Mark Sellke

Assistant Professor of Statistics at Harvard University and researcher at OpenAI. He works on high-dimensional probability, optimization, machine learning theory, and recent mathematical advances involving large language models.

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.

OpenAIMay 20, 20265 min read