In the eyes of his tutor, Qiao Yu is obviously not the kind of student who likes to brag. He can even be said to be very pragmatic.

Most of the older generation of professors are very rigorous.

They evaluate whether a person likes to brag by combining what he says with what he does. Although Qiao Yu's speaking style often sounds unpleasant, there is no doubt that he has done it all.

If you are known to be able to do something, it is not called bragging.

So after listening to Qiao Yu's words, Tian Yan really felt that Qiao Yu probably thought that he could solve the Riemann Hypothesis in half a year. The reason why he said it was one year was to give himself enough buffer time.

Although this sounds a bit unbelievable, but combined with the many scares given by Qiao Yu before, Tian Yanzhen feels that it is actually not bad. As for whether he can succeed, Qiao Yu may have simplified the problem...

Let's see. After all, he doesn't have much energy to understand deeply the things Qiao Yu studies.

I just know it, but I'm definitely not very proficient in it. If you know the specific method of mathematics and can operate it, it won't be that difficult.

So after understanding Qiao Yu's situation, Tian Yanzhen just warned: "Okay, don't talk nonsense before you can do it. It will be fine if you do it in the future, but if you don't do it, it will make people laugh!"

In addition, Academician Liu Zhaoyuan from the Institute of Computing Technology told me that he hopes to invite you to give a lecture. Do you think you can make time to come over and give a casual talk after the year?"

"I don't have time to answer this, right? Director Tian, ​​you know I will definitely be very busy recently. The chief engineer has said that the money for the construction of the data center will be paid after the year. I still have to do research myself.

I’m afraid I won’t be able to spare the time.”

Tian Yan was really annoyed and said: "Don't do this. You can't spare a day? Besides, what does it have to do with you once the money arrives? Mr. Yuan took over this matter and will naturally help you arrange it."

appropriate.

Do you know why you should receive this investment in the name of Huaqing Digital Research Center? On the one hand, it is a qualification issue, and the most important thing is that if you want to build this data center, Huaqing can provide a lot of resources.

Leave professional matters to professional people. The school has experts who specialize in this, and they will give you optimal 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 hacking your money. Having Mr. Yuan help you keep an eye on it will be more effective than keeping an eye on it yourself. If Mr. Yuan gets angry, it can really affect other people's jobs!

In this case, let me help you set a time. Just go there on Friday the 27th. You don’t need to go into detail, but don’t be too perfunctory to make people feel that it is worth the money.

When you talk about it, think about it, at least half of the 30 million you spent to build the computer room was calculated by others. This amount of money is not a small number for those who do mathematics!"

After scolding Qiao Yu, the other party immediately became honest.

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

"That's it. Liu Zhaoyuan and I will confirm the time. I may not be in the capital by then, so I will arrange for someone to take you there."

After hanging up the phone, Tian Yan felt inexplicably relieved.

If Qiao Yu can really solve the Riemann Hypothesis...

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

After all, the greater the hope, the greater the disappointment, so just pretend you don’t know! And really speaking, if Qiao Yu really does what he said, he would have solved the Riemann Hypothesis in one year...

He probably wouldn't force him to give a lecture on mathematics like he did today.

It's not that Qiao Yu is no longer his student after he solved this problem, but he should give such a great mathematician 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 status is, he must be a great mathematician! Otherwise, other mathematicians will feel embarrassed.

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

…

United States, Princeton University.

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

Zhang Shuwen stood on the podium, carrying the students in the audience, and quickly started writing on the blackboard.

After finishing writing, Zhang Shuwen tapped the blackboard lightly and said: "Today, as entrusted by Professor Dugan, I will discuss with you in depth this very 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.

Then we start from the modal space. Assume that the modal space M is a high-dimensional geometric space, and each point r represents the state of a system. The coordinates of this point are defined by the key parameters of the system..."

There were not only students but also many professors in the audience. In fact, this was not a formal class, but a Colloquium.

The research on generalized modal axiom systems 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 has made a start. No one can refuse to re-describe and quantify complex mathematical problems through geometry and algebra.

After all, a new perspective means being able to break through traditional methods and adopt new methods to solve those annoying problems.

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

For example, he didn't know much about the calculation work Qiao Yu was doing.

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

It does not take just three lectures for everyone to fully grasp the entire generalized modal axiom system.

Simply because as a field of mathematics that is still developing, 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 compiled yet. With the current depth and breadth of Zhang Shuwen's research, the content can be completed in about five or six hours.

"...To sum up, the core idea of ​​the generalized modal axiom system is to map number theory problems to high-dimensional geometric space and use the structural relationship between point states and path evolution in modal space to transform the originally abstract number theory into

The problem is geometricized and structured to achieve more intuitive description and quantitative analysis.

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

In order to realize the mathematical description and application of more complex systems, we also need to delve into how to modularize the generalized modal axiom system to form a more operational mathematical tool. This will be the main content of our next lesson.

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."

After Zhang Shuwen finished speaking, someone in the audience soon raised their hands.

"Say." Zhang Shuwen pointed to the person raising his hand in the audience. He knew this young man. He was a graduate student of his colleague Peter Sarnak. He was currently mainly studying L functions.

His teacher is also there, but sitting in the back row.

"Professor Zhang, when you were talking about the modal path just now, the picture you used was, well, it was the dynamic picture of the red curve in the 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 zero point of the Riemann zeta function. I want to know if this judgment is accurate?"

Zhang Shuwen smiled and replied: "If I could make an accurate judgment, I wouldn't use such inaccurate words. I can only say that the relevant research is still at a relatively early stage.

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

If you want to completely combine the two, there are still three directions of work to be done. First, you need to define the properties of the modal density function more accurately. There is no doubt that the proposer of the theory was lazy in this area.

Everyone who is here today must have read Qiao Yu's paper, which is the document we mainly quoted today. Qiao Yu did not accurately describe the symmetry and local properties of the modal density function.

Secondly, we also need to prove the relationship between the integral form and the analytic continuation of the ζ function under modal path symmetry. We must know that Pm is not arbitrary, it needs to satisfy specific geometric constraints. This is not clearly stated in Qiao Yu's paper.

.

Of course, the most important thing is to construct a two-way mapping, which is also the most difficult point. From the perspective of number theory, we also need to find a broader equivalence relationship between the modal path and the prime number distribution.

From a geometric point of view, the zero point distribution of the ζ function is reanalyzed through the symmetry of the path or the modal distance. In Qiao Yu's paper, some work was done, 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, I personally guess that this may involve some kind of high-dimensional symmetry group, or special constraints on a custom modal space.

As far as I know, a team from Huaxia Yanbei University is already involved in this problem, including the introduction of the modal space of the group structure. I guess that after this problem is solved, we will have more sufficient tools to pry into the truth of the ζ function.

"

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

After all, today is just a very basic content and not in-depth. The real difficulty level starts with modularizing the modal system and converting it into usable mathematical tools.

When Zhang Shuwen was packing up course materials on the podium, his colleague Peter Sarnak, the supervisor of the graduate student who had just asked the question, came to the podium and asked: "Are you in a hurry to go home? If you are not in a hurry, why not go for a drink?"

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

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

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

"Oh my god, didn't your doctor tell you that you might be allergic to caffeine?" Peter Sarnak said exaggeratedly.

Zhang Shuwen smiled, then sped up his movements. After finishing the courseware, he said, "Let's go."

The issue of allergies was not discussed.

When Zhang Shuwen first went abroad, he only thought it was hypocritical for people around him to regard allergies as a scourge. After all, in Zhang Shuwen's original understanding, in addition to the dangers of drug allergies, the things he encountered in life were really different.

I think allergies are a big deal.

But after I actually saw people around me who were admitted to the ICU due to anaphylactic shock due to allergy to some kind of foreign pollen, I realized that these people may not be pretentious, but have physical reasons.

Who would have thought that I usually don’t have symptoms of pollen allergy, but just because I encountered a flower I had never seen before, I thought it was very beautiful, so I picked it and smelled it a few times, and I went into shock within a few minutes...

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

Even if he is really allergic to coffee, Zhang Shuwen feels that it is at least much better than alcohol. There is no other way, he will feel a headache after drinking alcohol.

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

After all, in this country, professors are different from professors. Unless they are the kind of big bosses, the salary of professors is generally not high, so they naturally save as much as they can.

"Zhang, you know, my tutor Paul has been doing research on the Selberg conjecture. Well, actually I am also interested in this problem, but there is no good way yet. So do you think using that... um,
To be continued...