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New Delhi: OpenAI says one of its internal AI models has solved a famous maths problem that kept researchers busy for nearly 80 years. The problem, first posed by Paul Erdős in 1946, is called the planar unit distance problem, and it asks a simple-looking question: if you place points on a flat plane, how many pairs can be exactly one unit apart?

The company said the proof was found by a general-purpose reasoning model, not a maths-only system built just for this puzzle. OpenAI has listed the work under its research section as a model that “has disproved a central conjecture in discrete geometry,” making this a major AI and maths story, not just a lab curiosity.

OpenAI model cracks old Erdos puzzle

For decades, mathematicians believed square grid-like point patterns were close to the best way to create the most unit-distance pairs. In basic words, imagine dots on graph paper. The game is to place them in such a way that the maximum number of dot pairs sit exactly one unit apart.

Erdős believed the answer would grow only a little faster than a straight line as more points were added. OpenAI now says its model found an infinite family of examples that beat that old belief by a clear margin.

The company said, “Today, we share a breakthrough on the unit distance problem.” It added that the proof “has been checked by a group of external mathematicians.”

Why this AI result matters

This is not a small classroom puzzle, even though it sounds like one. The unit distance problem sits inside combinatorial geometry, a serious area of maths. OpenAI said the result marks “the first time that a prominent open problem, central to a subfield of mathematics, has been solved autonomously by AI.”

AI tools have helped with coding, writing, search and data work for years. Here, the claim is bigger: the model found an original proof for a long-standing open problem.

Mathematicians react to the proof

Fields Medal winner Tim Gowers, writing in the companion paper, called it “a milestone in AI mathematics.” Number theorist Arul Shankar said, “In my opinion this paper demonstrates that current AI models go beyond just helpers to human mathematicians – they are capable of having original ingenious ideas, and then carrying them out to fruition”.

The proof used ideas from algebraic number theory, including infinite class field towers and Golod-Shafarevich theory. Yes, that sounds heavy. The simple version is this: the AI found a surprising link between deep number systems and a dot-arrangement problem on a flat plane.