Go back to the past and be a schoolboy

Chapter 10 Algebraic Number Theory
Because Cai Yuanpei, a layman, was beside him, Cheng Nuo's previous narration 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 and drew on it: "And number theory has a lot of connection with our ancient Chinese civilization."

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

It is recorded in "Zhoubi Suanjing", the earliest mathematics work in our country, that Shang Gao, a man of the Western Zhou Dynasty, knew that the lengths of the three sides of a right triangle satisfy the equation x+y=z, and gave the positive integer solution of this equation system (x, y, z) = (3, 4, 5), this is elementary number theory, that is, using arithmetic methods to study the properties of rational integers, including integer divisibility, 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 "Research on Number Theory" provided a broader perspective, studying quadratic forms and subcircular domains.
As the explanation deepened, Mr. Cai Yuanpei began to lose track of the rhythm, and gradually began to lose track of the conversation of the three of them.

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

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

No matter from which point of view, Cai Yuanpei is one of its main beneficiaries.

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

Germany is currently the center of mathematics in the world, while Japan mainly learns mathematics from Germany. Therefore, Feng Zuxun, who came back from studying in Japan, admires Hilbert very much. He also refers to Germany in the selection of textbooks and curriculum settings at Peking University. The several equations I learned were all adapted from Hilbitt's teachings.

Cheng Nuo is also full of respect for this big cow: "It is not so much a report as it is a compilation of the development of algebraic number theory in the past 100 years. Without his contribution, the development of algebraic number theory would have to be delayed."

Qin Fen interrupted and said excitedly: "It seems that there is not much research on algebraic number theory in the world, and Zhiyuan's research is already ahead."

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

"Are you sure?" Out of safety, Feng Zuxun asked again: "A few days ago, I communicated with some students in Japan. They have made some progress in the study of number theory. I don't know if it is in algebraic number theory."

"Exactly that."

"Ah, isn't it possible that they may also be ahead." Feng Zuxun was a little worried: "Their mathematics 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 achievements 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 carry-on bag and handed it to Feng Zuxun.

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

After receiving the manuscript, Feng Zuxun and Qin Fen gathered together and read it carefully.

At this time, Cai Yuanpei also wanted to join in the fun, but when he took a big look, he found that they were all numbers and symbols, which he couldn't understand, and immediately lost interest.

Turning his hands away, he picked up the teapot again, and said in a low voice, "Should I drink Longjing or Pu'er, forget it, let's drink some black tea in winter."

After finishing speaking, he leisurely went through the inventory.

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

The more I read the manuscript, the faster my body became hotter, and the redder my face became. After reading it all at once, I feel refreshed and warm.

In the end, Qin Fen couldn't help jumping up, and held Cheng Nuo tightly with both hands: "Zhiyuan, you wrote this? It must have been written by you!"

"Brother, I wrote it. Only those of us present have seen this manuscript."

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

At this time, Cai Yuanpei, who came back from making tea, could not help but be stunned when he saw this scene.

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

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

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

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

Since the end of the Qing Dynasty, the country was poor and the people were weak, the great powers took turns to invade and humiliate, and the country was in turmoil. If you want to open your eyes to see the world, you find that you have been left far away by others.

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

Among the students who have studied abroad in recent years, which one has not been bullied and scolded by foreigners, and who can say that he has not suffered blank stares.

But they went on to study one by one, and then returned to this devastated home, wasn't it 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 it has been seen from the current perspective, 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 might they catch up, but they would also surpass these high nose bridges and step forward to the point of establishing a sect.

The dawn of hope is just around the corner, how can Feng Zuxun and the others be kept from being 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 mind.

Later, when the Department of Mathematics at Peking University was changed to a Department, the school council divided each department into groups, and Cai Yuanpei directly designated the Department of Mathematics as No.1 in the first group.

The original words are: "The purpose of the university is that those who study philosophy, literature, and applied science must start with pure science; those who study pure science must start with mathematics. Therefore, the order of each department is to list the Department of Mathematics as the first department."

Now he is not happy to hear that the mathematician of Peking University is going to establish a school in the mathematics world.

"Okay, okay." He was only fifty years old and couldn't help trembling 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 knowledge education have moved from the campus to the society, and factories have sprung up, and they are no longer bullied by foreigners.

I couldn't hide my excitement.

"Oh, why are these glasses worn out? I'm getting 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 fully understand this feeling, especially when he first stepped into the American territory in the late Qing Dynasty, he had a braid on his head, which made him even more discriminated against.

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

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

"Correct!"

"With Mr. Cai and everyone here, Peking University will definitely produce more talents!"

(End of this chapter)