I kidnapped an alien civilization

Li Mo came to the library with his schoolbag on his back. Standing on the steps of the library, he looked at the students carrying their schoolbags outside. Now he understood the saying high school depends on teachers, and university depends on oneself.

Yanda's library is Li Mo's mysterious treasure. The books on the bookshelf here are all attractive points in Li Mo's eyes. He is not in a hurry to read the book today, the most important thing now is to publish a paper that can complete the task. The requirement of the task is an A-level paper, which means that Li Mo can only submit the manuscript of the paper to the core journals. The papers published in the core journals are all influential papers, so this means that only some well-known difficulties can be selected as the title of the paper.

Li Mo flipped through the collection of math problems he brought from home, he knew that his current math level could not solve very high-level problems. NP-complete problems are not acceptable, Hodge's conjecture is not acceptable, Poincaré's conjecture is not acceptable, and the Riemann hypothesis is not acceptable.

At this time, a simple topic came into view: four-color conjecture. This one has hope!

Li Mo gained some experience from the last proof of Collatz's conjecture. The solution of some mathematical problems may not require particularly advanced mathematical knowledge, and sometimes only an inspiration can be solved.

He went on to read that the definition of the four-color conjecture is to color any (on a plane) map, requiring adjacent countries to have different colors, and only four colors are enough.

Li Mo thinks that the problem looks very simple, maybe only the knowledge of graph theory and topology can be solved.

If you want to solve an unsolved problem in mathematics, you should fully understand its history, because many mathematicians have studied it in history. You can stand on the shoulders of these mathematicians and see farther.

Li Mo carefully read the history of the four-color conjecture. Its first written record appeared in a letter from Morgan, a professor of mathematics at the University of London, to Mr. Hamilton in 1852. In the letter, Morgan described a problem: A student asked me today to explain the truth of a fact, and we don't know whether it can be regarded as a fact. He said that arbitrarily dividing a graph and coloring each part of it makes any Parts with common borders have different colors, and only four colors, no more. . What do you think? If this issue is true, can it attract people's attention?

In the following decades, everyone thought that this was a theorem that did not need to be proved. Until 1878, the head of the London Mathematical Society officially announced this problem, and the four-color problem was finally formed.

In 1978, a lawyer announced that he had proved the four-color conjecture. Eleven years later Heawood pointed out one of the grave mistakes. At the same time, it also pointed out that the lawyer's method can be used to prove that five colors are definitely enough-the five-color theorem.

In 1922 Franklin proved that each map with at most 25 countries could be colored with four colors.

In 1926 Reynolds extended this result to 27 countries.

In 1940 Winn certified 35 countries.

In 1950, the German mathematician Hich estimated that proving the four-color conjecture would involve about 10,000 different configurations.

In 1972, Haken and Appel joined forces. After four years of intensive work, they finally successfully proved the four-color theorem with a computer in June 1976.

For this violent solution proof method, many well-known figures in the mathematics field do not agree. They think that it should be proved by mathematical logical reasoning instead of this violent solution.

It's like someone asking how to put an elephant in the refrigerator. The answer is very simple. The first step is to open the refrigerator door. The second step is to push the elephant into the refrigerator, and the third step is to close the refrigerator door. As long as the refrigerator door is big enough, any kind of elephant can fit in it. This simple method is a violent solution, and it does not solve the problem logically.

Computer exhaustion is not a real mathematical proof. Mathematics is not a result-oriented subject, otherwise there would not be such famous conjectures that attract countless mathematicians all over the world.

It seems that solving the four-color conjecture requires the knowledge of graph theory and topology. Li Mo looked at the proof process of the four-color conjecture and calculated it in his mind.

1 hour, 2 hours, 3 hours, Li Mo stared at the simple topic in front of him. He finally understood why so many years had passed, and countless mathematicians had fallen on it.

Before he knew it, it was already ten o'clock in the evening, Li Mo still had no idea, he raised his head and looked around blankly. He found that the young man with gray hair on the seat next to him was still yawning and looking up documents.

Is this what I will look like in a few years? Li Mo thought with a little fear.

He stuffed the books into his bag indiscriminately and left the library. It was already dark outside, only the small street lamps on the side of the road radiated a little warm light.

The night at the end of October was already a bit chilly. Li Mo walked aimlessly along the path, with students passing by from time to time.

There seems to be a lake in front of it, the surface of the lake is rippling, and a bright moon seems to be rising in the lake. Li Mo looked at the lake and felt a sense of calm.

Didi. There is a new message on WeChat.

Li Mo opened WeChat, and Ying Sasa, who was wearing a fox head, sent a message: Hello, Li Mo, your orientation meeting will be held in self-study room 501 at 4:00 tomorrow afternoon, hope to attend on time.

It seems that the monitor's execution efficiency is very strong, Li Mo replied: Got it, I will attend on time, thank you monitor (smiley face).

As soon as Li Mo opened the door of the dormitory, he saw the fat man poking his head out from the bed. He stared at Li Mo for a long time.

Fatty, what's the matter? Li Mo couldn't stand being stared at like this, so he asked directly.

Fatty asked faintly: When did you become so familiar with Ying Sasa? She actually went to the Student Affairs Office to borrow a classroom for your orientation meeting.

Li Mo was a little confused, so he had to perfunctory: I only met the English monitor in the linear algebra class. As for her special use of the classroom, I think it's because she is an enthusiastic person.

The fat man cast a glance at Li Mo, and got under the covers with a disbelieving expression.

The dormitory was completely dark, Li Mo lay on the bed and stared.

Pajero, Li Mo called softly in his heart.

The gray fog filled the air, and a pink learning machine appeared in front of his eyes.

Current properties:

1. Mathematics grade: 3 (150/10000)

2. Physics grade: 0 (0/100)

3. Chemical grade: 0 (0/100)

4. Biology grade: 0 (0/100)

5. Wisdom level: 1

Current available credits: 5050

Li Mo decided to add all available points to mathematics, which might be helpful for the thesis task.

1. Mathematics grade: 3 (6200/10000)

2. Physics grade: 0 (0/100)

3. Chemical grade: 0 (0/100)

4. Biology: 0 (0/100)

5. Wisdom: 1

Current available credits: 0

I don't know if it is a psychological factor, but Li Mo feels that his thinking is much clearer. Various mathematical logics of the four-color conjecture kept appearing in his mind, and he fell asleep unconsciously.