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Four Color Theorem

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.

  1. 01

    The Map Coloring Problem

    What is the four color conjecture and why does it matter?

    3 demos
  2. 02

    From Maps to Graphs

    Dual graphs, planar graphs, and the graph theory reformulation

    3 demos
  3. 03

    Euler's Formula & Planarity

    V - E + F = 2, Kuratowski's theorem, and why planarity matters

    3 demos
  4. 04

    Kempe Chains & Early Proof Attempts

    Kempe's proof attempt, Heawood's correction, and the five color theorem

    3 demos
  5. 05

    Reducibility & Discharging

    The two pillars of the proof: reducible configurations and the discharging method

    3 demos
  6. 06

    The Computer-Assisted Proof

    Appel-Haken 1976, the proof controversy, and modern verification

    3 demos
  7. 07

    Extensions & Applications

    Chromatic polynomials, list coloring, and beyond four colors

    3 demos

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