Mark Sellke

General-Purpose AI Finds Better Construction for Planar Unit Distance Problem

OpenAI says a general-purpose reasoning model has found a new family of constructions for the planar unit distance problem, a combinatorial geometry question posed by Paul Erdős in 1946. The result challenges a decades-old expectation that roughly square-grid arrangements were essentially best possible, and mathematicians including Timothy Gowers and Mark Sellke describe it as a clear case of AI producing a breakthrough on a prominent open problem. OpenAI frames the result as evidence that AI can accelerate research by exploring long, delicate chains of reasoning, while leaving problem choice and interpretation to human experts.