Explore one of mathematics' most celebrated theorems through 21 interactive demonstrations.
See also: Graph Theory for the graph coloring framework the proof reduces to, Topology for the planarity that makes four colors enough, and Proof Techniques for the case-analysis style of the computer-assisted proof.
What is the four color conjecture and why does it matter?
Dual graphs, planar graphs, and the graph theory reformulation
V - E + F = 2, Kuratowski's theorem, and why planarity matters
Kempe's proof attempt, Heawood's correction, and the five color theorem
The two pillars of the proof: reducible configurations and the discharging method
Appel-Haken 1976, the proof controversy, and modern verification
Chromatic polynomials, list coloring, and beyond four colors