en.Wedoany.com Reported - An unreleased general-purpose reasoning AI system from OpenAI has independently generated a 125-page mathematical proof, overturning an 80-year-old famous conjecture in combinatorial geometry.
The problem, known as the unit distance problem, was posed by mathematician Paul Erdős in 1946. The core question is: given a set of points on a plane, what is the maximum number of point pairs that are exactly the same fixed distance apart? For decades, the mathematical community reached a consensus that a square grid is the optimal configuration for this problem, but this view had never been formally proven.
To refute this conjecture, the AI model identified an infinite family of point arrangements that outperform the grid. This means the model found not just isolated counterexamples, but an entire class of superior configurations, thereby overturning a decades-old proposition. The proof was verified by nine external mathematicians, including Fields Medalist Tim Gowers, who recommended that the result be submitted for publication in the Annals of Mathematics. Another verifier was mathematician Thomas Bloom, who had previously publicly pointed out false statements made by OpenAI itself in mathematics.
What makes this achievement particularly notable is that it did not come from a system specialized in mathematics, but from a general-purpose reasoning model, which can also be used for providing cooking advice, summarizing documents, and writing text. The model connected scattered threads of reasoning from mathematical literature, including work by researchers such as Golod-Shafarevich (1964), Ellenberg-Venkatesh (2007/2016), and Hajir-Maire-Ramakrishna (2021).
The paper published on the preprint platform arXiv, titled "Remarks on a Refutation of the Unit Distance Conjecture," translates the AI-generated 125-page proof into a shorter, clearer, and more verifiable mathematical language. In an independent verification article, the authors simplified and generalized the original argument, placed the proof in the context of existing literature, and reflected on the relationship between mathematicians and AI systems.
Experts noted that the problem that produced this result did not explicitly require refuting the conjecture; it was merely an open question about the truth of the conjecture. The model independently concluded that the conjecture was false and completed the proof. OpenAI stated that this is the first time artificial intelligence has autonomously solved a core open problem in mathematics. The proof is awaiting formal publication on arXiv, but the tool that generated it remains non-public. OpenAI mathematician Mark Sellke commented to Nature magazine: "This is a huge leap from what we were used to seeing just a month ago."
