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Chapter 177 Why Not Come Back?

In the eyes of his tutor, Qiao Yu was obviously not the kind of student who liked to brag. He could even be said to be very pragmatic.

Most of the professors of the older generation are very rigorous.

When they judge whether a person likes to brag, they will look at what he says and what he does together. Although Qiao Yu's speaking style is often not pleasant to listen to, there is no doubt that he has done it.

If someone can do something that everyone knows he can do, it is not called bragging.

So after hearing what Qiao Yu said, Tian Yan really felt that Qiao Yu probably thought he could figure out the Riemann hypothesis in half a year. The reason why he said a year was to give himself enough buffer time.

Although this sounds a bit unbelievable, combined with the many scares Qiao Yu had given her before, Tian Yanzhen felt that it was actually not that bad. As for whether it would succeed, did Qiao Yu think the problem was too simple...

Let's wait and see. After all, he didn't have much energy to deeply understand the things that Qiao Yu was studying.

I just know it, but I'm definitely not proficient in it. If I knew the specific methods of mathematics, I would be able to operate it and it wouldn't be that difficult.

So after understanding Qiao Yu's situation, Tian Yanzhen just said: "Okay, don't talk nonsense if you haven't done it yet. It will be good if you can do it in the future, but if you can't do it, you will be laughed at!

In addition, Liu Zhaoyuan, an academician from the Institute of Computing Technology, told me that he hopes to invite you to give a lecture. Do you think you can spare some time to give a talk after the New Year? "

"I should answer that I don't have time, right? Director Tian, ​​you know I'll be very busy recently. Chief Engineer Yu said that the money for the data center construction will be in the account after the New Year. I also have to do research myself, so I'm afraid I won't be able to spare the time."

Tian Yan was really annoyed and said, "Don't give me that. Can't you spare a day? Besides, what does it have to do with you if the money arrives? If Mr. Yuan takes over this matter, he will naturally help you arrange it.

Do you know why the investment was accepted in the name of Huaqing Data Center? On the one hand, it was a question of qualifications, but the most important thing was that Huaqing could provide a lot of resources for you to build this data center.

Leave professional matters to professionals. The school has professionals who specialize in this. They will give you the best configuration suggestions. In addition, they can also solve the problem of the location of the computer room.

Do you still plan to do these things yourself? Don't worry about someone stealing your money. It's better to have Mr. Yuan to help you keep an eye on it than to do it yourself. If Mr. Yuan gets angry, it can really affect other people's jobs!

Well, I'll set a time for you. It's Friday the 27th, and you come over. You don't have to go into detail, but don't be too perfunctory either, so that people feel it's worth it.

Think about it when you talk about it. At least half of the 30 million you spent on building the computer room was paid by the Institute of Computing. This amount of money is not a small number for a mathematician! "

After Qiao Yu was scolded, the other party immediately became obedient.

"Oh, okay! I'll go there then."

"It's settled. I'll confirm the time with Liu Zhaoyuan. I might not be in the capital by then, so I'll arrange for someone to take you there."

After hanging up the phone, Tian Yanzhen inexplicably felt much better.

If Qiao Yu could really solve the Riemann hypothesis...

As soon as this thought came to his mind, Tian Yanzhen shook his head subconsciously and stopped thinking about it.

After all, the greater the hope, the greater the disappointment, so let's just pretend we don't know! And to be honest, if Qiao Yu really solved the Riemann hypothesis in one year as he said...

He probably wouldn't be forced to give a lecture at the Institute of Mathematics like he was today.

It doesn’t mean that Qiao Yu is no longer his student just because he solved this difficult problem, but we should give such great mathematicians a certain amount of respect.

Yes, as long as Qiao Yu can really solve the Riemann hypothesis, no matter how old he is or what his identity is, he will definitely be a great mathematician! Otherwise, other mathematicians will feel embarrassed.

After all, this problem is the crown jewel of mathematics!
……

Princeton University, USA.

In the small classroom, the electronic screen next to it displayed the words "Introduction to the Generalized Modal Axiom System: Fundamentals and Applications".

Zhang Shuwen stood on the podium, with his back to the students below, and began to write quickly on the blackboard.

After finishing writing, Zhang Shuwen tapped the blackboard and said, "Today, Professor Dugan has entrusted me to discuss with you this cutting-edge mathematical framework, the generalized modal axiom system.

Our goal today is to master the basic concepts of modal space, the construction of modal paths, and how to use modal distances to quantify state changes in complex systems.

So let's start with the modal space. Let the modal space M be a high-dimensional geometric space, each point r of which represents the state of a system, and the coordinates of this point are defined by the key parameters of the system..."

There are not only students but also many professors in the audience. In fact, this is not a formal class, but a colloquium.

The research on generalized modal axiom system is really hot now. Many Princeton professors, including Zhang Shuwen, have also begun to try to introduce this method into their respective research fields.

Especially number theory and analytic number theory.

After all, Qiao Yu had already made a start. No one could resist re-describing and quantifying complex mathematical problems through geometry and algebra.

After all, a new perspective means breaking through traditional methods and taking new approaches to solve those annoying problems.

Zhang Shuwen's advantage in this regard is that he can maintain smooth academic exchanges with China. Of course, most of them are purely theoretical.

For example, he was not very clear about the calculation work that Qiao Yu was doing.

After more than an hour of explanation, the class was coming to an end. Zhang Shuwen prepared about three class hours for the same seminar.

It is not possible for everyone to fully master the entire generalized modal axiom system in just three classes.

Simply because as a still developing field of mathematics, the core idea of ​​the generalized modal axiom system has been initially formed, but it still lacks a systematic and completely unified theoretical framework.

There is no corresponding textbook yet. Given the depth and breadth of Zhang Shuwen's current research, the content can be explained in about five or six hours.

“…In summary, the core idea of ​​the generalized modal axiom system is to map number theory problems into high-dimensional geometric space and utilize the structural relationship between point states and path evolution in the modal space to geometricize and structure the originally abstract number theory problems, thereby achieving more intuitive description and quantitative analysis.

This method not only opens up new avenues for number theory research, but also has the potential to provide new tools for solving classical problems such as analytic number theory. Therefore, understanding the basic construction of modal space is only the first step.

In order to achieve mathematical description and application of more complex systems, we also need to explore how to modularize the generalized modal axiom system to form more operational mathematical tools. This will be the main content of our next class.

If you have any questions about the content of this class, or have ideas that need to be discussed, you can start asking questions now. "

As soon as Zhang Shuwen finished speaking, someone in the audience raised his hand.

"You go ahead." Zhang Shuwen pointed to the person who raised his hand in the audience. He knew this young man. He was a graduate student of his colleague Peter Sanak and was currently focusing on L functions.

His teacher was there too, but was sitting in the back row.

"Professor Zhang, when you were talking about the modal path just now, the picture you used was, um, a dynamic picture of the red curve in three-dimensional space.

When you showed this picture, you mentioned that it seems that under certain conditions, the symmetry of the path is related to the zeros of the Riemann zeta function. I wonder if this judgment is accurate? "

Zhang Shuwen smiled and replied: "If I could make an accurate judgment, I would not use such an inaccurate word. I can only say that the relevant research is still in a relatively early stage.

Whether there is a specific connection between the two needs further rigorous proof. But we have observed and deduced some interesting symmetry phenomena.

If we want to fully combine the two, there is still work to be done in three directions. First, we need to define the properties of the modal density function more precisely. There is no doubt that the proposers of the theory were lazy in this regard.

Everyone who has come here today must have read Qiao Yu's paper. That is the paper we mainly cited today. Qiao Yu did not give an accurate description of the symmetry and local properties of the modal density function.

Secondly, we also need to prove the relationship between the integral form under the modal path symmetry and the analytical extension of the zeta function. It should be noted that Pm is not arbitrary, it needs to satisfy specific geometric constraints. This point is not clearly stated in Qiao Yu's paper.

Of course, the most important thing is to build a bidirectional mapping, which is also the most difficult point. From the perspective of number theory, we also need to find a more extensive equivalence relationship between modal paths and prime number distributions.

From a geometric point of view, the zero distribution of the zeta function can be re-analyzed through the symmetry of the path or the modal distance. Qiao Yu's paper did some work, but it was not comprehensive.

In other words, if you are interested in this direction, you need to find a geometric structure in the modal space whose symmetry completely matches the deep laws in number theory problems.

Here... well, my personal guess is that this may involve some kind of high-dimensional symmetry group, or special constraints on some custom modal space.

As far as I know, a team at Huaxia Yanbei University has already been involved in this problem, including the introduction of the modal space of the group structure. I guess once this problem is solved, we will have more sufficient tools to explore the truth of the zeta function. "

After answering this question, Zhang Shuwen briefly answered a few more questions and then announced the end of the get out of class.

After all, today's content is just very basic and not in-depth. The real difficulty level is to start from modularizing the modal system and converting it into usable mathematical tools.

When Zhang Shuwen was putting away his course materials, his colleague Peter Sanak, the supervisor of the graduate student who had just asked the question, came to the side of the podium and asked, "Are you in a hurry to go home? If not, why not go for a drink?"

Zhang Shuwen looked at Peter and said with a smile, "Forget about the wine, but coffee is fine."

"Haha, Zhang, drinking coffee at night is not a good habit. It will cause insomnia." Peter Sanak said with a smile.

"No, I sleep better when I drink coffee at night." Zhang Shuwen shook his head and said.

"Oh my God, didn't your doctor tell you that this means you might be allergic to caffeine?" Peter Sanak said exaggeratedly.

Zhang Shuwen smiled, then quickened his pace, packed up his courseware, and said, "Let's go."

The issue of allergies was not discussed.

When Zhang Shuwen first went abroad, he thought that the people around him were just being hypocritical when they looked down on allergies. After all, in Zhang Shuwen's mind, apart from the more dangerous allergies to drugs, allergies to things in life were not considered a big deal.

But after seeing people around me being admitted to the ICU due to anaphylactic shock caused by allergic reaction to some foreign pollen, I realized that these people might not be being pretentious, but it might be due to physical reasons.

Who the hell would have thought that I normally don’t have symptoms of pollen allergy, but just because I came across a flower I had never seen before and thought it was beautiful, I picked it up and sniffed it a few more times, and within a few minutes I went into shock…

From that time on, Zhang Shuwen expressed respect and blessings for the word "allergy", but never discussed it.

Even if he was really allergic to coffee, Zhang Shuwen felt that it was at least much better than alcohol. He had no choice but to feel a headache as soon as he drank alcohol.

So the two of them didn't go out to find a small bar, but simply chatted in the professor's lounge. After all, there was a ready-made coffee machine here.

After all, in this country, professors are not the same. Unless they are big shots, professors' salaries are not high, so they save as much as possible. "Zhang, you know, my mentor Paul has been doing research on the Selberg conjecture. Well, I'm actually interested in this problem, but I don't have a good solution yet. So do you think that... um, Qiao Yu's method can solve this problem?"

The coffee was ready, Peter Sarnak took the initiative.

The Selberg conjecture can be considered as a special case of the generalized Riemann conjecture. Its mathematical expression is that all self-conserving L-functions in the critical band 0

Since this conjecture covers all automorphic L-functions, including the Riemann zeta function and the Dirichlet L-function, it is also a subset of the generalized Riemann hypothesis.

Throughout the history of mathematics, there have always been people who like to ask some strange but significant questions.

The Selberg conjecture is undoubtedly one of them. Although it is not as well-known as the Riemann hypothesis, its significance is also profound.

For example, it inspired the study of modular forms, automorphic forms and spectral theory, and was even crucial to the Langlands program.

Of course, it is also because of this that the Selberg conjecture relies on more advanced tools and has a high research threshold, so there are relatively few researchers. In addition, it does not have a long history like the Riemann conjecture, so it is naturally not as well-known.

Zhang Shuwen shrugged and replied, "How should I answer your question? Well, Peter, in theory I can answer you with certainty, yes!

But for now, there is no clue on how to do it. I believe you should have read relevant literature before asking this question! Although there are many relevant papers, most of them are still superficial.

In fact, we are the same. Qiao Yu's theory is still in a stage that needs to be enriched. As I said in class, there is still a lot to be done on this axiom system. "

Peter Sanak smiled and said, "See, that's why I came to talk to you. I went to see Professor Dugan this morning and hoped he could make an introduction for me.

I think I can work with Qiao Yu to solve this problem. You know the significance of this topic. But Professor Dugan said maybe I can talk to you. "

Zhang Shuwen was stunned, then looked at Peter Sanak in confusion and asked, "You can send an email to Qiao Yu directly. I think if he is interested, he should reply to you, right? I have met that kid, and he is very polite."

Peter Sarnak spread his hands and said self-deprecatingly: "Maybe I'm not well-known. I wrote him three emails, all of which were automatic replies. I doubt he has the habit of checking his mailbox at all."

Zhang Shuwen really didn't know about this situation. He hadn't contacted Qiao Yu recently.

He had originally planned to go to Huaqing in March and then discuss with Qiao Yu how to better integrate the generalized modal system into the number theory system.

"Is that so? Then let me ask for you. Of course, I'm not sure if he is interested in this topic. I heard that he has been quite busy recently and has at least two collaborative research projects on hand."

Zhang Shuwen thought about it and agreed.

"Thank you, Zhang! By the way, please tell Qiao Yu that I am very interested in his theory. If he agrees, I can share all my current research materials with him.

You know, although we are still some distance away from the final solution to the Selberg conjecture, some groundbreaking work has been done.

For example, we have verified several special cases of zero-point distribution on some specific types of automorphic L-functions, as well as the analogy study of zero-point distribution in random matrix theory.

Especially the Berry-Keating model. In short, I believe this preliminary work should be able to provide some help for the mapping of modal space." Peter Sanak said confidently.

Zhang Shuwen nodded.

"By the way, tell him that if his method can really help us solve this problem, we can work together."

Peter Sarnak gave another explanation.

There is no way.

Just like many unsolved mathematical problems, the reason why they cannot be effectively solved is mostly because the existing mathematical tools are simply unable to explore the truth.

After thinking about a math problem for more than ten years or even decades, basically all the available tools have been tried.

Zhang Shuwen expressed his understanding, but he certainly would not take on too much responsibility. There was no way, Qiao Yu was not his student. It was even difficult to say whether the relationship between the two was good.

After all, when the two met for the first time, he scolded Qiao Yu severely and even criticized him for being too ambitious.

Although he did have good intentions at the time, there was after all a huge gap between today's young people and their generation, and Zhang Shuwen had no idea what Qiao Yu was thinking.

Maybe she has been secretly criticizing him as an old-fashioned person who likes to teach others - this is very likely. Especially since this guy has grown into a genius so quickly that it is difficult for him to evaluate him...

This is even more embarrassing. But even if we go back to the time when the two first met, Zhang Shuwen still feels that he should say what he should say. He can't let the trajectory of fate change...

If he had not said that, and Qiao Yu had not constructed the generalized modal axiom system, it would definitely be a great loss to the mathematics community.

Recalling the scene of his first meeting with Qiao Yu, Zhang Shuwen nodded absentmindedly and promised, "Don't worry, I will convey my original words to him."

"Thank you, Zhang! I'll wait for your news."

After saying this, Peter Sanak couldn’t help but glance at his untouched cup of coffee, and commented seriously: “You should protest to Professor Dugan and change the coffee.

This coffee is sour and bitter, I don't understand how you can stand it. Come to the institute next time, believe me, the coffee there is much better than this rubbish coffee of yours."

Zhang Shuwen smiled.

This guy is not the first one to complain about the taste of free coffee in the School of Mathematics, and he certainly won't be the last one.

After seeing Peter Sunak off, Zhang Shuwen sat in the tea room and thought for a while before returning to his office and calling Yuan Zhengxin on the office landline.

"Hello, is this Shuwen?"

"Yes, hello, Mr. Yuan, how are you feeling recently?"

"It's OK. I can still eat. I should have no problem living another ten years."

Hearing Yuan Zhengxin's angry voice on the phone, Zhang Shuwen subconsciously smiled.

You can tell the old man is in a good mood. It's not surprising. Although there are still many disputes between the two sides, with a genius like Qiao Yu acting as a lubricant in the middle, it's only natural that they are happy.

After people reach the age of knowing their destiny, they don’t ask for much. Given Yuan’s status, it is obviously most important for him to inherit his knowledge.

He had heard in Princeton that not only was Qiao Yu very talented in mathematics, but Qiao Yu's mother seemed to be talented as well. She was just a little older. It was a pity, but it was said that there would be no problem in inheriting the mantle.

"Take care of yourself." Zhang Shuwen said sincerely.

"Shu Wen, what's the matter with you calling at this time? It's already nine o'clock in the evening in Princeton, right? I'm still in the office."

Zhang Shuwen said quickly: "Professor Sanak just talked to me specifically. He has also spent a lot of time on the Selberg conjecture and has been stuck in a bottleneck for a long time.

During this period, I came across Qiao Yu's method and was very interested in it. I wanted to invite Qiao Yu to collaborate on this research topic, and I sent Qiao Yu three emails but he never responded.

So he came to me and asked me to help ask if Qiao Yu hadn't read the email. If possible, I hope to facilitate this cooperation. "

After saying this, Zhang Shuwen didn't say anything else. To his surprise, Mr. Yuan on the other end of the phone didn't speak immediately either, and the phone fell into silence.

Zhang Shuwen did not urge him, but waited quietly, but he began to wonder. To be honest, this was not an excessive request. Whether agreeing or refusing, given Yuan Lao's temperament, he should be very straightforward.

There was silence for nearly thirty seconds. Just as Zhang Shuwen was about to speak to break the silence, Yuan Zhengxin spoke up: "Shuwen, have you ever thought about coming back recently?"

Such a heavy topic. Zhang Shuwen thought for a few seconds and then asked, "Do you mean resigning from your teaching position at Princeton?"

"Yes, come back and teach at Huaqing. I won't be here for many more years. Come and help me look after the Mathematical Research Center and Qiao Yu. This kid is too young after all. I'm not worried about mathematics, but he still doesn't understand some other issues clearly enough.

Someone has to keep an eye on him and not let him go astray. Tian Yanzhen, I am not too sure. Really, if it weren't for Qiao Yu, I wouldn't have advised you like this. But think about it, now even your colleagues are looking forward to working with him, what does that mean?
Do you dare to imagine? Will China develop from a mathematical power to a mathematical powerhouse in the near future? Or even become the center of the world's academic community? Perhaps China's national strength could not support such a grand vision in the past, but what about now?

Think about the current relationship between China and the other side of the strait. Shuwen, think about it carefully! Maybe the vision of our generation can be realized in Qiao Yu's generation!

History is a cycle, and I have a feeling that another era of technological explosion may be about to begin. This time, our national strength is no worse than any other country, and we even have many advantages that other countries do not have! "

Zhang Shuwen could feel Yuan Zhengxin's heart surge when he said this. After thinking carefully for a moment, his heart began to waver.

He was a little hesitant to just leave everything he had here and go back.

After thinking for a moment, he said, "Mr. Yuan, let me think about it."

"Well, this is a big deal, and we need to think about it carefully. As for the matter you mentioned, I will talk to Qiao Yu about it. But don't get your hopes up. There is a reason why he didn't reply to the email.

Many teams and organizations have invited him to work with them recently. The little guy is a little overwhelmed and complained to me a while ago. And he has indeed been busy recently. You have to understand. "

Zhang Shuwen replied, "I understand. I'm just asking for Peter. Qiao Yu should still focus on his own plans."

"Okay, think about what I just mentioned. Let me know as soon as you make a decision."

"Okay, Mr. Yuan."

After hanging up the phone, Zhang Shuwen sat there in a daze. He was a junior in front of Mr. Yuan, but to be honest, he was already sixty-one years old.

Whether or not to go back at this age is indeed a question. After thinking for a while, Zhang Shuwen focused his eyes on the courseware on the table.

There was a paper underneath the courseware. Zhang Shuwen subconsciously took out the paper and flipped through a few pages casually.

This is exactly the paper that Qiao Yu published in the Annals of Mathematics.

Almost every blank space at the top and on both sides of the page is densely filled with various annotations, ideas, and additional derivation processes.

It is still just a vision for China to become a mathematical powerhouse, but it is true that if I go back, I will be able to be exposed to the most cutting-edge mathematical ideas.

A huge system that converts all numbers into elements. It's amazing that the guy could think of it and do it.

Maybe it's time to go back?

(End of this chapter)