OpenAI says its reasoning model solved a mathematical proof for a decades-old problem. (Image: OpenAI)
OpenAI has said that its unreleased AI reasoning model solved a decades-old mathematical problem that had remained unsolved for nearly 80 years.
The model produced an original mathematical proof disproving a famous geometry conjecture, OpenAI said in a blog post published on Wednesday, May 20.
At the centre of the purported breakthrough is the ‘Planar unit distance problem’ first posed by [who is he?] Paul Erdos. The problem asks a deceptively simple question: if points are placed on a flat two-dimensional plane, how many pairs of those points can be exactly one unit apart from each other?
For decades, mathematicians believed the most efficient arrangements resembled square-grids structures. Although researchers kept refining the theory, the prevailing assumption remained uncontested.
The model has discovered an entirely new family of mathematical constructions that outperform traditional grid-based arrangements, according to OpenAI. In simple terms, the model found a more efficient way of arranging points in a plane than experts had so far considered possible.
AI reasoning models have increasingly shown progress in mathematical capabilities over the past few years. In 2024, researchers from Google DeepMind introduced Alpha Geometry, an AI model capable of solving complex geometry problems at a level comparable to International Mathematical Olympiad contestants.
OpenAI and Google DeepMind’s unreleased models posted similar results at the prestigious math competition held in 2025. However, OpenAI has also sparked controversy surrounding its mathematical claims.
Last year, the company faced criticism after former OpenAI vice president Kevin Weil claimed on X that GPT-5 has solved multiple unsolved Erdo’s problems. The post was later deleted after AI researchers including Yann LeCun and Google DeepMind CEO Demis Hassabis said that the model had rediscovered solutions already present in academic literature rather than solving it from scratch.
“This result marks an important moment in the interaction between AI and mathematics: an AI system has autonomously resolved a longstanding open problem at the center of an active field. It also offers an early glimpse of a new kind of collaboration between AI and human mathematicians,” OpenAI said.“Those capabilities matter beyond mathematics. If a model can keep a complicated argument coherent, connect ideas across distant areas of knowledge, and produce work that survives expert scrutiny, those are also useful abilities in biology, physics, materials science, engineering, and medicine, and they are part of our longer-term path toward more automated research: systems that can help scientists and engineers explore more ideas and pursue harder technical questions,” it added.
To support its announcement on Wednesday, OpenAI published comments from mathematicians including Noga Alon, Thomas Bloom and Tim Gowers, who reviewed or commented on the findings.
“AI is helping us to more fully explore the cathedral of mathematics we have built over the centuries,”
— said Thomas Bloom, while hinting at the possibility of further discoveries. Fields medalist Tim Gowers, writing in the companion paper, calls the result “a milestone in AI mathematics.”
(This article has been curated by Shivani P Menon, who is an intern with The Indian Express)
