Second mathematician questions OpenAI’s math claims

Andreas Thom, Professor of Geometry at TU Dresden, says his own conversations with ChatGPT may have fed into one of the mathematical results OpenAI presents as the work of its model. He also accuses the company of being dishonest about its training data. Thom made the charge in posts on Mastodon, and Quartz reported it on September 10.

The result at issue is in his own field. OpenAI says an internal version of its next major model, Astra, produced ten new results in mathematics and theoretical computer science, each on a problem that had been open for at least a decade. It published them on August 1 with a 249-page manuscript and Lean 4 certificates for every result on GitHub. The headline result is the first explicit construction of a non-sofic group, a group that cannot be approximated by finite permutation groups. The question had been open since Mikhail Gromov introduced soficity in 1999.

The Verge reports that OpenAI’s non-sofic construction built heavily on earlier work by Thom and Gábor Kun. Thom’s complaint goes beyond citation. He says his interactions with ChatGPT may have contributed to the announcement itself, so the question is whether something OpenAI credits to Astra partly started with the expert whose work it builds on. Lean files let anyone with the compiler check a proof without trusting the model or the people running it, as TNW notes. But they only show that the proofs hold. They say nothing about where the ideas came from, and that is the part Thom disputes.

Thom is the second mathematician to go public, by The Verge’s count. The first was Tristan Buckmaster, who disputed OpenAI’s account of a Navier-Stokes proof only days earlier.

Mathematicians had raised attribution as an issue before either complaint. In June they issued the Leiden Declaration, which the International Mathematical Union endorsed. TNW says it warns that AI companies are using published research without consent, bypassing peer review and threatening the integrity of proof and attribution.

The ten results also have strong supporters. Thomas Bloom, who runs erdosproblems.com, called them “big news” on X and rated them as more significant than the model family’s earlier counterexample to the Erdos unit distance conjecture.