Great Country Academician

In terms of basic natural sciences, it has to be admitted that there is indeed a big gap between Huaguo and those western countries.

If he was in Princeton, Xu Chuan could easily find people who could exchange mathematics with him. Deligne, Fefferman, Sarnac, Witten, Nash, and Xu Yuer were only Fields Medal winners, and Princeton could find them and slap them number.

In China, there are currently only two people who have won the Fields Medal.

One is him, and the other is Qiu Chengtong, who served as the dean of the Yanqi Lake Institute of Applied Mathematics at Shuimu University after returning to China last year.

In terms of top Chinese mathematicians, Huaguo is actually not in short supply. For example, the golden generation of Peking University in the 1980s, Zhang Wei, Xu Chenyang, Yun Zhiwei and others can all be called mathematicians.

And Zhang Wei, Zhang Yitang and others are even more popular candidates for the Fields Medal, even in the international arena, they are all top mathematicians.

But unfortunately, these people are basically not working in China now.

This also caused Xu Chuan to find someone in the country to talk about mathematics, but he couldn't find a suitable candidate.

Taking the high-speed rail, Xu Chuan came to the capital again.

In Mizuki University, energetic students come and go on the campus.

Because he had visited once before, this time he found Qiu Chengtong's office smoothly.

The name Qiu Chengtong is also well-known in the country, but the reputation is mixed, some praise it and some dismiss it.

On the one hand, it is because he is a Fields Medal winner and one of the top international mathematicians.

On the other hand, it was because of the sharp conflict with Peking University School of Mathematics and his nationality.

He and his student Tian Gang once caused a stir because of academic plagiarism. Let alone the academic world, even ordinary people who can surf the Internet knew about it.

However, at that time, Peking University, as the two top universities in China, had a considerable influence in the academic world. In addition, Tian Gang had already become a leader in the Department of Mathematics of Peking University at that time, and was supported by Peking University.

In addition, Qiu's nationality is from the United States, which is quite criticized in the country, so this matter was left alone.

But in the international mathematics community, Qiu's reputation is still quite large.

In the field of mathematics, in addition to the Abel Prize, he has won other top prizes, such as the Fields Medal, the Wolf Prize in Mathematics, and the Craford Prize in Mathematics.

He is also hailed as the "Ace Professor" by Harvard University, the emperor of mathematics, one person can reach a mathematics department;

He was also praised by the international mathematics master Donaldson as "the most influential mathematician in the past 1/4 century", which shows that his mathematical ability is top-notch.

Knocked on the door, there was a quick movement inside.

The person who opened the door was a student who didn't seem to recognize Xu Chuan. He asked curiously, "Who are you looking for?"

Xu Chuan: "Excuse me, is Professor Qiu Chengtong here?"

"What can you do with Professor Qiu?" Looking at the visitor who felt younger than himself, the middle school student in the office frowned and asked.

Since his teacher returned to China and settled in the Institute of Applied Mathematics of Mizuki University, students have come to ask questions almost every day.

It's not that it's bad for students to ask questions from their teachers, but the questions those students ask are too low-level for his teacher.

These are ordinary problems that can be solved by any mathematics professor, but they have to come here.

It may be that he wants to win the favor of the teacher by asking questions, so as to be favored, but this will only waste a lot of time for the professor and delay his research.

The visitor in front of me, who looks younger than himself, might also have this idea.

Xu Chuan didn't think too much about it. He hadn't seen this young man in front of him the last time he came here, but he was able to study in Qiu Chengtong's office, so he reckoned that he might be a new student recruited behind Mr. Qiu.

Smiling, he said, "I want to talk to Professor Qiu about the NS equation."

Hearing this, the student suddenly sneered in his heart.

This is another person who pretends to win the favor of the teacher with high-level questions, but the teacher hates this kind of pretending to understand the most in his life.

Studying the NS equation, do you think you are Chuan Shen?

He groaned in his heart, and just as he was thinking, the student looked at Xu Chuan and suddenly froze.

Looking at it, he suddenly shuddered, why did he feel that this person looked so familiar? Like Chuan Shen?

Suddenly, he shuddered again, and the figure of the idol in his memory gradually overlapped with the person in front of him.

Lying down a big hole, the one in front of me can't really be Chuan Shen, right?

Swallowing nervously, he asked tremblingly, "Are you Xu Chuan, God of Chuan?"

Xu Chuan raised his eyebrows and said with a smile, "It's me."

"Chuan God! Is it really your old man?!"

Hearing this, the corners of Xu Chuan's mouth twitched. How did he become an old man? This seniority has risen too fast.

"Please come in quickly, God Chuan, the teacher just went out to do something, he should be back later, you old man sit down first."

The students blocking the door quickly stepped aside and invited Xu Chuan into the office with excitement and trembling respectfully.

Hearing this address, Xu Chuan shook his head dumbfounded, and said, "It's fine to call me Professor Xu, and it's fine to call me God Chuan and the old man. This title is inappropriate."

"Professor Chuan Xu, what would you like to drink? Here are coffee, tea, juice and Red Bull." The young student asked nervously.

Xu Chuan smiled and said, "Just a glass of water, it doesn't need to be so troublesome."

As he spoke, he casually found a chair and sat down. His eyes fell on the manuscript paper on the desk. There were several questions on it, which belonged to the field of partial differential equations. His research was not conventional mathematics, but computational applied mathematics, and intelligent neuroscience. There was something about the networking side, which piqued his interest.

It has to be said that Qiu Chengtong's knowledge in the field of partial differential equations can be described as the pinnacle, which can be seen from the questions in this test paper for a graduate student.

He skillfully moved the partial differential method into differential geometry, and compiled these highly spiritual problems.

Partial differential equations are an amazing and widely used field of mathematics. They are very good at describing changes over time and space. They are very useful for describing all kinds of phenomena. They can be used to describe everything from planetary motion, weather changes, to changes in the structure of space and time. .

But it is notoriously difficult to solve.

For example, if you try to model air turbulence, the Navier-Stokes equations are the pinnacle of the field.

By solving this partial differential equation, it is possible to know the motion of the fluid at any point in time and simulate how it will continue to move or how it was moving before.

But these calculations are complex and computationally intensive, often relying on supercomputers to do the math.

And this is where the field of artificial intelligence and intelligent neural networks can come into play. They can use deep learning to speed up the speed of solution, which will have great benefits for scientific exploration and engineering applications.

The few questions on the manuscript paper on the table were all about this. It was presumably Qiu Chengtong's homework left for his students, and there were some answers already written on it. What Xu Chuan saw was the part with the answers.

"This idea is interesting. By approximating the Fourier function in Fourier space, a series of calculations can be completed. However, this answer is not perfect. Without transformation, the entanglement cannot be reduced, and the answer cannot be obtained accurately."

On the manuscript paper, the answer to a question aroused Xu Chuan's interest.

For him, this kind of questions for graduate students or doctoral students can be said to be able to see the answers and methods at a glance, as well as the flaws and problems in the answers.

But the above idea did surprise him, it was a solution he hadn't thought of.

This is normal.

Everyone has their own unique thoughts and ideas. Even if Gauss Newton was reborn, he would not dare to say that he knows all mathematics and can find all the solutions to a mathematical problem.

Xu Chuan never thought that he could surpass everyone by winning the Fields Medal. In the field of mathematics, no one has such a qualification.

In the office, as soon as the young student came over with a glass of water, he heard Xu Chuan talking to himself, and his heart was shocked.

Is this what a Fields Medal winner is capable of? The flaw in his answer was immediately apparent.

After thinking about it, he couldn't hold back after all, and asked, "Then, Chuan Shen, is there a way to change this entanglement?"

He has been stuck on this problem for a long time, and he has never been able to think of a good solution. Now that a top mathematician is right in front of him, and he has become interested in the problem, how can he hold back from asking.

Hearing the question, Xu Chuan came back to his senses, took the water glass and said with a smile, "What's your name?"

"Wei Yong, Chuan God can call me Xiaowei or Xiaoyong." The young student replied quickly.

Xu Chuan smiled and said, "Your idea is quite interesting, but the follow-up expansion is not something you can solve at this stage."

"If I'm not mistaken, you should be Professor Qiu's new graduate student, right?"

Wei Yong nodded and said, "Well, I only studied with Professor Qiu in the second half of last year."

Xu Chuan continued: "Let me ask first, how did you come up with the idea of ​​using the Fourier space to approximate the Fourier function to complete a series of operations in the intelligent neural network data calculation?"

"According to common sense, solving this kind of problem is often promoted by the function between the input and the output defined in the approximate Euclidean space?"

Wei Yong scratched his head, smiled embarrassedly, and said: "I have minored in computer science in college, and I often use Fourier transform for simulation in signal processing, so I want to try the approximation in Fourier space. Can the function get the answer to this question."

As he spoke, he spread his hands: "The result is obvious, but I'm stuck, and I still can't find a way to calculate the exact value."

After a pause, Wei Yong continued: "But I always feel that this road should be able to go through, so I never gave up."

Xu Chuan picked up the test paper on the table with a smile, pointed to the answer on it and said, "Your feeling is correct, this road can indeed be passed through, but your knowledge reserve is not enough, and the second step is wrong. "

Just as he was speaking, the door of the office was pushed open, and an old man with glasses walked in. Seeing the figure in the office, the old man was stunned for a moment, then walked over with a smile on his face.

"A rare visitor, Professor Xu is free to come to my place today." Qiu Chengtong smiled and greeted him warmly.

Xu Chuan stopped the words in his mouth, stood up and said with a smile: "I have encountered a problem in mathematics, and I want to come to ask you for advice."

A trace of surprise flashed in Qiu Chengtong's eyes, and he said with a smile: "I would like to hear what it is that can make you feel difficult."

Xu Chuan said, "It's related to the NS equation."

Qiu Chengtong froze for a moment, although he knew that the problem that could stump the person in front of him would definitely not be simple, but he didn't expect that it would be directly at the level of the seven millennium problems.

Smiling, he took off his coat, hung it on the hanger beside him, and continued: "This is a big problem, and it probably won't be solved in a while. Sit down first, we have plenty of time to chat."

Xu Chuan said with a smile: "I have studied the NS equation with Fefferman for a period of time before, and I want to continue to study it."

"However, I encountered some problems in the field of partial differential equations, and in this field, Qiu Lao, you are the real master, so I thought of coming here and asking for your advice."

There is nothing wrong with what he said. In the field of partial differential equations, Qiu Chengtong is indeed the top expert, and he can even be said to be the No. 1 in this field.

He not only greatly expanded the role of partial differential equations in differential geometry, but also created an extremely important branch of mathematics "geometric analysis".

Not to mention other things, five mathematicians who came out of the field of geometric analysis won the Fields Medal, which shows the importance.

Qiu Chengtong shook his head with a smile, and said: "It's okay to give advice from Daniel in front of you. You are the first in history to win the Nobel Prize and the Fields Medal."

"Xiaowei, go make a pot of tea."

While directing the students to make tea, Qiu Chengtong's eyes also fell on the test paper in Xu Chuan's hand. He smiled and said, "This is just a homework for the students. Professor Xu can't just let it go."

Xu Chuan said with a smile: "This student is very interesting. He already has some ideas of his own on partial differential equations, which is pretty good."

"oh?"

Hearing Xu Chuan's praise, Qiu Chengtong was a little surprised, and reached out to take the manuscript paper and read it.

After a while, he shook his head with a smile, and said, "This line of thinking is really interesting, but there are problems with this answer, and it doesn't work."

Xu Chuan nodded, and said: "Yes, he made a crucial mistake. He forcibly took the conjugate to make the function space a Hilbert space, which would make it impossible to expand in the second step."

Qiu Chengtong thought for a while and asked, "If you want to solve this problem from this way of thinking, what do you think?"

Xu Chuan pondered for a while and then said: "To transform the approximated Fourier function, it is necessary to parameterize the integral kernel in the Fourier space, and then use the function to decompose and approximate the approximated Fourier function orthogonally, and then convert it into The wave function describing the momentum p."

Qiu Chengtong pondered for a while, and then praised: "This is indeed the most suitable way."

"What I just thought about is to use the Fourier series to do the intersection of orthogonal functions and make the basis function in the Lagrange interpolation polynomial, and then use the non-singular values ​​of the coefficient matrix to do the solution."

"But this method is much more complicated than your method, and the amount of calculation is also much larger."

"I didn't expect you to have such a deep understanding in the field of partial differential equations. It's really surprising."

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