In terms of basic natural sciences, we have to admit that there is still a big gap between China and those countries in the West.
If he were at Princeton, it would be easy for Xu Chuan to find people to communicate with him about mathematics, such as Deligne, Fefferman, Sarnak, Witten, Nash, Xu Qier... just the Fields Medal winners.
Princeton can find out in one slap.
In China, there are only two people who have won the Fields Medal so far.
One is him, and the other is Qiu Chengtong, who took up the post of dean of the Yanqi Lake Institute of Applied Mathematics at Shuimu University after returning to China last year.
If we talk about top Chinese mathematicians, China 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 popular candidates for the Fields Medal. Even internationally, they are among the top mathematicians.
But unfortunately, most of these people are not working in the country now.
This also caused Xu Chuan to find someone in China to discuss mathematics issues but could not find a suitable person.
...
Taking the high-speed rail, Xu Chuan came to Beijing again.
In Shuimu University, energetic students come and go walking on the campus.
Because he had visited once before, he found Qiu Chengtong's office smoothly this time.
The name Qiu Chengtong is also famous in China, but his reputation is mixed, with some praising him and others dismissing him.
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 Science and his nationality.
He once caused an uproar with his student Tian Gang over academic plagiarism. At that time, not to mention the academic world, even ordinary people who knew how to access the Internet knew about this matter.
However, at that time, Peking University, as one of the two top universities in China, had considerable influence in the academic world. In addition, Tian Gang had become a leading figure in the Department of Mathematics at Peking University and was strongly supported by Peking University.
In addition, Qiu's nationality was American, which was quite criticized in China, so the matter was settled like this.
But in the international mathematics community, Qiu's reputation is still quite high.
In the field of mathematics, in addition to the Abel Prize, he has won other top awards, such as the Fields Medal, the Wolf Prize in Mathematics, and the Crafford Prize in Mathematics.
He is also hailed as the "Ace Professor" by Harvard University, the emperor of mathematics, one person can equal the entire mathematics department;
He was also hailed as "the most influential mathematician in the past quarter of a century" by the international mathematics master Donaldson, which shows that his mathematical ability is top-notch.
.......
Knocked on the door, and soon there was movement inside.
The person who opened the door was a student-looking person who didn't seem to recognize Xu Chuan. He asked curiously: "Who are you looking for?"
Xu Chuan: "Is Professor Qiu Chengtong here?"
"Do you have anything to do with Professor Qiu?" The student in the office frowned as he looked at the visitor who seemed younger than himself.
Since his teacher returned to China and settled in the Institute of Applied Mathematics of Shuimu University, students 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 asked were too low-level for their teachers.
These are ordinary problems that can be solved by any mathematics professor, but they come here anyway.
Maybe you want to win the favor of the teacher by asking questions so that you can be favored, but this will only waste a lot of the professor's time and delay his research.
The visitor in front of me, who looks younger than me, might also have this idea.
Xu Chuan didn't think much about it. He hadn't seen the young man in front of him last time, but he was able to study in Qiu Chengtong's office. He guessed that he might be a new student after Qiu Chengtong.
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 ask advanced questions to win the favor of the teacher. Little does he know that teachers hate this kind of people who don’t know how to pretend to understand.
Studying the NS equation, do you think you are the God of Sichuan?
I snorted in my heart, and just as I was thinking about it, the student suddenly froze when he looked at Xu Chuan.
As he looked at it, he suddenly trembled. Why did he feel that this person looked so familiar? He looked like the God of Sichuan?
Suddenly, he shuddered again, and the idol figure in his mind gradually overlapped with the person in front of him.
I'm in a big trough, can't the person in front of me really be the God of Sichuan?
Swallowing nervously, he asked tremblingly: "Are you Xu Chuan, the God of Sichuan?"
Xu Chuan raised his eyebrows and said with a smile, "It's me."
"Sichuan God! Is it really you?!
"
Hearing this, the corner of Xu Chuan's mouth twitched. Why did he become an old man? He must have risen too fast in this generation.
"Quickly...please come in, Chuan Shen, the teacher just went out to do something. He should be back in a while. You old man, please sit down for a while."
The students blocking the door quickly gave way and respectfully invited Xu Chuan into the office with excitement and trembling.
Hearing this title, Xu Chuan shook his head in confusion and said, "Just call me Professor Xu. Forget about Sichuan God or Old Man. This title is inappropriate."
"Sichuan...Professor Xu, what would you like to drink? There are coffee, tea, juice and Red Bull here." The young student asked nervously.
Xu Chuan smiled and said: "Just a glass of water, no need to bother."
As he said that, he 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. The research was not conventional mathematics, but computational applied mathematics, and intelligent neuroscience.
There was something about the Internet, which aroused his interest.
It has to be said that Qiu Chengtong's knowledge in the field of partial differential equations is at its peak, and you can get a glimpse of it from the test questions given to a graduate student.
He moved the partial differential method into differential geometry with great proficiency, and compiled these extremely spiritual problems.
This chapter is not over, please click on the next page to continue reading! Partial differential equations are a very magical and widely used field of mathematics. It is very good at describing changes with time and space. It is very useful for describing various phenomena. It can be used to describe everything from planets to
Everything from movement, weather changes, to changes in the structure of space and time.
But it is notoriously difficult to solve.
For example, if you try to simulate air turbulence, the Navier-Stokes equation is the pinnacle of this field.
By solving this partial differential equation, you can know the motion of the fluid at any point in time and model how it will continue to move or how it was moving before.
However, these calculations are very complex and computationally intensive, so supercomputers are often relied upon to perform mathematical operations.
And this is where the fields of artificial intelligence and intelligent neural networks can come into play, using deep learning to speed up solutions, which will be of great benefit to scientific exploration and engineering applications.
Several questions on the manuscript paper on the table are all related to this aspect. It seems that they are assignments left by Qiu Chengtong to his students. There are also parts of them with answers written on them. What Xu Chuan looked at was the part with the answers.
"This idea is a bit interesting. By approximating the Fourier function in Fourier space, a series of operations are completed. However, this answer is not perfect. Without transformation, the entanglement cannot be reduced, and the answer cannot be accurately obtained.
"
On the manuscript paper, the answer to a question aroused Xu Chuan's interest.
For him, this kind of question for postgraduate 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. This was a solution he had never thought of.
This is normal.
Everyone has their own unique thoughts and ideas. Even if Gauss and Newton were reborn, they would not dare to say that they understand 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 qualifications.
.......
In the office, as soon as the young student came over with a glass of water, he heard Xu Chuan's soliloquy and was shocked in his heart.
Is this the ability of a Fields Medal winner? The flaws in his answers can be seen at a glance.
After thinking about it, he finally couldn't hold it back and asked: "So, Sichuan God, is there a way to change this entangled nature?"
He has been stuck on this problem for a long time and has never thought of a good solution. Now a top expert in mathematics is right in front of him and he is interested in the problem. How can he resist asking.
Hearing the inquiry, Xu Chuan came to his senses, took the water glass and said with a smile: "What's your name?"
"Wei Yong, Sichuan God can call me Xiao Wei or Xiao Yong." The young student quickly replied.
Xu Chuan smiled and said: "Your idea is quite interesting, but subsequent expansion is not something you can solve at this stage."
"If I guess correctly, 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 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 such problems is often promoted through functions between input and output defined in an approximate Euclidean space, right?"
Wei Yong scratched his head, smiled sheepishly, and said: "I minored in computer science in college. I often use Fourier transform for simulations in signal processing, so I want to try the approximation in Fourier space.
Can functions answer this question?"
As he said that, he spread his hands and said: "The result is obviously easy to see. I'm stuck and I can't find a way to calculate the exact value."
After a pause, Wei Yong continued: "But I always felt that this road should be possible, so I never gave up."
Xu Chuan smiled and picked up the test paper on the table, pointed to the answers on it and said: "Your feeling is right, this path can indeed be taken, but your knowledge reserve is not enough, and you took the wrong step in the second step.
......."
Just as he was talking, the door of the office was pushed open, and an old man wearing glasses walked in. Seeing the figures in the office, the old man was stunned for a moment, and then walked over with a smile on his face.
"I'm a rare visitor. How come Professor Xu is free to come and sit with me today?" Qiu Chengtong smiled and greeted him warmly.
Xu Chuan stopped talking, stood up and said with a smile: "I encountered a problem in mathematics, and I wanted to come to you for advice."
A trace of surprise flashed in Qiu Chengtong's eyes, and he smiled and said: "I would like to hear what the question is that can make you feel difficult."
Xu Chuan said: "It has something to do with the ns equation."
Qiu Chengtong was stunned for a moment. Although he knew that the problem that could stump the person in front of him would definitely not be simple, he did not expect that it would be directly on the level of the seven millennium problems.
Smiling, he took off his coat, hung it on a hanger nearby, and continued: "This is a big problem. It probably won't be solved for a while. Let's sit down first. We have plenty of time to chat."
Xu Chuan smiled and said: "I have studied the ns equation with Fefferman for a while before, and I want to continue studying it."
"But I encountered some problems when studying the field of partial differential equations, and in this field, Mr. Qiu, you are the real expert, so I thought I would come over and ask 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 can even be said to be No. 1 in this field.
He not only greatly expanded the role of partial differential equations in differential geometry, but also created the extremely important branch of mathematics "geometric analysis".
Not to mention others, five mathematicians who came out of the field of geometric analysis have won the Fields Medal, which shows its importance.
Qiu Chengtong smiled and shook his head and said: "It's okay to give advice from a great expert in front of you. You are the first person 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 an assignment left for the students. Professor Xu must not just solve it easily."
Xu Chuan smiled and said: "This student is quite interesting. He already has some ideas of his own on partial differential equations, which is quite good."
"oh?"
Hearing Xu Chuan's praise, Qiu Chengtong was a little surprised, reached out and took the manuscript paper and read it.
After a while, he smiled and shook his head and said: "This idea is indeed quite interesting, but there is a problem with this answer and it doesn't make sense."
Xu Chuan nodded and said: "Yes, he made a key mistake. He forcibly took the conjugate and made the function space a Hilbert space. This will make it impossible to expand in the second step."
Qiu Chengtong thought for a while and asked: "If we want to solve this problem from this idea, what do you think?"
Xu Chuan pondered for a moment and then said: "To transform the approximated Fourier function, we need to parameterize the integral kernel in the Fourier space, and then use the function to approximate it by orthogonal decomposition of the complex exponential signal, and then convert it into
Describes the wave function of momentum p."
Qiu Chengtong thought for a moment, and then praised: "This is indeed the most suitable way."
"What I just thought about is to use Fourier series to make orthogonal function intersections and Lagrangian interpolation polynomials to make basis functions, and then use the non-singular values of the coefficient matrix to solve it."
"But this method is much more complicated than your method, and the calculation amount 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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