Paul Erdős

New Capabilities

Deceased; legacy problems continue to drive research

On May 20, 2026, OpenAI disclosed that an internal AI model had found a counterexample to the planar unit distance conjecture, a problem Erdős posed in 1946. Mathematicians who checked the result say it is a genuine advance, the first historically significant proof by an AI model.

Updated Oct 16

New Capabilities

As of May 2026: Original problem-poser, deceased

For 80 years, mathematicians believed square grids were the best way to pack points at distance exactly 1 apart on a plane. On May 20, an internal OpenAI reasoning model produced a counterexample, using algebraic number theory to beat the grid by a small polynomial factor. Nine outside mathematicians verified the proof.

Updated May 24