OpenAI has reported a significant advance in artificial intelligence reasoning after one of its models successfully addressed an 80-year-old mathematical challenge.

The creator of ChatGPT said the breakthrough relates to the planar unit distance problem, a question first posed in 1946 by Hungarian mathematician Paul Erdős.

The problem is easy to state: given a collection of points on a plane, how many pairs of points can be exactly the same distance apart? Erdős conjectured that the number of such pairs would grow only slightly faster than the number of points.

However, OpenAI said its model reached a different conclusion, drawing on multiple areas of mathematics to identify a family of point arrangements that surpass the limit proposed in Erdős’s conjecture.

“For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids,” OpenAI wrote on X. “An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better.”

While the development has generated excitement among mathematicians, the broader problem remains unresolved. The AI did not determine a new growth rate for the number of equidistant point pairs; instead, it demonstrated that the upper limit proposed by Paul Erdős was too restrictive, leaving the central question of the problem unanswered.

OpenAI, which is preparing for a future stock market listing in the United States, said the result was achieved by a general-purpose reasoning model that tackles complex tasks by breaking them into smaller steps, rather than by a system designed specifically for mathematical research.

The company has previously faced criticism over claims of solving problems posed by Paul Erdős. Last year, OpenAI announced what it believed was a breakthrough, only for it to emerge that the model had reproduced findings already present in existing mathematical literature on which it had been trained.

This time, however, OpenAI said its work has been independently validated by mathematicians, including Thomas Bloom, who oversees the Erdős problems website and had previously criticised the company’s earlier claims regarding Erdős’s conjectures.