OpenAI announced May 20, 2026 that an internal general-purpose reasoning model produced a counterexample to Paul Erdős’s 1946 unit distance conjecture. Unlike the discredited October 2025 announcement, this arrived with a companion verification paper co-authored by nine external mathematicians, including Thomas Bloom — the researcher who publicly exposed the earlier false claim.
Fields Medalist Tim Gowers said he would recommend the result for acceptance in the Annals of Mathematics without hesitation.
The companion arXiv paper lists Noga Alon, Thomas Bloom, W.T. Gowers, Daniel Litt, Will Sawin, Arul Shankar, Jacob Tsimerman, Victor Wang, and Melanie Matchett Wood as authors. They describe their document as “a short, digested, human-verified version of the recent OpenAI-generated counterexample.”
The underlying proof file was generated in one shot by the model, with exposition subsequently refined through human interaction with Codex.