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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