Paul Erdős

New Capabilities

Deceased; legacy problems continue to drive research

For the first time, AI systems are independently solving mathematical problems that stumped human researchers for decades. Since Christmas 2025, 15 legendary Erdős problems have moved from 'open' to 'solved'—11 by AI, including the first on January 6, 2026, from OpenAI's GPT-5.2 Pro and Harmonic's Aristotle theorem prover.

Updated May 29

New Capabilities

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