[The Four Color Theorem] A Mathematical Drama Surrounding a Difficult Problem
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☆☆☆☆
~What is the Four Color Theorem?~
This book depicts a mathematical drama through the history of the struggles of mathematicians until the "Four Color Theorem" was solved.
First, what is the "Four Color Theorem"?
It is the question: Can any map be colored with at most four colors such that no two adjacent countries share the same color?
Many mathematicians challenged this seemingly simple problem, and it took 124 years before it was solved.
In the world of mathematics, it is said that the simpler a problem is, the harder it is to solve, and this Four Color Theorem is a good example of that.
The process leading up to the solution of this problem is exactly where the fascination of mathematics lies. The drama surrounding a problem that stumped numerous geniuses is extremely rewarding to read.
~What is human thought?~
Countless geniuses examined various patterns and conditions to solve this problem, engaging in trial and error, yet the "Four Color Theorem" refused to be caught, as if mocking them at every turn.
It is ironic that the existence of a computer was necessary to solve this problem.
As a result, the reality is that the "Four Color Theorem" was solved by brute force using a computer, and not by a simple, easy-to-examine proof—what is known as an "elegant proof."
Although the conclusion that "four colors are sufficient to color a map" was reached through massive calculations by a complex program, it is impossible for humans to verify the details of such large-scale computer processing.
Can we truly say this has been "proven"?
This question, posed toward the end, is in a sense also a question for modern society.
Does concluding that mathematics, as an activity of human thought, has been "solved" by the power of a computer negate human thought? Or do we accept the computer as an extension of human thought?
In any case, this question is close to the issue of how we will deal with the challenges and problems of our modern, AI-driven world.
The question expands into the philosophical realm of the relationship between machines and humans.
Whether or not to accept a "proof" that is complex and incomprehensible to humans—this judgment will become a resolve that determines our own behavior in an increasingly mechanized modern age.