I Kidnapped An Alien Civilization

2021-07-07

Chapter 27 Four-color conjecture

Li Mo came to the library with a schoolbag and stood on the steps of the library , He looked at the classmates who were carrying schoolbags outside. He now understood the phrase “high school depends on the teacher, university depends on yourself”.

Yan Da’s library is Li Mo’s mysterious treasure. The books on the shelves here are all attractive points in Li Mo’s eyes. He is not in a hurry to read books today, the most important thing now is to publish a paper that can complete the task. The requirements of the task are A-Rank papers, which means that Li Mo can only submit manuscripts to core journals. The papers published in the core journals are all influential papers, so this means that only some well-known “problems” can be selected as the paper topics.

Li Mo flipped through the set of math problems he brought from home, and he knew that he could not solve very proven problems with his current math level. NP-complete problem does not work, Hodge conjecture does not work, Poincaré conjecture does not work, Riemann hypothesis does not work.

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

Li Mo has gained some experience from the last proof of the Koraz conjecture. The solution of some mathematical problems may not require special mathematical knowledge, and sometimes it can be solved only by an inspiration.

He continued to read, the definition of the four-color conjecture is to color an arbitrary (planar) map, requiring adjacent countries to have different colors, and only four colors are enough.

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

To solve a mathematical unsolved problem, 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 further.

Li Mo went through the history of the four-color conjecture, the first written record of which appeared in a letter to Mr. Hamilton in 1852 by Morgan, a professor of mathematics at the University of London. In the letter, Morgan addressed a problem: “A student asked me today to justify a fact, and we don’t know if it could be considered a fact. He said that arbitrarily dividing a figure and coloring each of its parts makes any Parts with common borders have different colors, and only four colors can be used, no more.. What do you think? If this question is true, can it attract attention?”

Subsequent several For decades, everyone thought it was a theorem that didn’t need proof until 1878, when the London Mathematical Society Chief-In-Charge officially announced the 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, Sheawood pointed out one of the grave mistakes. It is 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 every map with up to 25 countries could be colored in four colors.

Reynolds extended this result to 27 countries in 1926.

In 1940 Winn proved 35 countries.

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

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

Many well-known figures in the mathematics community disagree with the proof method of this “violent solution”. They believe that it should be proved by mathematical logical reasoning instead of choosing this “violent” solution.

It’s like someone asks how to put an elephant in the refrigerator, the answer is simple, first step, open the refrigerator door. The Second Step pushes the elephant into the refrigerator, and the Third Step closes the refrigerator door. As long as the refrigerator door is large enough, any kind of elephant can be put in it. This simple method is a “brute force” solution, it does not solve the problem logically.

The exhaustiveness of computers is not a real mathematical proof, and mathematics is not a subject that pays attention to results. Otherwise, the famous conjectures would not have attracted countless mathematicians all over the world.

It seems that solving the “four-color conjecture” requires knowledge of graph theory and topology. Li Mo watched the proof process of the four-color conjecture and calculated in the heart.

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

Unconsciously it was ten o’clock in the evening, and Li Mo still had no clue. He raised his head and looked around blankly. I found that the gray-haired youngster in the seat next to him was still yawning and reading the literature.

“Is this what I will look like in a few years?” Li Mo thought a little scared.

He stuffed the books into his bag and left the library. It was already dark outside, and only the small street lamps on the roadside radiated warm rays of light.

It was already a bit chilly late at night at the end of October. 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 rise in the lake. Li Mo looked at the lake and felt calm.

“DiDi.” There is a new message on WeChat.

Li Mo opened WeChat, and Ying Sasa with a fox avatar sent a message: “Hello, Li Mo, tomorrow afternoon at 4:00 pm, your orientation meeting will be held in the self-study classroom 501, please be on time. Participate.”

It seems that the monitor’s execution is very efficient, Li Mo replied: “Yes, I will attend on time, thank you monitor (smiley).”

Li As soon as Mo opened the door of the dormitory, he saw fatty stick his head out of the bed, and he stared at Li Mo Li Mo for a long time.

“fatty, is there something wrong?” Li Mo couldn’t stand being stared at like this, he asked directly.

I just listened to fatty asking faintly: “When did you get to know Ying Sasa so well, she went to the Student Affairs Office to borrow a classroom for your orientation meeting.”

Li Mo I was a little confused, so I had to perfunctory: “I only met the monitor Ying in the linear algebra class. As for her borrowing the classroom, I think it’s because she is an enthusiastic person.”

fatty left Li aside. Mo glanced, and got into the bed with an expression of disbelief.

It was dark in the dormitory, Li Mo lay on the bed and stared.

“Pajelu”, Li Mo in the heart called softly.

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

Current attribute :

1. Math level: 3 (150/10000)

2. Physics level: 0 (0/100)

3. Chemistry grade: 0 (0/100)

4. Biological grade: 0 (0/100)

5. Spiritual wisdom grade: 1

p>

Currently available credits: 5050

Li Mo decided to add all available credits to mathematics, maybe it would be helpful for the thesis assignment.

1. Math level: 3 (6200/10000)

2. Physics level: 0 (0/100)

3. Chemistry level: 0 (0/100)

4. Biology: 0 (0/100)

5. spiritual wisdom: 1

Currently available credits: 0

p>

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

(End of this chapter)