Four-color theorem

Four-color theorem, also known as four-color conjecture and four-color problem, is one of the three major mathematical conjectures in the world. The essence of the four-color theorem is the inherent property of a two-dimensional plane, that is, two straight lines in the plane that cannot intersect and have no common points. The four-color theorem was first put forward by a British college student named Goodrich.

The content of the four-color problem is: "Any map with only four colors can make countries with the same border have different colors." In other words, a map only needs four colors to mark it, which will not cause confusion.

Expressed in mathematical language, it means "divide the plane into non-overlapping areas at will, and each area can always be marked with one of the four numbers 1234, without making two adjacent areas get the same number." The contiguous zone mentioned here means that there is a whole section of boundary that is common. If two regions intersect at only one point or a limited number of points, they are not adjacent because coloring them with the same color will not cause confusion.

In the years after the problem was put forward, many people proved that five or more two-connected regions could not be constructed on the two-dimensional plane, but they did not rise to the level of logical relationship and two-dimensional inherent attributes, which led to many wrong counterexamples. But these are precisely the textual research and development promotion of the rigor of graph theory.

The invention of high-speed digital computer urges more mathematicians to study the "four-color problem". After the emergence of electronic computers, the process of proving the four-color conjecture has been greatly accelerated due to the rapid improvement of calculation speed and the emergence of man-machine dialogue.

1in June, 976, it took 1200 hours to make 1000 billion judgments on two different computers of the University of Illinois in the United States. As a result, no map needs five colors, which finally proves the four-color theorem and causes a sensation in the world.

However, computer proof cannot give a convincing thinking process. Although the computer has made tens of billions of judgments, it has only succeeded in a huge number of advantages, which does not conform to the strict logic system of mathematics. So far, countless math lovers have devoted themselves to it.

For more than a century, mathematicians have racked their brains to prove this theorem, and the introduced concepts and methods have stimulated the growth and development of topology and graph theory. In the research process of "four-color problem", many new mathematical theories have emerged and many mathematical calculation skills have been developed.

For example, mathematicians turned the coloring problem of maps into a graph theory problem, which enriched the content of graph theory. Moreover, the "four-color problem" has also played a role in effectively designing airline flight schedules and designing computer coding programs.