What is Four color theorem?
[[File:Fourcolorsmap.svg|thumb|Three colors are not enough to color this map.]] [[Image:FourColorMapEx.png|right|thumb|Example of a four color map]] The '''four color theorem''' is a [[theorem]] of [[mathematics]]. It says that in any plane [[surface]] with [[region]]s in it (people think of them as [[map]]s), the regions can be colored with no more than four [[color]]s. Two regions that have a common [[border]] must not get the same color. They are called ''adjacent'' (next to each other) if they share a segment of the border, not just a point.<ref>{{cite journal |title=Formal Proof---The Four-Color Theorem |author=Georges Gonthier |journal=Notices of the AMS |volume=55 |issue=11 |date=December 2008 |pages=1382–1393}}From this paper: Definitions: A planar map is a set of pairwise disjoint subsets of the [[plane (geometry)|plane]], called regions. A simple map is one whose regions are connected open sets. Two regions of a map are adjacent if their respective closures have a common point that is not a corner of the map. A point is a corner of a map if and only if it belongs to the closures of at least three regions. Theorem: The regions of any simple planar map can be colored with only four colors, in such a way that any two adjacent regions have different colors.</ref> This was the first theorem to be proved by a [[computer]], in a ''[[proof]] by exhaustion''. In proof by exhaustion, the conclusion is established by dividing it into cases, and proving each one separately. There may be a lot of cases. For example, the first proof of the four color theorem was a proof by exhaustion with 1,936 cases. This proof was controversial because most of the cases were checked by a computer program, not by hand. The shortest known proof of the four color theorem today still has over 600 cases. Even though the problem was first presented as a problem to color [[map coloring|political maps of countries]], mapmakers are not very interested in it. According to an article by the math historian [[Kenneth May]] {{Harv|Wilson|2002|