submits a mathematical idea to a chatbot, that interaction may be logged, de-identified, and repurposed for model training in ways that users never explicitly authorized and cannot possibly track. A model trained on such material might internalize not just the broad contours of the ideas but the specific technical approach, without ever being able to point back to the original source.
Can Researchers Reverse-Engineer OpenAI’s Training Pipeline?
They cannot. Thom made this point explicitly, noting that researchers lack the technical capacity to reverse-engineer OpenAI’s training pipeline to determine whether their work has been used. “Only OpenAI has the relevant data for that,” he said.
This asymmetry of information lies at the heart of the current controversy. OpenAI, as the only party with access to its training datasets, data retention policies, and model architectures, is uniquely positioned to answer the question definitively. Thom’s argument is simple: if the company is going to deny that user research influenced its models, the burden of proof should fall on OpenAI itself. That means disclosing all relevant datasets, clarifying how user interactions are processed, and explaining the various settings and terms that govern data usage.
The Navier-Stokes Dispute Set the Pattern
Thom’s experience bears a striking resemblance to the controversy that erupted just days earlier over OpenAI’s Navier-Stokes solution. That result, which concerns the movement of fluids and represents one of mathematics’ legendary Millennium Prize problems, was announced by OpenAI after the company heard rumors that other researchers were close to a breakthrough. Tristan Buckmaster, a mathematics professor at New York University, had been working on the Navier-Stokes problem with Levent Alpöge, a researcher at Anthropic, in a personal capacity. Buckmaster publicly questioned whether OpenAI’s models had benefited from his own use of OpenAI’s Codex tool.
OpenAI’s blog post announcing the Navier-Stokes solution offered a categorical denial of any specific data misuse: “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.”
But the company stopped well short of ruling out indirect influence. In a carefully worded caveat, OpenAI said: “While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models.”
Why the De-Identification Defense Does Not Satisfy Thom
Thom sees this de-identification caveat as the same obfuscatory distinction the company deployed in its communications with him. And he is blunt about why he finds it unacceptable. “De-identification may remove a name; it does not remove the intellectual content of a mathematical idea,” he said.
This is a crucial point, and it cuts to the heart of what makes the controversy so difficult to resolve. In the world of data privacy regulation, de-identification is often treated as a meaningful safeguard; once the personal identifiers are stripped away, the data is considered less sensitive. But in the world of mathematical research, the value of an idea lies in its intellectual content, not in who said it first. A mathematical technique, a clever construction, a subtle proof strategy, these are not rendered harmless by removing the author’s name. If anything, the de-identification process makes the content more dangerous from a competitive perspective, because it allows a company to use the idea while claiming technical compliance with privacy norms.
Thom’s conclusion was withering. “Sellke’s categorical answer was, at minimum, unjustifiably broad and materially misleading; looking back it was plainly dishonest.”
He went further, articulating a standard that many researchers in the field clearly share: it “would be ethically indefensible” if nonpublic research supplied by users helped improve models that the company then used to race those very same users to publication, without consent, proper disclosure, or credit.
This Is Not a Typical Copyright Dispute
The ongoing fight over whether OpenAI used Thom’s work is not a re-run of the familiar copyright battles that have pitted authors, artists, and news publishers against generative AI companies. Those disputes generally concern published material, books, articles, images, that was already in the public sphere. Here, the material in question is different in kind: it is unpublished research, shared in confidence with a software tool that many mathematicians now treat as a legitimate research collaborator.
How Does This Affect Researchers Who Use AI Tools?
It fundamentally changes the calculus of whether mathematicians can trust AI systems with their most valuable asset: unpublished ideas. When a researcher pastes a partial proof or a novel construction into a chatbot window, they are acting on the reasonable assumption that the exchange is private and will not come back to haunt them.
If the chatbot provider is simultaneously using those exchanges to train models that will eventually compete for the same discoveries, the researcher is unwittingly funding and fueling the machine that could beat them to publication. The result, Thom and others have argued, would be a chilling effect on collaboration: researchers would stop using AI tools, or worse, stop sharing ideas even with each other, for fear of tipping off an increasingly powerful corporate competitor.
This is not a hypothetical concern. OpenAI’s own description of the Navier-Stokes episode makes clear that the company’s decision to pursue the problem was triggered by rumors that other researchers had made major progress. In that context, the line between legitimate competitive research and opportunistic data harvesting becomes disturbingly fine.
Mathematicians Fear a New Era of Secrecy
The cumulative effect of these incidents has left what mathematicians are already describing as a sour taste in the mouth of the field. Numerous researchers have expressed concern that behavior like this will push mathematics into a more secretive state. Mathematics has long been a discipline that prides itself on openness; preprint servers, public seminars, and collaborative problem solving are the lifeblood of the field. If mathematicians begin to worry that even rumors of progress could ignite a race with a well-resourced tech giant eager for glory, that culture could erode quickly.
The irony is not lost on observers: OpenAI’s achievements in mathematics are genuinely remarkable. Its announced solution to the Navier-Stokes problem, if verified, would be an extraordinary accomplishment, the kind of milestone that could redefine what AI systems are capable of. Its other results, including the non-sofic groups advance, similarly point to a future in which machines contribute meaningfully to the most abstract human intellectual pursuits. But these achievements are being overshadowed by the company’s apparent reluctance to engage transparently with the community whose work it so clearly depends on.
What OpenAI Can Do to Rebuild the Community’s Trust
Thom’s demands are specific and, by the standards of scientific integrity, not unreasonable. He wants OpenAI to prove that it did not use his work by disclosing all relevant datasets, clarifying its data retention and training policies, and explaining how user interactions are processed. He wants a clear answer to a clear question: Did his conversations with ChatGPT contribute to the non-sofic groups result?
OpenAI has not yet provided that answer. The company did not immediately respond to a request for comment on Thom’s accusations.
The broader question is whether OpenAI, or any company operating at this scale, is structurally capable of providing the kind of transparency Thom is demanding. Modern training pipelines are staggeringly complex. Data flows in from countless sources, is filtered, cleaned, and transformed, and then passes through multiple stages of model training and fine-tuning. Even the engineers who build these systems may not have a complete inventory of what went into a given model at a given time. And the competitive stakes are enormous: full disclosure of training data could reveal proprietary techniques and strategic priorities that OpenAI has no commercial interest in sharing.
Why Did OpenAI Choose to Race Researchers in the First Place?
The answer goes to the heart of how AI research is now conducted. OpenAI is no longer just a research lab; it is a commercial entity locked in a high-stakes competition with other tech giants, and prestige in frontier mathematics confers substantial strategic advantages. Early rumors of a Navier-Stokes breakthrough in a rival group were enough to trigger a response. When mathematical glory is on the line, the incentive structure pushes toward speed, and speed often comes at the expense of careful attribution and ethical deliberation.
But mathematics is not like software engineering. Credit, provenance, and the careful attribution of ideas are not mere formalities in the field; they are the currency of trust that makes collaborative progress possible. A company that burns that trust, even once, may find itself frozen out of the informal networks and preprint exchanges that are the lifeblood of modern research.
In the long term, the resolution of this dispute will shape how the mathematical community and the broader scientific world integrate AI tools into research practices. Mathematicians who double as AI users need clear, enforceable guarantees about how their data is stored, used, and disclosed. OpenAI has an opportunity to set a new standard for data ethics in the field, and its response to Thom’s demands will be watched closely by researchers far beyond the small circle of group theory specialists.
For now, Thom is left with a simple and uncomfortable observation: “Only OpenAI has the relevant data” to answer the question that now hangs over the company’s most celebrated mathematical achievement. Whether OpenAI is willing to provide that evidence, and whether it can do so convincingly, will determine not only Thom’s verdict on the company but also the willingness of the world’s mathematicians to participate in the age of AI-assisted discovery. The burden of proof is clear. The ball is in OpenAI’s court.
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