OpenAI’s AI solves 80-year-old maths problem, marking major breakthrough for artificial intelligence

For decades, one of mathematics’ most famous unsolved problems quietly frustrated some of the world’s brightest minds. Now, OpenAI says one of its AI models has cracked it — not with step-by-step human guidance, but autonomously.
The breakthrough involves the “planar unit distance problem,” a mathematical question first posed by legendary mathematician Paul Erds in 1946. While the name sounds intimidating, the core question is surprisingly simple: if you place points on a flat surface, how many pairs of points can be exactly one unit apart from each other?
For nearly 80 years, mathematicians believed the best possible arrangements looked roughly like square grids. Researchers kept refining the theory, but nobody could fully disprove the long-standing assumption.
According to OpenAI, its internal reasoning model has now done exactly that.
The company says the AI discovered an entirely new family of mathematical constructions that performs better than the traditional grid-like approach. In simple terms, the AI found a smarter way to arrange points than humans had believed possible for decades.
While the planar unit distance problem may sound highly theoretical, the mathematics behind it has applications in areas such as network design, computer chip layouts, wireless communication systems, robotics, and materials science. Problems involving how points are arranged efficiently in space are important in everything from sensor networks to crystal structures.
What makes the result especially significant is not just the solution itself, but how it was achieved.
OpenAI says the system was not specifically designed to solve this particular puzzle or even mathematics problems alone. Instead, it was a general-purpose reasoning model capable of handling long and complex chains of thought. The proof was later checked by external mathematicians, who verified the result.
This marks the first time an AI system has autonomously solved a prominent open problem considered central to an active field of mathematics.