# Essay on The Four Color Theorem

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Since hundred years ago, when people started to make maps to show distinct regions, such as states or countries, the four color theorem has been well known among many mapmakers. Because a mapmaker who can plan very well, will only need four colors to color the map that he makes. The basic rule of coloring a map is that if two regions are next to each other, the mapmaker has to use two different colors to color the adjacent regions. The reason is because when two regions share one boundary can never be the same color. Another basic rule of coloring a map is that if two regions share only one point, then they do not necessary have to be colored differently. Many evidence showed that coloring a map required at least four colors but no more than five. Then mathematicians started to asked questions, such as “ Is it true that using only four colors are enough? Is there any exception that one has to color a map that requires more than four colors? Or is it has to do with a special sequence of arrangement that involved with different regions in order to make the theorem true?” However, the first mathmatician who asked these questions is a man named Francis Guthrie. He was the first one who posed the four color problem in1852.
Francis Guthrie was a mathematician and at the time he was a student of Augustus De Morgan at University College London. While Francis Guthrie was coloring the map of counties of England, he noticed that there should be at least four colors to color regions in order to make two adjacent regions have two different colors. Later he tried to prove this theorem but he failed. After he graduated from London and started to study law but at the same time his brother, Frederick Guthrie, became a student of ...

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...s were found and the mistakes were easily fixed. They said if the four color theory was false, then there should be at least one map that has a very small number of regions that have five colors. But the proof showed that this kind of situation cannot exits, one reason is because if the small part of the original map can be colored with four colors, then the original map can also be colored with four colors. This suggests that if the original map can not be colored with four colors, its small part of map can not either.
The Four Color Theorem was one of the first major theorem that was proved by the computer. It is the proof that can not be verified by many mathematicians. But the independent verification had convinced people that the theorem was finally proved. I believe because of the new technology, the proof of Four Colo Theorem will be improved in later time.

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