In May 2026, two AI efforts reported results on genuinely open problems in mathematics - questions to which no one knew the answer - rather than on known competition problems with existing human solutions. This is a different and harder bar than the olympiad results of prior years, where the problems were new to the system but already solved by the contest organizers.
On 20 May 2026, OpenAI announced that one of its models had produced a counterexample disproving the Erdos unit distance conjecture, an open question in discrete geometry dating to the 1940s about how many pairs of points among n points in the plane can be exactly one unit apart. OpenAI’s announcement, published at its canonical news URL and corroborated by independent reporting and the mathematical writeup below, framed the result as coming from a general-purpose reasoning model rather than a system built specifically for mathematics. The result was taken seriously enough by the mathematical community that a group of mathematicians - Noga Alon, Thomas Bloom, W. T. Gowers, Daniel Litt, Will Sawin, Arul Shankar, Jacob Tsimerman, Victor Wang, and Melanie Matchett Wood - posted a short paper to arXiv the same day (2605.20695) presenting, in their words, “a short, digested, human-verified version of the recent OpenAI-generated counterexample to the Erdos unit distance conjecture, and a sequence of reflections on it.” That the result was independently digested and verified by named mathematicians is the load-bearing point; the library notes this verification rather than relying on the lab’s claim alone.
The following day, 21 May 2026, researchers at Google DeepMind posted a paper to arXiv (2605.22763), “Advancing Mathematics Research with AI-Driven Formal Proof Search,” describing a framework they call AlphaProof Nexus. According to the paper, an agent built on the framework autonomously resolved 9 of 353 open problems from a curated list of Erdos problems and proved 44 of 492 open conjectures from the Online Encyclopedia of Integer Sequences (OEIS). The DeepMind approach pairs a language model that proposes proofs with the Lean proof assistant, which mechanically checks every step, so a result that passes is a formally verified proof rather than persuasive-looking text. AlphaProof Nexus builds on the earlier AlphaProof system that reached silver-medal level at the 2024 International Mathematical Olympiad.
These results extend the AI-for-science pattern into the frontier of open mathematics. They are distinct from the competition milestones that preceded them: AlphaGeometry solved olympiad geometry problems near gold-medal level in 2024 (see 2024-alphageometry), and AI systems reached certified gold-medal standard at the 2025 IMO (see 2025-imo-gold-ai), but in both cases the problems had known solutions. The May 2026 results concern questions that were genuinely unsolved. Two notes of caution are worth keeping in view: the headline counts (nine Erdos problems, dozens of OEIS conjectures) come from the labs’ own papers, and the significance of the OpenAI counterexample rests on the independent human verification described above rather than on the announcement by itself.