Four color theorem | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-27

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Four_color_theorem


00:01:39 1 Precise formulation of the theorem
00:04:58 2 History
00:05:07 2.1 Early proof attempts
00:09:09 2.2 Proof by computer
00:14:14 2.3 Simplification and verification
00:15:44 3 Summary of proof ideas
00:17:14 4 False disproofs
00:27:00 5 Three-coloring
00:29:24 6 Generalizations
00:29:47 7 Relation to other areas of mathematics
00:33:08 8 Use outside of mathematics
00:34:52 9 See also
00:35:15 10 Notes
00:36:12 11 References



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SUMMARY
=======
In mathematics, the four color theorem, or the four color map theorem, states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color. Adjacent means that two regions share a common boundary curve segment, not merely a corner where three or more regions meet.Unlike the five color theorem, a theorem that states that five colors are enough to color a map, which was proved in the 1800s, the four color theorem was proved in 1976 by Kenneth Appel and Wolfgang Haken, but only after many false proofs and counterexamples. It was the first major theorem to be proved using a computer. Initially, their proof was not accepted by all mathematicians because the computer-assisted proof was infeasible for a human to check by hand. Since then the proof has gained wide acceptance, although some doubters remain.To dispel any remaining doubts about the Appel–Haken proof, a simpler proof using the same ideas and still relying on computers was published in 1997 by Robertson, Sanders, Seymour, and Thomas. Additionally, in 2005, the theorem was proved by Georges Gonthier with general-purpose theorem-proving software.