I kidnapped an alien civilization

For five days in a row, Li Mo has been crouching in a small corner of the library, writing papers on the four-color conjecture. He is only now discovering how difficult it is to write a paper in a foreign language.

The professionalism of words used and the standardization of the quoted theorems. He used to think that vocabulary was the most difficult. In fact, when I was writing a thesis, I realized that the vocabulary is not the most difficult thing, the real trouble is the logic expressed in a foreign language.

After consulting countless documents and racking his brains, Li Mo finally wrote the paper completely.

We can convert the four color conjecture,

At the same time, we call the number of points of the largest complete graph subgraph included in Figure F as “clique number“, and note it as X. It is easy to find that a complete graph of n points requires at least n different colors because the two points are adjacent

It is obvious from the above that any part of a graph is divided and dyed to make any part with common sidelines have different colors, and can only use four colors, no more. The proposition is true.

I have finished the certificate.

Looking at the thesis he wrote, Li Mo was as satisfied as seeing his own child.

Li Mo remembered Wei Xiaonian's words, he took out his mobile phone and dialed Professor Wu's number: Professor Wu, hello, I'm Li Mo, and I recently finished a paper. I'm going to submit a manuscript, and I want you to check it first.

Thesis? Okay, okay, I'm free in the afternoon, so how about you come to my office at two o'clock in the afternoon. Professor Wu replied while accepting the document handed over by the assistant.

The female assistant wearing a professional skirt next to her saw the professor put down the phone, and whispered: Mr. Wu, you have a meeting with Mr. Zhang from the Dafang Group this afternoon. Check it out.

Reject it, just say I'm busy this afternoon. Professor Wu replied while looking at the document.

The female assistant nodded and said yes while wondering: Who is the student on the other side of the phone, who actually made Mr. Wu postpone the meeting in the afternoon? You must know that Dafang Group invests a lot of money in the Department of Mathematics every year.

Li Mozai carefully checked his thesis several times, and then carefully put it into his schoolbag.

Seeing Li Mo's cautious actions, the fat man next to him asked curiously, Mozi, what's in the schoolbag, let me show you, be careful.

Li Mo replied without turning his head: Thesis. After finishing speaking, he took his schoolbag and left the dormitory. He still had to go to the library to continue writing.

The fat man looked at Li Mo's back a little strangely: Have you started writing papers since you were a freshman? Are young people these days really so aggressive?

At two o'clock in the afternoon, Li Mo arrived at the office building of the Department of Mathematics on time. He knocked on the door of Professor Wu's office, but the door was opened by a beautiful young woman in a sleeve skirt.

The young woman opened the door and asked softly, Student, who are you looking for?

Li Mo said: Professor Wu asked me to come at two o'clock, isn't he here?

The young woman's eyes lit up, and she turned sideways gently to let Li Mo into the office, and said, Professor Wu just went out for something, and I'll be right back, just wait a moment.

Then she hesitated and added: I am Professor Wu's assistant, my name is Fang Xiaoyun, may I ask who you are?

Li Mo said generously: I'm Li Mo, nice to meet you.

The two were exchanging greetings when Professor Wu opened the door and came in. Seeing Li Mo, he was very happy and said, Come on, let me see your thesis inside. Then he turned around and told the young woman, Xiaoyun, make two cups of tea. .”

Professor Wu put on his glasses and looked at the thesis handed in by Li Mo. He was startled when he saw just one title: Four-color conjecture? Did you really prove the four-color conjecture?

Professor Wu's movement startled the young woman who was pouring water, and the boiling water spilled on the floor. She was about to dry off with a mop, but was stopped by Professor Wu: You go out first, and push back the afternoon schedule for me.

The young woman nodded in agreement, and looked at Li Mo carefully.

Professor Wu was sure that his assistant had left, so he started to read the paper.

Li Mo could see that foreign languages ​​were no obstacle to Professor Wu in front of him.

Ingenious, the changes here are amazing. Professor Wu looked at the paper and couldn't help saying in admiration.

Li Mo sat on the chair calmly, like a student waiting for an exam. He looked at Professor Wu facing him, sometimes frowning and sometimes relaxing, but he didn't feel any anxiety, because he was very confident in the thesis he wrote.

Did you make a mistake in your coordinate system? Why does it look so strange here? Professor Wu frowned and pointed at a determinant.

Li Mo smiled and took a piece of scrap paper from the side, wrote two lines of calculation formulas on it and handed it over.

Professor Wu saw the calculation formula on the straw paper, slapped his head and said, It's really ingenious, what do you think?

Eagle and hedgehog. Li Mo said calmly.

Eagle and hedgehog? Professor Wu couldn't understand. Let's read the paper first. Is there something wrong with your constant term?

Li Mo turned to the second page of the thesis, pointed to the above lines of calculations, and Professor Wu's doubts disappeared.

Professor Wu read the paper carefully, and if he had any doubts, he asked Li Mo to explain. Fortunately, so far, he has not found any mistakes in Li Mo's thesis.

Gulu. Gulu Before he knew it, several hours had passed, and Li Mo's stomach rang.

Professor Wu looked at the embarrassed Li Mo, put away the paper, and told his assistant to deliver two takeaways via the intercom.

Tell me your main idea. Professor Wu was still thinking about the thesis while eating takeaway.

I transformed the four-color conjecture of the plane into a three-dimensional coordinate system. Li Mo explained in detail.

Professor Wu looked at Li Mo lovingly and said, Ingenious, really ingenious, how did your brain grow?

At ten o'clock in the evening, under Li Mo's explanation, Professor Wu finally read through the paper. He flipped through the more than 50 pages of the paper, and was surprised to find that he didn't find any mistakes.

Did you complete this thesis by yourself? Professor Wu asked as he took a sip from his teacup.

Yes, the main idea took about a month, and the writing of the thesis took about a week. Li Mo nodded and answered honestly.

Professor Wu looked at Li Mo's candid face, nodded and said, I guess you did it by yourself. If you wrote it with the help of some professor, you definitely wouldn't just sign your name. After thinking about it Thinking he asked again: Do you know what this paper means to you once it is published?

Li Mo shook his head, because he is not interested in reputation, so he doesn't care about these things on weekdays.

Professor Wu said solemnly: The four-color conjecture is very different from the Collats conjecture you completed last time. Although there is no distinction between high and low in mathematical problems, the mathematics world is very realistic. Although the Collats conjecture is difficult, it is just A remote subject, the four-color conjecture is different, it is well-known all over the world, maybe our textbooks will have to be rewritten.”

He paused here, picked up the water glass and took another sip of water, and then slowly said: Maybe you will become famous overnight because of this paper, after all, it is a four-color conjecture, to be honest, even I am very jealous.

Li Mo shook his head and said seriously: Actually, I didn't think that much. This paper is just an ordinary paper in my eyes.

Seeing Li Mo's nerdy appearance, Professor Wu sighed in his heart, maybe only such a pure person can solve the problems that the world cannot solve.