Germany, University of Göttingen.

Even with the impact of the war, Göttingen still retains the most exciting program of the school, namely the regular weekly meetings of the Mathematics Club.

The Math Club is a free world for mathematical activities. The club does not adhere to organizational forms and has no person in charge.

There are no members and no fees. Since the club is in Göttingen, and the reputation of Göttingen makes the club lectures a very high-level event. Foreign scientists often come here to report their recent work, but more often Göttingen

Their own people, they freely give speeches here and report their new achievements and new ideas.

As usual, Hilbert lowered the brim of his hat, found a seat and crossed his legs, sipping coffee and listening to the speech on the stage.

An old professor who was over seventy years old walked tremblingly to the blackboard, took off his hat and saluted, and then began to write and draw on it.

"What I'm talking about this time is ordinary differential equations. Here, the letter x (or the letter t) is usually used to represent the independent variables in the ordinary differential equation, and y(x) is used to represent its unknown function."

Before he finished writing on the blackboard, Hilbert couldn't stand it anymore. He put down his coffee and said disdainfully: "Speeches, especially mathematical speeches, must be highly concise and clear. Just like I am not interested in your approach when eating cakes, I only need to

Just pick out your bright spots 'raisins'. My dear colleague, please forgive me, you have written so much, I'm afraid you still don't know what a differential equation is, right?"

The old professor was shaking with anger: "I respect your mathematical talent, but I can't be so arrogant as to say that I don't understand differential equations. I noted it in the first paragraph. I won't blame you if you can't see clearly from a distance."

You can't bear to insult a gentleman."

Hilbert smiled, walked to the stage confidently, pointed at one of the lines with his pointer and said: "My dear colleague, you must have worked at home day and night for a long time to come to this conclusion, but let me tell you,

The Russian mathematician Lyapunov created a new direction in the study of nonlinear differential equations in his paper "General Problems of Stability of Motion". The theory of stability of motion proposed is completely used to solve the problem that the initial value perturbation of the solution of the equation does not affect the solution of the original equation.

tend."

Originally, I just wanted to erase this line, but after erasing it, I felt that the following line was not suitable. Mathematics is like this, and it is connected with each other. In the end, I directly erased all the writing on the blackboard at the end, and then wrote it into a correct paper.

Hilbert patted the dust on his hands and said with a smile: "I'm sorry, I accidentally wiped all your results, but it's okay. I don't know how many years since I was eliminated. It doesn't matter."

When the old professor saw this, his vision immediately went dark, and he almost fainted due to the crowd. However, the assistant next to him had quick eyesight and quick hands, supported him, waved his hand dejectedly, and left the venue in embarrassment.

As a result, before he could even take two steps, he tripped over an unnecessary roadblock and fell to the ground.

Hilbert, the other protagonist of the event, sat back on his chair, sipped his coffee again, and motioned for the next speaker to come on stage.

The colleague next to him was a little dissatisfied: "You shouldn't treat that old professor like this. He made a lot of contributions to the development of the School of Mathematics in our school earlier. For the sake of the original face, we must save some face for him no matter what."

Hibbert was nonchalant and raised his eyebrows at the place where the old professor left: "It's not that I don't care about the face of my former colleagues, but he really doesn't know what differential equations are. Look, the direction he left is not leading to the library.

Are you on your way to the library? I must be going to check out the papers."

My colleague was helpless, knowing that the other person had such a style, so he had no choice but to give up.

Seeing this battle, the young speaker who came next became a little trembling and bowed with a trembling voice.

"Dear teachers, hello everyone, first of all, let me state that the original author of this paper is not me. It is the latest research on "Theory of Class Domains" completed by Professor Tom Cheng from the mysterious Eastern country. It seems that everyone does not know this, so I specially mentioned it to me.

I will share my experience with everyone present.”

Despite the lessons learned just now, it is an honor to get Hilbert's comments, even just criticism, in person, so despite expecting the worst, young mathematicians from all over the world are still willing to go to the Göttingen Math Club

Give a speech.

Even so, the young man still stumbled when he spoke. He even accidentally lost control of his strength a few times and broke the chalk. People in the audience kept looking at Hilbert, their faces full of banter.

Hope to give this young man a head-on blow.

"Auguste, what do you think? Let's take a bet on this poor young man."

"What to bet on?"

"The bet is 100 marks on which line he wrote before Hilbert kicked him off. I think it was before the thirtieth line."

"Okay, then let me bet ten lines ago that this little guy was not prepared at all, and he took someone else's paper. This will only increase Hilbert's requirements. What a poor little sheep."

At this time, a young man took out a stack of marks and put it on the table.

"I want a thousand marks, and I bet that Teacher Hilbert will allow this classmate to complete the speech."

"Weiner, what do you mean? I know you have some talent in mathematics, but who can be sitting here who lacks this talent? Young people should not be too arrogant."

"You are wrong. I am not optimistic about this classmate, but Professor Tom Cheng behind him. Arrogant Germans, it's time to lower your heads!"

After saying this, Weiner stopped having useless arguments with these people. Even the most famous genius in mathematics this year was unknown. It can be seen that these people are only half as good as the old professor just now.

Unexpectedly, Hilbert spent more time on coffee than watching the speech, just as they expected. But at some point, Hilbert started to put his beloved coffee on the table.

On the other hand, I moved directly to the first row of seats, and my face turned serious.

When I saw the blackboard writing completed, I couldn't help but stand up, clapped my hands, and said with disbelief: "Speeches today are far worse than in the past. When I was young, people were very particular about the art of speech, and the speaker was very

There are a lot of considerations about what you want to say and how to say it well. Young people nowadays don’t do this, especially in Göttingen. I think the worst speech in the world was probably given in Göttingen.

This year has been even worse. I haven’t heard a single good speech at all, and it’s been especially bad lately. However, there was an exception this afternoon.”

"To be able to see the proof of the principal ideal theorem one day means that the nearly thirty-year-old problems of class domain theory have been solved. All conjectures about the nature of class fields are correct. In the face of absolute strength, no need for any

All the bells and whistles!”

The subsequent process was relatively simple. Under the leadership of Hilbert, a group of people began to analyze Cheng Nuo's research intensively. The deeper they went, the more they could appreciate the meticulousness of the thinking, and even all the possible controversial issues.

Every area has been patched in advance so that no one can find the place where errors can be corrected.

Professor A sighed: "With the strength of Professor Tom Cheng's paper, even my unsatisfied students can deduce it step by step after seeing it. It is really incredible, but if you think about it carefully, Kronecker's youth

He has proven that he can keep improving on the basics, and he has already surpassed us in this area."

Professor B smiled and said: "But it is not without its shortcomings."

Professor C asked curiously: "The thinking is so rigorous and every step can be considered repeatedly, so what are the shortcomings?"

Professor B explained: "The biggest shortcoming is that he is not German and has never even come to study in Göttingen. As far as I know, their government has just declared war on us. In the face of the interests of the German Empire, this is the biggest and most deadly

shortcoming."

Hilbert's face darkened when he heard this: "Science has no boundaries. In national life, every country can only prosper when it coordinates and lives in harmony with its neighboring countries. The interests of the country

It requires the establishment of a general order not only within each country, but also in the relations between countries - and the same is true in scientific life."

However, the two countries are in the political background of warring countries. After the meeting, Hilbert not only publicly expressed his high recognition of the "National" magazine, but also did not hesitate to praise Professor Tom Cheng who was far away in the East, directly talking about his theory of category fields.

The conjecture was renamed "Hilbert-Theorem on Programmatic Fields", and Cheng Nuo's status was recognized in a semi-official capacity on behalf of the European Göttingen School.

Looking at the somewhat decadent duo of professors and gamblers in front of him, Weiner excitedly took the mark from their hands, counted it carefully, confirmed that the number was correct, and said with a smile: "Two gentlemen, if you go back and review "Class Domain"

I am very interested in the study of "On", and I will find that it is full of formula theorems and formula axioms. The reason why I dare to make such a big bet is not just relying on intuition. You Germans will eventually usher in the sunset."

The two were unconvinced and said that it was their mistake not to contact the professor for the paper, but there was no need to be so mocking. Besides, they were completely indifferent to the mere one thousand marks. The mysterious Eastern Professor Tom Cheng had not shown off yet.

, it’s Weiner’s turn to be arrogant here.

Weiner took the money in his hand, patted it and said: "It's a coincidence. Who made Professor Tom Cheng my junior fellow student? If he speaks ill of his junior fellow apprentice in front of me, I won't look good on you.

Already."

There are two flowers blooming, one on each side. The people over at Princeton in the United States are both happy and sad.

Fan Yin, dean of the Princeton Mathematics Department, was delighted that he had indeed seen the right person. This Tom Cheng had made such great achievements in silence. In his opinion, he had even simplified the subject to an irreducible level. Undergraduate admission

Then you can appreciate the charm of it, rather than like before, where several professors gathered around to chew on the paper, and they may not be able to complete the second proof.

The worrying thing is that apart from answering a few common questions, Tom Chengzhong never responded to any other questions. Even the appointment letter from Princeton University that he personally invited was put on hold, making him always think that he was from Germany.

Göttingen was half-assed, but after asking around a lot, he found out that he himself had misunderstood.

It was not easy to feel relieved, but as a result, the new paper was put aside in their "Annals of Mathematics" and published in his own magazine, which inexplicably gave Fein a feeling of resentment.

"If you want to publish a paper, come to us. Not a single punctuation mark will be changed. All editors will automatically proofread grammatical errors. The entire manuscript fee will be paid."

Veblen raised his head and said with a smile: "Dean, as far as I know, although Tom Cheng did not accept our offer letter, he also did not accept Harvard's. We still have many opportunities at Princeton."

Fan Yin held a pipe in his mouth, took a puff and held it in his hand: "For us, it may not be a good thing. Besides, with Tom Cheng's age, there may be greater academic achievements in the future. By that time

, our professor appointment letter from Princeton seems not that important."

Veblen smiled and joked: "At that time, we will directly invite him to be the dean in the name of the Princeton School of Mathematics."

Unexpectedly, Fein actually thought that this idea was not bad. He pondered for a moment and nodded: "It's not impossible. As long as he is willing to come and continue to maintain this review and produce academic results, we will be the dean of the School of Mathematics."

It’s cheap. When the time comes, he will be the dean and I will be the principal, so there will be no influence on each other.”

Veblen was stunned and said with a sour tone: "If this is the case, it will be difficult for the board of directors to explain, after all, you can be the president of Princeton at such a young age."

Fein said disdainfully: "Those guys only talk about benefits. If I personally tell them the value of Tom Cheng's coming, I believe they will be crazier than me. I wonder if there is such a person who can elevate the School of Mathematics to the Göttingen School."

Level, that will mean that more upper-class people will wave their checks and come to sponsor us. Not everyone can resist the charm of 'Franklin'."

Veblen originally wanted to continue to argue a few words, but in the end he suddenly felt that what he said was all in vain. You must know that judging from Tom Cheng's age, he is far from reaching the age of academic peak. He can continue to make more achievements in the future.

No one can say what kind of academic achievements he will make, but as long as he does not die prematurely, the place where he is located will gradually become a new mathematics center.

In this industry, the gap in intelligence between people is wider than the gap between people and dogs.

After hesitating for a moment, Veblen regained his composure and asked, "But Dean, right now Tom Cheng has not even accepted our appointment as professor. It may not be that easy to talk about other things later."

Fan Yin was confident: "This is simple. Didn't Tom Cheng invite us to attend their annual scientific meeting at the end of the year? At that time, I will personally lead a team to invite him and let him see with his own eyes our sincerity at Princeton."

In this way, similar plots also happened in the United Kingdom, France, Italy and other places. People once again turned their attention to the East, the barren soil of modern science, and it was hard to imagine that different flowers bloomed in the cracks of the rocks.

The first International Exchange Annual Conference of the Academy of Sciences, held at the end of 1917, also began to attract the attention of the international academic community.

By the way, although "National" magazine is still not as good as its predecessors "Science" and "Nature", it seems to have firmly occupied the second echelon, which is also a good result for the Academy of Sciences.
Chapter completed!