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. It can even be said that he is 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.
What everyone knows you can do is not 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 I say one year is to give myself enough buffer time.
Although this sounds a bit unbelievable, combined with the many scares Qiao Yu gave him before, Tian Yanzhen felt that it was actually not bad. As for whether he can succeed, does Qiao Yu think of the problem simply...
Let's see. After all, he didn't have much energy to understand deeply the things Qiao Yu studied.
I just know it, but I’m definitely not very proficient. If you know the specific method of mathematics and you can operate it, it won't be that difficult.
So after understanding the situation at Qiao Yu's side, Tian Yanzhen just warned: "Okay, don't talk nonsense before you can make it. It'll be okay if you make it in the future, but if you can't, it's okay.
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 take some time to come over and have a chat after the new year? ”
“You shouldn’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 data center construction will be available after the year. I still have to do some research myself, but I’m afraid I won’t be able to spare the time. "
Tian Yan was really annoyed and said, "Don't do this. Can't find time in the day? Besides, what does it have to do with you if the money arrives over there? Mr. Yuan has taken over this matter and will naturally help you make arrangements.
Do you know why this investment should be received in the name of Huaqing Digital Research Center? On the one hand, it is a question of qualifications. 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 professionals. The school has someone who specializes in this, and they will give you optimal configuration suggestions. In addition, it can also solve the problem of the location of the computer room.
Are you still planning to do these things yourself? Don't worry about someone hacking your money. With Mr. Yuan helping you keep an eye on it, the effect will be better than if you keep an eye on it yourself. If Mr. Yuan gets angry, it can really affect other people's jobs!
In this case, let me set a time for you. 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’s worth the money.
Think about it when you talk about it. At least half of the 30 million you spent to build a computer room was calculated by others. This amount of money is not a small amount 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 have decided on a 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 Yanzhen felt inexplicably relieved.
If Qiao Yuzhen could solve the Riemann Hypothesis...
As soon as this idea came to his mind, Tian Yanzhen shook his head subconsciously. Stop thinking about this problem.
After all, the greater the hope, the greater the disappointment, so let’s just pretend we don’t know! And really speaking, if Qiao Yu is really as 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 will definitely be a great mathematician! Otherwise it will make other mathematicians 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 System: Fundamentals and Applications" were 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 distance to quantify state changes in complex systems
So let's start with 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 are more than one audience. students, and many professors. In fact, this is not a formal class, but a study of Colloquium's current generalized modal axiom system. It is really hot. 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. 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 breaking through traditional methods and adopting new methods to solve annoying problems.
Zhang Shuwen’s advantage in this regard is that he can maintain smoother academic exchanges with the country. 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, this class is coming to an end. Zhang Shuwen prepared the same seminar for about three hours.
It does not take three classes 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 use the structural relationship between point states and path evolution in the modal space by mapping number theory problems to high-dimensional geometric 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 a new field of number theory research. This approach is also expected to provide new tools for classic problems such as analytic 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 still need to go deeper. Discuss 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 lesson, 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.
"You said it. "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 was also there, but he was sitting behind him. Row.
"Professor Zhang, when you were talking about the modal path, the picture you used was, well, 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 have an accurate judgment, I would not use such inaccurate words. I can only say that 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 derived some interesting symmetries.
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 this theory is stealing. Too lazy.
Everyone who is here today must have read Qiao Yu’s essay. That is the document we mainly quote today. There is no precise description of the symmetry and local properties of the modal density function.
Secondly, we also need to prove the relationship between the integral form and the analytical continuation of the ζ function under modal path symmetry. It is important to know that Pm is not arbitrary, it needs to satisfy specific geometric constraints. This point was not clearly stated in Qiao Yu’s paper.
Of course the most important thing is to build a two-way mapping, which is also the most difficult point. From a number theory perspective, we also need to find a broader equivalence relationship between finding modal paths and prime distributions.
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. 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, 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, there is already a team at Huaxia Yanbei University involved in this issue, including the introduction of the modal space of the group structure. I suspect that once this problem is solved, we will have more adequate tools to peek into the true nature of the zeta 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 only a very basic content and not in-depth. The real difficulty level is the part. Or model from the modal system? Blocking and converting it into usable mathematical tools began
When Zhang Shuwen was packing up the courseware on the podium, his colleague Peter Sarnak, the supervisor of the graduate student who had just asked the question, came to the side of the podium and asked. Sentence: "Are you in a hurry to go home? If you're not in a hurry, why not go have 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 packing up the course materials, he said, "Let's go."
He did not discuss the issue of allergies.
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, apart from drug allergies being dangerous, allergies to things he encountered in life really didn't seem to be a big deal.
But after I actually saw people around me who were admitted to the ICU due to anaphylactic shock due to some kind of foreign pollen allergy, 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 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 was nothing he could do, he felt a headache when the alcohol entered his mouth.
So the two of them didn't go out to find a small bar, and simply started chatting in the professor's lounge. There is a ready-made coffee machine after all.
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 very high, and they naturally save as much as they can. "Zhang, you know, my mentor 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, Can Qiao Yu’s method solve this problem?”
After making the coffee, Peter Sarnak took the initiative.
The Selberg Hypothesis can be regarded as a special case of the generalized Riemann Hypothesis. Its mathematical expression is that the non-trivial zero points of all automorphic L-functions on the key strip 0 Because this conjecture covers all automorphic L-functions, including the Riemann ζ function and the Dirichlet L-function, it is also a subset of the generalized Riemann conjecture. In the history of mathematics, there have always been people who like to ask questions that are strange but of great significance. 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 research on modular forms, automorphic forms and spectral theory, and was even crucial to the Langlands Program. Of course, because of this, Selberg's conjecture relies on higher-level tools and has a high research threshold, so there are relatively few researchers. In addition, the history is not as long as the Riemann Hypothesis, so its popularity is naturally not that high. Zhang Shuwen shrugged, and then replied: "How should I answer your question? Well, Peter, theoretically I can answer you for sure, yes! But for now, how to operate, I don’t have a clue yet. I believe you should have read the relevant literature before asking this question! Although there are many papers on Guan, most of them are still very shallow. In fact, Qiao Yu’s theory is still at a stage where it needs to be fully developed. There are still many articles to be written about the axiom system.” Read the error-free version at 69 Book Bar! 6=9+Book_Bar debuts this novel. Peter Sarnak smiled and said: "Look, this is exactly why I came to talk to you. I went to see Professor Dugan this morning, hoping that he could help me introduce it. Zhang Shuwen was stunned, then looked at Peter Sarnak in confusion and asked: "You can send an email directly to Qiao Yu. I think if he is interested, he should reply to you, right? I've seen that kid before, and he's still very polite. " Peter Sarnak spread his hands and laughed at himself: "Maybe it's because 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 originally planned to wait until March to go to Huaqing, and then talk to Qiao Yu Discuss how the generalized modal system can be better integrated into the number theory system "Well, let me ask for you. Of course, I'm not sure he is interested in this proposition. I heard that he has been quite busy recently and has at least two collaborative research projects on hand." "Thank you, Zhang! By the way, help me tell Qiao Yu that I am very interested in his theory. If he agrees, I can share all the current research materials with him. For example, we have verified several special cases of zero-point distributions and random matrices on some specific types of automorphic L-functions. A theoretical analogy to the zero-point distribution Especially the Berry-Keating model. In short, I believe that this part of the preliminary work should provide some help for the mapping of modal space. "Peter Sarnak said confidently. Zhang Shuwen nodded. "By the way, tell him, if his method can really help us solve this problem , we can work together. " Peter Sarnak explained again. There is no other way.
Just like many unsolved mathematical problems, the reason why they cannot be effectively solved is mostly because the existing mathematical tools cannot explore the truth at all. I have been thinking about a certain mathematical problem for more than ten years or even decades, and basically I have tried all the available tools. Zhang Shuwen expressed his understanding, but he would definitely not take over everything. There was no way, Qiao Yu was not his student. Even the relationship between the two is difficult to say. After all, when the two met for the first time, he severely punished Qiao Yu and even criticized him for not being too ambitious. Although he did have good intentions at the time, there is a deep gap between today's young people and his generation. Zhang Shuwen didn't know what Qiao Yu was thinking. Maybe he has been slandering him as an old antique who is good at teaching others - this is very possible. Especially since this guy has grown into a genius so quickly that it is difficult to evaluate him... This is even more embarrassing. But even if we go back to the first time the two met, Zhang Shuwen felt that what should be said at that time still had to be said. We can't let the trajectory of fate change... If he hadn't said those words and Qiao Yu hadn't constructed the generalized modal axiom system, it would definitely be a great loss to the mathematical community. Recalling the scene of his first meeting with Qiao Yu, Zhang Shuwen nodded absently and promised: "Don't worry, I will convey the original words to him." After speaking, Peter Sarnak couldn't help but look at his cup of coffee that had not been touched much, and commented seriously: "You should protest to Professor Dugan and change the coffee. This The coffee is sour and astringent, I really don’t know how you can bear it. Next time you come to the institute, believe me, the coffee there is much better than your garbage coffee.” Zhang Shuwen. smiled. This guy is not the first to complain that the free coffee here at Mathematics College is terrible, and he will certainly not be the last. After seeing Peter Sarnak off, Zhang Shuwen sat in the tea room and thought for a moment before returning to his office and dialing Yuan Zhengxin's phone number from the office phone. "Hey, is this Shuwen?" "Yes, hello Mr. Yuan, how is your health lately?" "It's not bad, I can still eat, and I should live for another ten years. No problem.” Listening to Yuan Zhengzhong’s angry voice on the phone, Zhang Shuwen subconsciously smiled. I can tell that the old man is in a good mood. It's not surprising. Although there are still many disputes between the two parties, with a genius like Qiao Yu acting as lubricant in the middle, it is reasonable to be happy. After a person has passed the age of knowing his destiny, he actually doesn’t want much. Given Mr. Yuan's status, it is obviously the most important thing to inherit his knowledge. He had heard it all at Princeton. Not only was Qiao Yu very talented in mathematics, but Qiao Yu's mother seemed to be very talented as well. Just a little older. It's a pity, but it is said that there is not much problem in inheriting the mantle. "Take care of yourself." Zhang Shuwen said sincerely. "Is Shuwen calling you for something at this time? It's already nine o'clock in the evening at Princeton, right? It's still in the office." Zhang Shuwen said quickly: "Sana just now Professor Ke talked to me specifically. He put a lot of thought into Selberg's guess and has been stuck in a bottleneck for a long time. During this time, I came across Qiao Yu's method and was very interested. I wanted to invite Qiao Yu to collaborate on this topic, so I sent Qiao Yu three emails but no reply.
So you found me here and thought about asking me to help ask if Qiao Yu didn't read the email. If possible, I still hope to promote this cooperation. ” After saying this, Zhang Shuwen said nothing. What surprised him was that Mr. Yuan on the other side didn’t speak immediately, and the phone fell into silence. Zhang Shuwen didn’t urge him either. I waited quietly, but I started to wonder. To be honest, this was not the case. It's not an excessive request. Regardless of whether he agrees or refuses, Mr. Yuan's temperament should be very straightforward. After nearly thirty seconds of silence, Zhang Shuwen was about to speak to break the silence, and Yuan Zhengxin spoke. "Shuwen, have you thought about coming back recently?" ” Such a heavy topic, Zhang Shuwen thought for a few seconds and asked: "You mean to resign from the teaching position at Princeton?" "Yes, come back and teach at Huaqing. I can't work for a few more years. Come and look at the Numerical Research Center for me. Look at Qiao Yu. After all, this kid is too old. I'm not worried about mathematics, but I still don't have a thorough understanding of other issues. Someone has to keep an eye on him to prevent him from going astray. I'm really worried. Yes, without Qiao Yu, I wouldn't advise you like this, but you want to. , now even your colleagues are looking forward to cooperating with him. What does it mean? Do you dare to imagine that China will develop from a big country in mathematics to a world academic power in the near future? The center of the world? Maybe the country of China in the past? We are still unable to support such a grand vision, but what about now? Think about the current relationship between China and the other side. Shuwen, think about it carefully! Maybe the vision of our generation may lie with Qiao Yu. Realized in one generation! History is a cycle of reincarnations, and I have a hunch that another era of technological explosion may be about to begin. This round 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 surging when he said these words. After thinking seriously for a moment, his heart began to waver. Just put down everything he had here and go back directly, There was some hesitation. After thinking for a moment, he said: "Yuan Laorong, let me think about it. " "Well, this is a big deal, you need to think about it. As for the matter you mentioned, I will talk to Qiao Yu. But don't get your hopes up. There's a reason why he doesn't reply to emails. Recently, many teams and organizations have invited him to collaborate. The little guy is a little unbearable and even complained to me some time ago. And he does have a lot of things going on lately. You have to understand. " Zhang Shuwen replied: "Understood. I was just asking questions for Peter. Naturally, Qiao Yu still had to put his own plans first. " "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 for a while. In front of Mr. Yuan, he is a junior, but really speaking, he is sixty-one this year. Whether or not to go back at this age is indeed a question. After thinking for a while, Zhang Shuwen's eyes focused 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 at random. This is exactly the paper Qiao Yu published in the Annual Journal of Mathematics. The blank spaces at the top and sides of almost every page are densely filled with various annotations, ideas and additional derivation processes. China becoming a powerful country in mathematics is only a vision, but if we go back, it will be real to be exposed to the most cutting-edge mathematical ideas. A huge system that converts all numbers into elements. It's a shame that this guy can think of it and can do it. Perhaps it’s really time to go back? (End of this chapter)
I think we can work with Qiao Yu to overcome this proposition. You know the significance of this subject. But Professor Dugan said maybe I could talk to you. "
Zhang Shuwen thought for a while and agreed.
You know, although we are still far away from the final solution of Selberg’s conjecture distance, but some breakthrough work has been done.
< br>"Thank you, Zhang! I'm waiting for your news."