Everyone is familiar with maps, but not everyone knows that drawing a map should use at least several colors to distinguish neighboring countries or different regions. This map coloring problem is a famous mathematical problem, which has attracted several generations of outstanding mathematicians to fight for it, and has achieved outstanding results one after another, adding luster to the development of mathematics.

Distinguish two neighboring countries or regions on the map and paint them with different colors. For example, you can see a map representing the provinces and regions of a country, where the dotted line represents the provincial boundaries. Two colors don't matter, three colors are enough. A, B and C provinces each use one color, and D and B provinces use the same color.

Another example is the picture on the left (picture P 170), where 1, 2, 3 and 4 represent four countries. Because any two of the four countries in this map have a common border, they must be distinguished by four colors.

Therefore, some mathematicians suspect that only four colors are enough to color any map.

The time when the problem of map coloring was formally put forward was 1852. At that time, Francis, a student of the University of London, asked his teacher, Morgan, a famous mathematician and professor of mathematics at the University of London, this question. Morgan couldn't solve it, so he turned to his mathematician and couldn't solve it. Therefore, this problem has been handed down.

Until September 1976, the Bulletin of the American Mathematical Society published a news that shocked the global mathematical community: Abel and Hagen, two professors at the University of Illinois in the United States, used computers to prove that the four-color conjecture of the map was correct! They turned the four-color problem of the map into the four-color problem of 2000 thematic maps, then calculated 1200 hours on the computer, and finally proved the four-color problem.