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Chapter 10 Algebraic Number Theory

Because there was a layman named Cai Yuanpei next to him, Cheng Nuo's previous description was naturally as simple as possible.

"Sir, algebraic number theory is an important branch of number theory." Cheng Nuo borrowed a pen and paper and wrote on it: "And number theory has a lot to do with our ancient Chinese civilization."

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

It is recorded in our country's earliest mathematical work "Zhou Bi Suan Jing" that Shang Gao, a man from the Western Zhou Dynasty, knew that the three side lengths of a right triangle satisfy the equation x+y=z, and gave the positive integer solution to this equation system (x, y,

z)=(3,4,5), this is elementary number theory, which is the use of arithmetic methods to study the properties of rational numbers and integers, including the divisibility of integers, congruence, prime numbers, primitive roots, indefinite equations, etc. It is the oldest in mathematics

One of the branches.

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 perspective and studied quadratic forms and cycloidal fields.

As the explanation progressed, Mr. Cai Yuanpei began to be unable to keep up with the rhythm, and gradually began to be unable to follow the conversation of the three of them.

He kept boiling water to make tea, and from time to time he added some manuscript paper for their use.

However, he enjoyed it instead. The more powerful Cheng Nuo was, the better his vision became, and he would be more and more helpful to the development of the school.

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

Feng Zuxun picked up the draft and admired it carefully, and finally praised it sincerely: "You said you got the inspiration from Hilbert's "Report on Number Theory". That is not an ordinary report. I admire him very much."

Germany is still the center of mathematics in the world, and Japanese mathematics mainly learns from Germany. Therefore, Feng Zuxun, who returned from studying in Japan, admired Hilbert very much. He also referred to Germany in the selection of textbooks and curriculum at Peking University.

The several equation theories I learned were all adapted from Hilbit's teachings.

Cheng Nuo is also full of respect for this great man: "It is not so much a report as it is a compilation of the development of algebraic number theory over the past one hundred years. Without his contribution, the development of algebraic number theory would have been postponed."

Qin Fen interjected and said excitedly: "It seems that there is not much international research on algebraic number theory, but Zhiyuan's research is already at the forefront."

When it came to his own subject, Cheng Nuo was very confident. He took a sip of tea and said, "I can't say that I am ahead. I can only say that I have taken a few more steps than them."

"Are you absolutely sure?" Out of caution, Feng Zuxun asked again: "I recently communicated with some students in Japan. They have made some progress in number theory research. I don't know if it is algebraic number theory."

"Exactly this aspect."

"Ah, wouldn't it be possible for them to be ahead of the curve?" Feng Zuxun was a little worried: "Their mathematical research started earlier than ours, and the overall gap in mathematics between the two countries has always been relatively obvious."

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

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

"Senior, please take a look. This is the manuscript I just submitted to the "Mathematical Yearbook" of the United States of America today. It contains my latest achievement - the theory of class fields."

After receiving 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 at a glance, he found that they were all numbers and symbols that were difficult to understand, and he immediately lost interest.

He put his hands behind his back and picked up the teapot, and whispered: "Should I drink Longjing or Pu'er? Forget it, I'm getting older and drink some black tea in winter."

After saying that, he leisurely went to look through his inventory.

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

The more I read the manuscript, the faster I read it. My body became hotter and my face became redder and redder. After reading it in one sitting, I felt so comfortable and warm all over my body.

In the end, Qin Fen couldn't help but jump up and held Cheng Nuo tightly with both hands: "Zhiyuan, you wrote this? You must have written it!"

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

Hearing this, Qin Fen couldn't control his emotions at all. He hugged Cheng Nuo tightly and couldn't help but shed tears. He 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. Even though he was well-informed, he couldn't help but be stunned.

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

Feng Zuxun was more restrained, but his eyes were slightly red, and he explained: "I can understand Jingyang, mainly because Zhiyuan's article is too useful. Cai Gong, do you know what it means if it is published?"

Seeing the seriousness of the other party, Cai Yuanpei also understood the importance, quickly put down the teapot and asked, "Uncle Han, please speak."

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

Since the end of the Qing Dynasty, the country has been poor and the people are weak, and the foreign powers have taken turns to invade and humiliate. There has been endless domestic turmoil. I want to open my eyes to see the world, but I find that I have been left far behind.

Those who fall behind will be beaten, and those who are ignorant will be bullied.

There is no student who has studied abroad in these years who has not been bullied and scolded by foreigners, and who can say that he has not been looked down upon.

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

In order to better catch up with the pace of other countries' natural sciences, extreme people even proposed to abolish Chinese characters and fully use Latin to integrate with the West.

Although looking at it from the current perspective, it has no reference value at all.

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

Now Cheng Nuo told them that it was not only possible to catch up, but also to surpass these high-nose people and step up to the point of establishing a sect.

The dawn of hope is right in front of us, how can we not make Feng Zuxun and the others excited.

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

In fact, mathematics also plays a large role 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 first in the first group.

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

Now that he heard that the mathematics disciple of Peking University was going to establish a sect in the field of mathematics, how could he not be happy?

"Okay, okay." Even though he was only half a century old, he couldn't help but tremble slightly.

When I close my eyes, I seem to see that the ideal of teaching and educating people has been realized. Groups of students who have received the latest scientific education are moving from campus to society. Factories are rising from the ground. They will no longer be bullied by foreigners.

I couldn't conceal my excitement.

"Oh, why are these glasses so old?" Cai Yuanpei took off his glasses, picked up a handkerchief and wiped them carefully over and over again.

Cheng Nuo, who has studied in the United States for several years, can completely understand this feeling. Especially when he first entered the United States in the late Qing Dynasty, he had pigtails on his head, and he was even more discriminated against.

So he remained silent and silently patted Qin Fen on the back.

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

"right!"

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