Mathematicians demand proof OpenAI didn't use their work
Andreas Thom, a mathematician who studies non-sofic groups, published a series of posts on Mastodon accusing OpenAI of dishonesty and a lack of transparency about the sources of its models' training data. The claim comes days after Tristan Buckmaster, a mathematics professor at New York University, raised a similar suspicion about possible use of his work through Codex. The two cases point to a pattern: researchers who interact with the company's tools subsequently see breakthroughs in their fields and wonder whether their conversations fed the model.
Non-sofic groups and Thom's connection
One of the ten mathematical achievements OpenAI announced last month concerned precisely Thom's specialty — non-sofic groups, infinite mathematical structures that cannot be approximated by finite ones. The company acknowledged the achievement relied heavily on prior work by Thom and the mathematician Gábor Kun. Thom noted the model displayed "detailed mastery of our techniques," which he said were not the obvious or most promising path to a solution at the time. The fact the original announcement did not mention their recent contribution drew criticism from the mathematical community, and OpenAI quietly corrected the document.
The answer that didn't satisfy Thom
Thom emailed OpenAI researchers Sébastien Bubeck and Mark Sellke, a statistician at Harvard, asking whether his conversations with ChatGPT were "part of the training data or accessible to the reasoning process." The reply addressed only direct access to conversations, not whether their content entered the vast training datasets the company uses to improve its models. "No explanation, qualification or evidence was provided," Thom wrote. "I see this as dishonesty at the very least." Researchers, he argued, are not equipped to reverse-engineer OpenAI's training pipeline; only the company holds the relevant data.
The pattern repeats: Navier-Stokes and "hidden" data
That evasion recalls how OpenAI defended its millennium-prize breakthrough, a solution to the Navier-Stokes equations governing fluid motion. In an official post the company denied using specific user data: "We did not see any of their work through any means until they published it publicly." In the same breath it added: "While unlikely, we cannot rule out that de-identified data derived from their use of our products helped improve our models." Thom calls it the same vague distinction: "De-identification may remove a name; it does not remove the intellectual content of a mathematical idea." Buckmaster, for his part, worked on the problems with Anthropic researcher Levent Alpöge in a personal capacity.
What this means in practice
The problem is not only legal; it is methodological. When a model achieves a breakthrough in a narrow field with few active researchers, the ability to separate "general knowledge" from a specific user's concrete contribution becomes theoretical at best. OpenAI demands trust without supplying the transparency required to verify it — disclosure of datasets, training configurations and the conditions that determine how user data enters, or does not enter, the development cycle. Until that happens, the academic community will continue to treat every breakthrough as suspect, and with good reason.