The Four-Color Theorem Gets a Rare New Proof

The four-color theorem asks whether any map drawn on a flat surface can be colored using only four colors so that no two neighboring regions share the same color.

This problem, first noticed in 1852 by mathematician Francis Guthrie, seems straightforward but has baffled experts for over a century.

The theorem applies to planar graphs, which are mathematical representations of maps where regions become vertices (points) and borders become edges (lines connecting points).

For example, a map of Europe can be converted into a planar graph where countries like France and Germany are vertices connected by an edge.

The goal is to assign one of four colors to each vertex so no two connected vertices share a color.

Despite its simplicity, proving this theorem required decades of work and, eventually, the use of computers.