Combinatorics · Oct 6, 2026
The Euclidean plane cannot be colored with five colors
Proves that every five-coloring of the Euclidean plane has a monochromatic pair at distance one, with no restriction on the color classes. This advances the Hadwiger–Nelson problem: together with the classical seven-coloring, only six and seven remain possible chromatic numbers of the plane.
Contributors
Unreleased OpenAI model
AI systems: Unreleased OpenAI model