“There is still a long way to go in mathematics, and I feel that I am most interested in number theory recently.

The most famous problems of prime number distribution are Riemann's conjecture, Goldbach's conjecture and twin prime conjecture.

However, if I want to solve Riemann's Hypothesis and Goldbach's Hypothesis with my current strength, I'm afraid it's not just one or two points of difficulty. Even if I can get away with solving one of the conjectures, I'm afraid I won't be able to do it until middle age.

If I use the system, the points I have now are simply not enough to solve either of these two conjectures.

As for the twin prime conjecture, although Zhang Yitang's article "Bounded gaps between prime numbers" has reduced the gap to 246.

But Mr. Zhang's method has probably reached its limit. If you want to truly prove the twin prime conjecture, you have to find another way and you can't follow his path anymore.

In this case, it is not easy to prove the twin prime conjecture..."

After Zhao Xiancai turned his attention to number theory, he began to think about where his next research direction should be. Anyway, he had temporarily given up on the Riemann Hypothesis, Goldbach's Hypothesis and the Twin Primes Hypothesis.

Zhao Xiancai thought about the next research direction for several days before deciding on it.

His final direction was the twelfth of Hilbert's twenty-three questions, which was about the composition of class fields, that is, extending the Kronecker-Weber theorem on Abelian fields to any algebra.

Go up to the rational domain.

The reason why number theory is called the brightest crown in mathematics is because almost all branches of mathematics can be used to deal with number theory problems.

The most mainstream among them is algebraic number theory. Algebraic number theory analyzes the algebraic properties of number fields from the perspective of abstract algebraic structures.

Algebra originated from the study of polynomial equations, and solving equations corresponds to the expansion of the number field. The most important type of expansion is called Abelian expansion.

This problem belongs to the category of algebraic number theory. It has already produced some research results, and after this thing has some results, Zhao Xiancai can publish it as an undergraduate thesis, and there is no need to devote it to subsequent undergraduates.

Paper distraction.

Some scholars have studied this stuff all their lives and became professors by relying on it.

However, this problem started with Kronecker in the 19th century, Hilbert in the 20th century, and now in the 21st century. Numerous mathematicians have been working on this road successively.

not enough.

But there is still a long way to go before this problem is solved.

The reason why I chose this question is that when Zhao Xiancai looked at the problems that Hilbert asked twenty-three, whether they were solved or unsolved, he had some answers to the twelfth question.

Got some ideas.

Zhao Xiancai has no idea about other unresolved issues.

In order to complete the task of "publishing a paper in a top mathematics journal before graduating from college", the reason why Zhao Xiancai finally chose the Erdős arithmetic sequence conjecture was precisely because he had a question in his mind when he saw this problem.

So some ideas.

The same is true now.

Regarding Hilbert's 12th question, the number of related research contents, papers, and various literature materials is much greater than Erdös's arithmetic sequence conjecture.

After all, it only took a few decades from the time the Erdős arithmetic sequence conjecture was proposed to the time it was solved by Zhao Xiancai, but now this problem has been raised for more than a hundred years.

The rest of this winter vacation and Zhao Xiancai’s last semester at Peking University will probably be spent reading relevant literature and researching the issues.

At least for this relevant literature, Zhao Xian couldn't read it all in the little time left during the winter vacation.

When Zhao Xiancai read literature before, he either used a laptop or a mobile phone.

This phone can be carried around, which is convenient, but the screen is too small.

The screen of this laptop is large, but it is not convenient to carry.

Therefore, during the winter vacation, Zhao Xiancai went to the city to buy a tablet computer with a screen larger than a mobile phone and more convenient to carry than a laptop.

"When we went to your uncle's house two days ago, you didn't know how to buy it, and now you have to make a special trip to the city.

If you go to the city, you just happen to stop by your class teacher's house. Remember to buy some gifts.

The last time we went to the city, I only thought about visiting your uncle and your grandmother, but I forgot to go to your high school teacher's home to say New Year."

After learning that Zhao Xiancai was going to the city to buy a tablet computer, Wang Qiuyue said to him.

"I know, I'll buy a carton of milk, a gift bag and a bottle of wine. Is that okay?"

Zhao Xiancai had little experience in giving gifts.

"Does your class teacher drink? The last time he came to our house for dinner, he didn't seem to drink much. Please don't buy wine and buy something else.

But don’t make your gift too expensive. If it is too expensive, your teacher may not accept it.

You can just send some tea, or something for children to play with." Wang Qiuyue said.

"Then let me give you a pen? Teacher Fang will definitely be able to use it," Zhao Xiancai said.

…

It didn't take long to get from the village to the city by car. After arriving in the city, Zhao Xiancai didn't buy a tablet first, but went to the homeroom teacher's house first.

"Hello, Teacher Fang, I'm here to wish you a Happy New Year. I wish you and your family good health and happiness in the New Year."

After carrying some gifts and meeting Teacher Fang at Fang Qiu's house, Zhao Xiancai smiled and said some New Year blessings.

"Happy New Year, Happy New Year, come in.

You're here right now, why are you bringing gifts? You're still in school and don't have a job."

After seeing Zhao Xiancai, Fang Qiu was also very happy. Seeing that the gift in Zhao Xiancai's hand was not too expensive, he took it and said.

"Teacher, I haven't started working yet. But because I published a paper in the "Annual Review of Mathematics", the school gave me some scholarships, so I still have some money."

Zhao Xiancai explained with a smile, but did not say the specific amount of the bonus.

"You're talking about the paper in which you proved Erdös's arithmetic sequence conjecture, right?"

Fang Qiu poured water for Zhao Xiancai and said it again and again. He was able to express this conjecture so smoothly. It can be seen that this was not the first time he said it. It is very likely that he has told this matter more than once to his current students before.

After all, Zhao Xiancai is the one who has made the greatest achievements and experienced the most legendary experiences in all the years Fang Qiu has been a teacher.

Moreover, Zhao Xiancai still has the transformation from a scumbag to a top student, and then to a god of study. His experience is the most inspiring to those high school students with poor grades.

"Teacher Fang, have you also read my paper?" Zhao Xiancai asked in surprise.

"Haha, that's not true. I wanted to read it, but I couldn't understand it. But at that time, your matter was very popular on the Internet. Later, there was a special report by the Flower Club and an exclusive interview. How could I not know about this?

"

[The book-chasing app recommended to me by an old book friend who I have known for ten years is the Changyuan app! It is so easy to use. I rely on this to read and listen to books while driving and before going to bed. You can download it here. huanyuanapp ]

Fang Qiu also said with a smile.

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