The four colour theorem and computer-assisted proof
Kenneth AppelWolfgang HakenGeorges Gonthier
This page delivers no verdict; it presents claims and evidence with their sources. No theory in science is absolute. Method
For everyone
In 1852 it was conjectured that every map can be coloured with at most four colours so that neighbouring countries differ. Appel and Haken proved it in 1976, but part of the proof relied on computer calculations too long for a human to check by hand. This started the debate over whether a computer calculation counts as a proof. In 2005 the proof was formally verified end to end with the Coq proof assistant.
For specialists
The proof shows the existence of an unavoidable set of 1,936 (later 1,476) "reducible configurations", each checked for reducibility by computer. Robertson, Sanders, Seymour and Thomas (1997) gave a simpler proof with 633 configurations. Tymoczko argued that the proof introduced an empirical element into mathematics and changed the concept of "proof".
Claims
Evidence
Connections
Sources
- Article (1977). Every planar map is four colorable. Part I: Discharging. Illinois Journal of Mathematics 21(3), 429–490DOI 10.1215/ijm/1256049011archive
- Article (2008). Formal proof — the four-color theorem. Notices of the American Mathematical Society 55(11), 1382–1393
- Article (1979). The four-color problem and its philosophical significance. The Journal of Philosophy 76(2), 57–83DOI 10.2307/2025976archive
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Cite this page
Athena contributors. (2026). The four colour theorem and computer-assisted proof. Athena: The tree of human knowledge. Retrieved November 1, 2026, from https://latifkedi.github.io/athena/en/d/dort-renk/
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title = {The four colour theorem and computer-assisted proof},
author = {{Athena contributors}},
year = {2026},
howpublished = {\url{https://latifkedi.github.io/athena/en/d/dort-renk/}},
note = {Athena: The tree of human knowledge. Accessed: 2026-11-01}
}Added: September 27, 2026 · Last changed: September 27, 2026 · Page history