Chapter 10 Algebraic Number Theory

Because there is Cai Yuanpei, a layman, next to him, Cheng Nuo's narration in front of him is naturally as popular as possible.

"Sir, algebraic number theory is an important branch of number theory." Cheng Nuo borrowed a pen and paper and wrote and drew on it: "The number theory has a lot of roots with our ancient Chinese civilization. ā€

Ancient number theory was intertwined with geometry in the early stages of research.

It is recorded in our country's earliest mathematical work "Zhou Ji Sutra" that Shang Gao, a person of the Western Zhou Dynasty, knew that the length of the three sides of a right triangle satisfies the equation x²+y²=z², and gave the positive integer solution of this equation (x,y,z)=(3,4,5), which is elementary number theory, that is, the use of arithmetic methods to study the integer properties of rational numbers, including the divisibility of integers, congruence, prime, roots, indefinite equations, etc., is one of the oldest branches of mathematics.

Later, with the development of number theory, algebraic number theory began to gradually separate from it, until Gauss's "Studies in Number Theory" provided a broader vision and studied quadratic forms and circular fields......

As the explanation deepened, Mr. Cai Yuanpei began to lose control of the rhythm, and gradually began to fail to keep up with the conversation between the two of them.

They kept boiling water to make tea, and from time to time added some manuscript paper for them to use.

But he enjoyed it, the more powerful Cheng Nuo was, the better his vision proved to be Bole, and it was more and more helpful to the development of the school.

No matter how you look at it, Cai Yuanpei is one of its main beneficiaries.

Feng Zuxun took the draft and carefully admired it, and finally praised it sincerely: "You said that you got the inspiration from Hilpot's "Number Theory Report", it is not an ordinary report, and I yearn for him very much. ā€

Germany is still the world's mathematics center, and Japan's mathematics is mainly learned from Germany, so Feng Zuxun, who returned from studying in Japan, admires Hilbert very much, and also refers to Germany in the selection of textbooks and curriculum of Peking University, and several equation theories learned by students are also adapted from Hilbit's teachings.

Cheng Nuo is also full of respect for this big bull: "It is not so much a report, but a collation of the development of algebraic number theory in the past hundred years. ā€

Qin Fen interjected and said excitedly: "In this way, there is not much research on algebraic number theory in the world, and Zhiyuan's research has been in the forefront. ā€

When it comes to his own disciplines, Cheng Nuo is very confident, took a sip of tea and said: "I don't dare to say that I am ahead, I can only say that I have taken a few steps more than them." ā€

"Are you sure?" Out of prudence, Feng Zuxun asked again: "I communicated with some Japanese students a few days ago, and they have made some progress in the study of number theory, but I don't know if it is algebra number theory. ā€

"That's exactly what it is."

"Ah, wouldn't they be ahead of the curve too?" Feng Zuxun was a little worried: "Their mathematical research started earlier than ours, and the overall gap between the mathematics of the two countries has always been relatively obvious. ā€

Cheng Nuoxin said, what I take is their results in the next few years, of course, I know that I am ahead of them at present.

So he took out the first version of the submitted manuscript from his bag and handed it to Feng Zuxun.

"Senior, please see, this is the manuscript I just submitted to the "Mathematical Yearbook" of the United States of America today, and it is my latest achievement-class field theory."

After taking the manuscript, Feng Zuxun and Qin Fen gathered around and read it carefully.

At this time, Cai Yuanpei also wanted to join in the fun, but when he glanced at it, he found that they were all numbers and symbols, and he couldn't understand them, so he immediately lost interest.

He picked up the teapot again with his back and whispered: "Do you want to drink Longjing or Pu'er, forget it, let's drink some black tea in winter when you are old." ā€

After speaking, he went through the inventory leisurely.

The two of them have studied number theory themselves, so it is much easier to get started with algebraic number theory, and from time to time they have to talk to Cheng Nuo next to them.

The more I read the manuscript, the hotter it gets, the hotter it gets, the redder my face becomes, and I only feel comfortable and warm after reading it in one go.

In the end, Qin Fen couldn't help jumping up directly, and grabbed Cheng Nuo tightly with both hands: "Zhiyuan, this is what you wrote?" It must have been you who wrote it! ā€

"Senior brother, I wrote it, and only those of us here have seen this manuscript so far."

Hearing this, Qin Fen couldn't control his emotions at all, hugged Cheng Nuo tightly, tears couldn't help but stay, and his mouth kept repeating: "Zhiyuan, Zhiyuan, you are really my good junior brother......"

At this time, Cai Yuanpei, who came back from making tea, saw this scene, and Rao couldn't help but be stunned when he was well-informed.

"Jingyang, what's wrong with you? Let go of Zhiyuan first, sit down and talk slowly. ā€

Feng Zuxun was a little more restrained, but his eyes were slightly red, and explained: "I can understand Jingyang, the main reason is that Zhiyuan's article is too useful, Cai Gong, do you know what it means if it is published?" ā€

Seeing the other party's solemn appearance, Cai Yuanpei also knew the importance, quickly put down the teapot, and asked, "Uncle Han, please speak." ā€

"It means that we have not only solved the mathematical problem that has been in the dust for half a century, Kroneck's youthful dream, but also led the world in algebraic number theory, and the most important thing is that we at Peking University may open up a new discipline in the mathematical community!"

Since the end of the Qing Dynasty, the country is poor and the people are weak, the great powers have taken turns to invade and humiliate, and the domestic turmoil is endless.

If you are backward, you will be beaten, and if you are ignorant, you will be bullied.

Among the students who have been studying abroad all these years, which one has not been bullied and scolded by foreigners, and who can say that he has not suffered from white eyes.

But they went to study one after another, and then returned to this devastated home, not just to bring back new knowledge and new culture, to seek a hope for him, to make her better as soon as possible, and to restore her former glory.

In order to better catch up with the pace of other people's natural sciences, the extremists even proposed to abolish Chinese characters and use Latin in an all-round way to integrate with the West.

Although from the current point of view, it has no reference value at all.

But from the side, it is enough to know their desire to catch up with Western science.

Now Cheng Nuo told them that not only could they catch up, but also surpass these high noses and step to the point of founding a sect.

The dawn of hope is just around the corner, how can you not let Feng Zuxun and them get excited.

Everyone knows that Cai Yuanpei attaches great importance to liberal arts and has hired many masters of Chinese studies.

In fact, mathematics also occupies a considerable weight in Cai Yuanpei's heart.

Later, when the mathematics department of Peking University was changed to a department, the school council divided the departments into groups, and Cai Yuanpei directly ranked the mathematics series as the first place in the first group.

The original words are: "The purpose of the university is that all those who study philosophy, literature, and applied sciences must start from pure science; Pure science. Start with math. Therefore, the departments are in order, and the Department of Mathematics is the first department".

Now that he heard that the mathematics sect of Peking University was going to start a sect in the mathematics community, how could he not be happy.

"Yes, yes." At only half a hundred years old, he couldn't help but tremble slightly.

When I close my eyes, I feel as if I see that the ideal of teaching and educating people has been realized, and batches of students who have received the latest scientific knowledge education have gone from the campus to the society, and factories have sprung up from the ground, and they will no longer be bullied by foreigners.

I couldn't hide my excitement.

"Oops, what's wrong with these glasses, it's getting old." Cai Yuanpei took off his glasses, picked up a handkerchief and wiped it carefully over and over again.

This mood can be fully understood by Cheng Nuo, who has studied in the United States for several years, especially when he first stepped into the United States in the late Qing Dynasty, he still had a braid on his head, and he was even more discriminated against.

So he didn't say anything on the side, patting Qin Fen's back silently.

After everyone calmed down, Cheng Nuo said firmly: "With everyone here, I believe that the future will be better." ā€

"Yes!"

"With Cai Gong here and everyone here, Peking University will definitely be able to produce more talents!"