Preprint in the OpenAI Math release
The Euclidean plane is not five-colorable
OpenAI
Abstract
We prove that every coloring of the Euclidean plane with five colors has a monochromatic unit-distance pair, with no regularity assumption on the color classes. Consequently, the chromatic number of the plane is either six or seven.
open until 1 Jan 2028
est. 50% chance this result is independently verified by the end of 2027.
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