OpenAI's internal reasoning model has solved an 80-year-old mathematical puzzle. The planar unit distance conjecture, first posed by legendary mathematician Paul Erdős in 1946, has been disproven by the AI.
Erdős believed the maximum number of unit-distance pairs among n points on a flat plane grew slowly. The AI found a construction achieving approximately n^(1+0.014) unit distances, breaking through the decades-old ceiling. The exponent 0.014 may seem small, but it represents a fundamental breakthrough.
The model's proof was rigorously verified by Fields Medalist Tim Gowers and formalized by Princeton mathematician Will Sawin. OpenAI says this was not a general chatbot but a specially designed reasoning model for sustained logical thought.
This disproof reshapes combinatorial geometry, with implications for computational geometry, network design, and optimization.