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The four colour theorem says that:

Given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colours are required to colour the map so that no two adjacent regions have the same colour.

From http://en.wikipedia.org/wiki/Four_colour_theorem

The theorem has been proved using computers. But I am wondering, is there a more simple proof than using computers to do it? I feel that using brute force to prove something is like the last resort. So, is there a simple proof of the Four Colour Theorem, or is it yet to be proved?

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Anonymous Computer
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3 Answers3

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A completely computer-free proof has yet to exist. However there are easy proofs for the five(and up) color theorems.

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no, there isn't. This has been proved using a computer which took hundreds of hours as you have to go through every proof separately.

user146126
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The four colour theorem was supposedly proved by 'Appel and Haken' by using a computer as a tool. They used the tool to supposedly go through every example possible. However there is no 'proof' that the proof actually happened and exists. I guess it can be proved by hand but it would take you years.. So the answer is no there is no simple proof of the four colour theorem.

user146215
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    There have been formally verified proofs of 4CT. Georges Gonthier created a proof verified by the coq proof assistant. Details here – NovaDenizen May 13 '14 at 14:54
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    You wrote "However there is no 'proof' that the proof actually happened and exists". What do you mean by this? Details were published in Appel, Kenneth; Haken, Wolfgang (1989), Every Planar Map is Four-Colorable, Providence, RI: American Mathematical Society, ISBN 0-8218-5103-9 – Casteels May 13 '14 at 14:58