An internal OpenAI reasoning model has done something that no AI system had pulled off before: it independently disproved a famous open conjecture sitting at the center of an active subfield of mathematics. The result was announced in late May, and OpenAI has now released a podcast conversation with the three researchers who ran the experiment, Alex Wei, Hongxun Wu, and Lijie Chen, walking through how it actually happened.

The headline is striking on its own. The proof is an important milestone for the math and AI communities, marking the first time that a prominent open problem, central to a subfield of mathematics, has been solved autonomously by AI. But the details of how the model got there are arguably more interesting than the result itself.

The 80-year-old puzzle

The problem in question is the planar unit distance problem, posed by Paul Erdős in 1946. It is a deceptively simple question that asks how many pairs of points can sit exactly one unit apart on a flat plane, and it has challenged mathematicians since 1946 as one of the best-known questions in combinatorial geometry.

For decades, the working assumption was that you could not do meaningfully better than a square grid. As the number of points grows, grid-like arrangements continue to appear to be remarkably effective. For decades it was widely believed these highly regular structures were about as good as it gets. Erdős himself conjectured that no construction could improve substantially on these intuitive arrangements, even for an extremely large number of points. Formally, he believed the answer was bounded by n^(1+o(1)), meaning the number of unit-distance pairs could only grow a hair faster than linearly.

What the model actually found

OpenAI's model produced a counterexample, not a tight solution. The construction gives a polynomial improvement. The model produced an infinite family of point configurations with at least n^(1+δ) unit-distance pairs for some fixed δ greater than zero.

Princeton mathematician Will Sawin then sharpened the argument shortly afterward. A refinement by Princeton mathematician Will Sawin made the improvement explicit, giving sets of arbitrarily large n points with more than n^1.014 unit-distance pairs. That fixed exponent above 1 is what makes the result decisive: the grid is no longer the ceiling.