One of the world s three major mathematical problems in modern times, the four color conjecture, cam

Francis of England. Guthrie.

So farFour-color conjectureIt is still a unique example of a mathematical problem proved by a computer, but it shows the advent of the era of machine proofs. It may open up a new avenue for people to work with machines to solve problems, becoming a mathematical seriesNew thinkingThe starting point. Second, the proof of the four-color conjecture is a verification of the relationship between the AI machine and the human being.

Through the application of artificial intelligence, finding a way to solve some mathematical problems should not cause some concerns to people in front of artificial intelligence machines.

Humans seem to be so small and incompetent that this even leads to the fear of machines replacing the human brain, the four-color conjecture was the first big theorem to be proved with the aid of a computer, but mathematicians dominate the whole proof, and computers are only mechanically operated, the four-color conjecture seems to be an isolated problem in the nature of mathematical games, but it creates many new branches of graph theory. Mathematicians are able to turn complex things into simple objects.

This can be done from the four-color problem.

, a region can be considered as a point, any two regions are either adjacent, i.e. a common boundary, or not adjacent, if the points representing the two regions are adjacent, then we connect a line between the two points, otherwise it will not be connected. Such a structure is called a graph. The problem of four colors becomes a problem of coloring the vertices of the graph, that is, if two vertices are joined together.

Then they must be drawn in different colors, and in order to fully prove the stability theorem of the four-color conjecture, we still need to work hard conceptually, especially to find a reducible configuration, i.e., the case of reducing the problem of a large number of regions to a small number of regions. In the '60s and '70s, there were an estimated 8,000 to 10,000 such configurations, which computers couldn't do.

The question of why the question of what the four-color conjecture is has puzzled mathematicians for nearly half a century is explained today.

Generally speaking, the four-color theorem is that it is impossible to construct five or more regions connected by pairs on a sphere or plane, and if there are more than five regions connected by pairs, the fifth region is the same color as the other region. The reason that has plagued mathematicians for half a century is that many people do not take into account the inherent properties and logical relationships of two-dimensional planes.

The essence of the four-color theorem is the intrinsic property of the two-dimensional plane, that is, two straight lines that cannot cross without a common point in the plane. Many people have proved that it is impossible to construct five or more two-by-two regions in a two-dimensional plane, but they have not raised them to the level of logical relations and intrinsic properties of two-dimensional, so that many pseudo-counterexamples have appeared.

For any one map, you can paint adjacent areas with different colors with just four colors. The reason why it has been bothered for more than half a century is that for a map, the composition of different regions is too complex and there are too many possibilities.

The four-color conjecture is still a unique example of a mathematical problem proved by a computer, but it shows the advent of the era of machine proofs. The four-color conjecture may seem like an isolated problem in the nature of mathematical games, but it has created many new branches of graph theory.