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A historic moment for mathematics and artificial intelligence.

An OpenAI reasoning model has achieved a major breakthrough on the famous Unit Distance Problem of Paul Erdős — one of the best-known problems in discrete geometry and one of Erdős’s favorite questions.

The problem asks:

How many pairs of points among points in the plane can be exactly one unit apart?

For nearly 80 years, mathematicians believed that the best constructions were essentially based on square-grid type arrangements.

Now, an OpenAI model has discovered entirely new constructions that outperform the classical ones, disproving a longstanding Erdős conjecture related to the problem. The result has been checked and discussed by leading mathematicians including Tim Gowers and Noga Alon.

The complete unit distance problem itself remains open, but this is already being viewed as a landmark moment in AI-driven mathematical discovery.

A fascinating glimpse into the future of mathematics.

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