Models Doing Science

An OpenAI reasoning model has autonomously solved the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946.

For nearly eighty years, mathematicians believed the optimal constructions looked roughly like square grids. The model discovered entirely new families of point configurations that perform better — and it did so by reaching across algebraic number theory, a field not traditionally connected to this geometry problem.

The resulting proof runs to 125 pages. It has been reviewed and validated by leading mathematicians, including Fields Medalist Timothy Gowers, who described the result as a milestone. Princeton’s Noga Alon called it an outstanding achievement.

What makes the result significant beyond mathematics is the nature of the reasoning involved. The model did not simply search known techniques. It formed novel connections between distant domains and produced a rigorous argument that human researchers had not found in eight decades. This is no longer retrieval or pattern matching — it is original scientific discovery.