The top student must be diligent.

Chapter 208 The server of the Annals of Mathematics crashed

It is indeed a bit unreasonable for a professor to have never taught students.

Although there are some professors who have students but never care about their students' life or death and are always busy with their own careers.

But at least these professors still have students under their names.

People like Xiao Yi are a little rare.

He touched his nose with a little embarrassment. It was indeed because of the Science Island Laboratory and the need to write the book Principles of Experimental Analysis. So when the school asked him if he was ready to teach students, he temporarily declined.

Well, now that the science laboratory is on the right track, it is time for me to take on my responsibilities as a teacher.

So he said, "Okay, then it depends on the school's arrangements. But it should be almost December now, right? I've already missed the graduate school enrollment."

Hearing that Xiao Yi agreed to teach students, Tang Fucheng and Shen Gensheng both laughed.

Tang Fucheng said, "Don't worry. The postgraduate recommendation interviews were completed in October. In two weeks, our college will set the time for recommended students to choose their supervisors. We will provide an online communication opportunity for recommended students and college supervisors."

"These recommended students are basically excellent students, so we also hope that these students can choose the instructors they prefer."

Shen Gensheng beside him also nodded and said, "Our college has also decided to hold the meeting in two weeks. By then, you can arrange the communication time with those students."

Xiao Yi nodded: "Okay, then I'll be ready when the time comes."

"Well, we will put your name on the list of available tutors, and then send you the list of students who want to apply for you." Tang Fucheng said, "By the way, do you need us to help you screen the candidates? After all... I suspect that when the time comes, most of the students will try to choose you when they see your name on the list of available tutors."

Xiao Yi thought about it, then shook his head and said, "Forget it. If people are willing to choose me, but in the end they can't even meet me, they will be disappointed. Anyway, if it's just a recommended student, there shouldn't be many people, right?"

"Not much indeed." Both deans laughed.

"I think there are only about a hundred of them in total."

Xiao Yi was immediately sweating profusely.

"One hundred? That many?"

Both deans shrugged and said with a half-smile, "So are you sure?"

Not to mention the School of Mathematics, the School of Physics of USTC can be regarded as the largest school in the whole university. When USTC was first established, physics accounted for half of the school. At the same time, the physics major of USTC is firmly ranked among the top two in the subject evaluation of universities.

Naturally, among the students recommended for physics majors every year, there are quite a lot of people who want to apply to the School of Physics of USTC, basically more than a hundred people.

Then, after eliminating students who may not be in line with Xiao Yi's research direction, there are probably seventy or eighty people in the School of Physics who want to apply for Xiao Yi. Add to that the School of Mathematics, the mathematics department of USTC is also top-notch in the country. Together, let alone a hundred people, it would be easy to exceed a hundred.

Xiao Yi wiped the sweat from his forehead. He was almost exhausted to death when he interviewed so many people at the Science Island Laboratory before. Now...

But in the end he gritted his teeth and said, "Come on, it's only a matter of a few days anyway."

The two deans laughed and then patted him on the shoulders.

"Since Professor Xiao has the energy to do this, I believe the recommended students will be very happy."

"Professor Xiao, you have perseverance!"
"Then we won't bother you for now. We have to go back and contact the principal to inform him about this model. Once we have finalized it, you can send out this paper."

Looking at the two people's faces trying to hold back their laughter, Xiao Yi always felt that what he had just agreed to was a bit hasty.

Forget it, why bother with these things.

He said, "Okay, I'll wait for your notification at any time."

Tang Fucheng and Shen Gensheng nodded and were about to leave.

But before leaving, Tang Fucheng said, "Also, when you publish this paper, where do you plan to publish it? Don't tell me that you will only publish the Chinese version and then publish it on your personal website, right?"

Xiao Yi shrugged and said, "I know, don't worry, I will submit it to the Annals of Mathematics when the time comes."

"That's fine, that's fine."

Tang Fucheng and the other man nodded.

It's not that they don't allow Xiao Yi to not submit to a journal, but for their ultimate plan of calling on the international community to jointly develop a burst trend identification model, if the paper is only published on Xiao Yi's personal website, it will obviously not be conducive to the dissemination of this matter.

If you want to accomplish something like this, the most important thing is to spread it first.

After that, the two of them left without saying anything more.

Xiao Yi was the only one left in the office again.

Naturally, he had no objection to publishing the paper in the Annals of Mathematics.

If you want to gain international appeal, you still need the influence of this kind of top journal.

"Okay, now I just need to wait for the results from the school, and then I will submit it to the Mathematics Yearbook."

"As for what's next..."

Xiao Yi turned the computer screen back again and looked at the paper on it.

Now that he has found the principle of the formation of the explosive solution, he can then use this principle to construct a sufficiently perfect initial condition.

From a mathematical point of view, the proof of the existence and smooth solutions of the NS equations often requires setting an initial condition. Initial conditions are crucial in the study of partial differential equations because they determine the state of the fluid at time t=0, thereby affecting the behavior and properties of the solution during the entire time evolution process.

But just when Xiao Yi was about to start thinking further along the common thinking habits in the mathematics community, his eyebrows suddenly raised.

"In the past, in the study of the NS equations, the reason for setting initial conditions was to avoid effects such as the blast solution."

“But now, with the explosion tendency theory, it seems that we can try to prove it from more general initial conditions?”

Thinking of this, Xiao Yi began to ponder.

If a more general proof of initial conditions can be achieved, its significance to the entire industry will certainly be quite high.

First of all, if a specific initial condition is set, the function of this initial condition must be smooth, which is also for the convenience of the subsequent proof.

However, in real life, initial conditions are often not so smooth. For example, data in atmospheric and ocean dynamics may be irregular or incomplete. Studying more general initial conditions will enable the NS equations to model these practical problems more accurately.

For simulations of complex flows such as aerospace and automotive industries, the initial conditions may contain irregular boundaries and multi-scale features. More generalized initial conditions can help improve the accuracy and predictability of these complex flow simulations.
Of course, these are all of application value. Theoretically speaking, more general proofs can also help improve the NS equations, making them more abstract and thus covering a wider range of initial condition types.

In short, a more general proof is definitely more valuable than a proof under specific conditions.

The latter is more about solving the problem rather than ensuring wider applicability of the final answer.

"But inevitably, this makes the proof more difficult."

Xiao Yi rubbed his head and thought helplessly.

The more general and abstract it is, the more difficult it is.

Well, let’s think back to why he wanted to prove the NS equations in the first place.

For the sake of that plate of vinegar, the dumplings were made in more and more varieties.

However, he quickly put these thoughts aside.

It's just a little more difficult and challenging, which is exactly what he wants.

"Consider more general initial conditions for the NS equations, where one can consider a variety of related function spaces."

"Well... first is the Lebesgue space."

【Definition: L^p(R^n)={f:R^n→R∣∥f∥L^p=(∫_R^n∣f(x)∣^pdx)^(1/p)<∞}, where 1≤p≤∞】

I simply wrote down the first type of function space on a piece of scratch paper.

Then he immediately started thinking about the second type of function space with generalized initial conditions. "Sobolev space, well, this space can be used to study functions with a certain smoothness."

[H^s(R^n)={f∈L2(Rn)∣∥f∥H……]

The number of spaces he listed on the draft paper gradually increased, including Besov space, Morrey space, and so on.

If we want to explore more general proofs, it is very effective to discuss them from different function spaces.
In this way, as time passed, his analysis gradually entered a deeper level.

……

Soon, Tang Fucheng and Shen Gensheng discussed the matter with President Bao. Just as they had expected, President Bao was of course very supportive of this matter. They even knew how great an impact this would have on enhancing USTC's status in the entire industrial field.

After all, fluid mechanics covers every little corner of the industrial field.

In addition to the industrial field, fluid mechanics analysis may also be used in other places, whether it is atmospheric science or even in games. Maybe in the future, game manufacturers will use this model to simulate sufficiently realistic fluids in their games?

This is almost inevitable.
In order to spread the message more widely, HKUST also contacted the government and some large companies with which it had good relations, both state-owned and private enterprises, and they all participated in this matter.

As everything was ready, Xiao Yi received the news, and then his paper was delivered to the editor-in-chief's mailbox of the "Annals of Mathematics" through an exclusive channel.

……

In the editor-in-chief's office of the Annals of Mathematics at Princeton University.

Peter Sanak looked at the new submission in his mailbox, raised his eyebrows slightly, and became interested.

"Xiao Yi's thesis?"

It has been a long time since he saw Xiao Yi's pure mathematics paper.

It seems that this mathematical genius, who was considered somewhat heretical in the eyes of many people in the mathematics community, has now returned to the embrace of pure mathematics.

But after he opened the paper and saw the title, he finally shook his head helplessly.

"Okay, it seems I was overthinking it."

"The Formation Mechanism of PDEs and Explosion Solutions of Dynamical Systems". Judging from the title, it is definitely not entirely in the field of pure mathematics, but also involves applied mathematics and physics to some extent.

However, Sanak narrowed his eyes again at this time.

"But...his paper actually claims to have solved the formation principle of explosive solution?"

He has some knowledge about blasting problems and knows very well how difficult it is to solve in related fields.

Unexpectedly, Xiao Yi actually set his sights on this issue?

He began to look down.

But soon, he shook his head with a little regret.

This paper was not his cup of tea and he couldn't understand it.

"Well... since it mainly involves the field of partial differential equations, let's find Terence Tao."

As a person who knows a little bit about everything, Terence Tao has also made great achievements in the field of partial differential equations.

Then, Sanak contacted Tao directly.

"Hey, Tao, I have a paper on partial differential calculus and I need your help reviewing it."

Tao Zhexuan's voice came from the phone: "Oh? If I can get Professor Sarak to contact me personally, it seems that I might know the author of this paper?"

Sanak is the editor-in-chief, and the authors of the manuscripts he commissions are basically acquaintances in the industry.

The top circle of mathematics is not that large compared to other subjects.

Sanak smiled and said, “Of course, this paper is Xiao Yi’s.”

"Oh?"

Tao's voice immediately showed a little more interest. "OK, send me his paper quickly. I haven't read his math paper for a long time. I hope it can bring me some surprises."

Sanak: "You won't be disappointed."

……

Terence Tao’s office at UCLA.

As a notification popped up on his computer that he had received a new email, Terence Tao couldn't wait to check his mailbox and download the attachment.

After opening the paper, the title immediately aroused his great interest.

"How does the explosive solution form?"

His brows widened slightly, feeling quite surprised.

He knew very well how difficult it was to study this thing, and it was almost hard for him to imagine how Xiao Yi could find this law hidden in the chaotic system.

His impatience prompted him to continue reading.

Just like that, the more he looked, the more shocked he felt.

Xiao Yi actually analyzed these results from more than 300 TB of data?
How did he do that?
From so much data, we can unravel the conditions for the formation of the explosive solution...

He was simply unimaginable.

Looking down further...

As Xiao Yi's analysis became more in-depth and he finally gave the concept of explosive trend, Tao could only sigh in his heart that Xiao Yi's mathematical ability was getting better and better.

It was not until the last part of the paper, in which Xiao Yi gave a model for identifying explosive trends and made a call for action, that Tao's eyes lit up.

"This model... looks really good. If we can feed enough of them, it will be a great help to the industrial field. Well, I have to help him."

Afterwards, after he responded to Sanak, he opened his blog and started his daily routine - water blog.

Every time he reads a paper that he finds interesting or valuable, he will also comment on the paper here.

[Today I reviewed a manuscript from the Annals of Mathematics, and this manuscript brought us three good news.

The first good news is that Xiao Yi still hasn't forgotten mathematics, and his mathematical ability has become stronger and stronger. Now I am looking forward to what kind of mathematical problems he can solve in the future.

The second good news is that in the field of partial differential equations or dynamical systems, the conditions for the formation of explosive solutions have been solved, which will be of great significance to the entire industry. Perhaps in the future, research involving these fields will be able to avoid the risks brought by explosive solutions. Of course, if we can propose a model based on Xiao Yi's paper and use machine learning to cultivate this model, perhaps we will be able to create a model that can be specifically used in various fields such as industry, thereby saving a lot of computing resources.

The third good news is that Xiao Yi has proposed such a perfect model and called on us. If we can feed this model with enough data, it will be able to help us apply it to research in the future. I think this is a very meaningful thing. It will become an innovation in the future industrial field!
In addition, the formation principle of the blow-up solution has been explained, which means that we are one step closer to proving the existence and smoothness of the solution of the NS equation. I even have an idea, which is to use the blow-up trend theory proposed by Xiao Yi to prove the NS equation under generalized initial conditions. Of course, I have to admit that this is a very difficult idea. To do this, I think we still need at least some new mathematical tools...

...]

As soon as Terence Tao published this blog, it immediately attracted a lot of attention.

For the pure mathematics community, the fact that the principle of the explosive solution has been solved is a very amazing achievement. As Tao said, this can help them achieve a deeper understanding of the NS equations.

For the field of applied mathematics, especially related fields such as fluid mechanics, it is an even bigger deal. Saving computing resources has always been the direction they are committed to researching. If Xiao Yi's paper is really as written in this blog post by Terence Tao, then it can really be called an innovation for them.

In this way, amid the expectations of both fields, the "Annals of Mathematics" finally put Xiao Yi's paper on its website first.

However, on the day when this paper was online, the editors of the Annals of Mathematics did not know how much influence this paper would have in the end, but what they did know was that their server had crashed.

……

(End of this chapter)