Research starts with PhD students

Chapter 140: You should do this kind of advanced research yourselves!
Anton Kapustin is a professor at Caltech, specializing in linear and nonlinear numerical algebra and optimization, sparse optimization theory, and inverse problems in mathematical physics.

In the field of inverse problems in mathematical physics, Kapustin has achieved many world-class results, for which he has won several mathematics awards and is well-known internationally.

The study of inverse problems in mathematical physics requires the establishment of mathematical models to explain physical problems, which involves the complex problem of numerical solution of mathematical models.

Therefore, in response to Zhang Shuo's research results on the fermion Hubbard model, Anton Kapustin pays more attention to the "splitting and discretization" method rather than the research itself, because other mathematical models may also be split and discretized using the same method, and can be numerically solved using infinite discrete analysis.

Anton Kapustin is not the only one who thinks so. Many scholars in mathematics pay more attention to the methods used in research.

From this point of view, we can also understand how significant Zhang Shuo's research is.

Because of this, after Nakajima Kei noticed the research results, he immediately sent a message to other members of the Fields Committee and discussed with them the issues related to the Fields selection.

With such significant achievements, coupled with the research on numerical simulation of the NS equation, Zhang Shuo's position in the international mathematics field was established, and he became one of the most famous scholars in the field of mathematics.

At the same time, the two achievements combined were enough to allow him to surpass his peers and be directly nominated for Fields.

Domestic and international public opinion also holds this view.

There is no need to say much about the domestic public opinion. After Qiu Chengwen commented on Zhang Shuo's research results last time, many people were sure that Zhang Shuo would be the future Fields winner.

I haven’t won any award yet, but I will definitely win one in the future.

This idea is a bit crazy. After all, Fields did not win the award based on popularity. But many people think so. Some reports even said, "If Zhang Shuo's name is not among the two Fields winners, it means that the award is unfair."

In other words, if Zhang Shuo cannot win the award before he turns 30, it means that Fields' selection is unfair.

Foreign media reports also talked about the Fields Medal. Some media believed that Zhang Shuo was able to achieve such significant results and become the most outstanding young mathematician in recent years, and he is very likely to win the Fields Medal.

After these reports were sent back to China, many people became more confident that Zhang Shuo would win the award.

The Fields Medal is one of the highest awards in mathematics. Together with the Albert Medal and the Wolf Medal, it is known as the 'three major international mathematics awards'. However, in terms of real recognition, the Fields Medal far exceeds Albert and Wolf Medal.

For example, Qiu Chengwen is a Fields Medal winner. When mentioning the academic honors he has received, the Fields Medal comes to mind immediately.

In fact, Qiu Chengwen also won the Wolff Award, but few people call him a Wolff Award winner.

In the eyes of most people, Wolfe is still not as good as Fields, and this can only be regarded as an honor of "icing on the cake".

The same is true in the academic circle.

If a mathematician is very talented, he will definitely get Fields when he is young.

If he had not won the Fields Prize, but had won the Wolf Prize after the age of 40, many people would still feel that he was not as good as the Fields winner. Of course, the premise is that he had not achieved world-renowned results.

In short, Fields is recognized as the number one award in mathematics.

The Fields Medal is also of great significance to China, because no domestic mathematician has ever won the award.

The country has been increasing its investment in basic scientific research, mathematics being one of them, and the goal is to catch up with the international level in basic scientific research.

Mathematics in China has been developing continuously, but how can we say that it has made progress and how can we say that it has caught up with the international level?
Winning an award is a very important indicator!
If a domestic mathematician wins the Fields Medal, it naturally means that he or she has reached the world's most advanced level in a certain direction of mathematical research. That is why so much attention has been paid to whether Zhang Shuo can win the Fields Medal.

These attentions have brought Zhang Shuo a lot of popularity. For example, the number of followers of his account has been growing continuously.

At the same time, it also brought some troubles.

Many people believed that the research on the fermion Hubbard model was completed within a week, and the "amazing remarks" on the Internet remained popular for several days in a row.

Zhang Shuo had to send a message to clarify, "I started researching it three months ago."

He deliberately made the time seem longer, trying to make others think it was normal research.

This has no effect.

Most people pay more attention to the results rather than the duration of the research, because he did complete the numerical solution research of the fermion Hubbard model, and the research is also of great significance.

He had previously completed numerical simulation research on the NS equations and published three papers in one go.

When the two are combined, the length of the study is simply secondary.

Every day, reporters conduct interviews in a rush, and everyone they meet on the road casts curiosity and amazement at them.

Under the long-term attention, Zhang Shuo gradually got used to it. He continued to work normally every day and started his next research - the proof of the singularity of the NS equation.

This research is extremely difficult.

Zhang Shuo found that even if he worked hard on research every day, he could only complete an average of 0.1% to 0.2% of the progress. That was when his research was not stuck. He could think about a little bit every day, but the content of his thoughts was very small, and half a page of paper was enough to write it down.

There isn’t much content, and it’s very difficult to come up with.

"At this rate, with the krypton coins to guide the direction, the research will take more than two years..."

Two years is still acceptable.

Compared with the proof of the NS equation, two years is nothing, but it is still a long time.

Zhang Shuo no longer pursues quick research, but thinks about some points when he has time, and completes them slowly through accumulation. There will always be a day when it will be completed.

When you become famous, troubles will come to you automatically.

The School of Mathematics at Soochow University is going to hold a seminar on nonlinear partial differential equations.

Similar seminars can be understood as small academic conferences in a single field, usually attended only by professors, associate professors or other scholars in the professional field.

Some postdoctoral fellows and doctoral students on campus can also give reports or attend lectures at the conference.

This type of seminar is very small in scale, with the number of participants generally not exceeding a hundred people, and is planned to last only one or two days.

At the seminar, professors in their professional fields will share their experiences, and some scholars who have submitted papers can also give reports, but because seminars are not authoritative, reports can be made as "pre-reports" for large-scale academic conferences or submitted papers.

In other words, by making a report at a seminar, professors in related fields can take a look at whether there are any problems with the research and comment on the content. In the future, you can also get research reports from other academic conferences.

Such academic seminars are very inconspicuous.

Zhang Shuo was invited to serve as a judge for the seminar on nonlinear partial differential equations held by his own school, so it was natural for him to serve as a judge.

As a result, trouble came.

"We received a lot of submissions, more than 200 in total," Tan Youming said with a wry smile. "For this kind of seminar, submissions from PhD students and above are generally accepted. After all, it's just a report at the conference, but there are too many submissions."

"I don't know if there will be any follow-up. We are not holding a professional academic conference, and we don't have any conference committee. It's impossible for us to review each paper one by one, right?"

"besides……"

"Many professors have applied to attend the seminar, including researchers from the Institute of Mathematics of the Academy of Sciences, and even Academician Yan Chongwen. They all came for you!"

Tan Youming spoke helplessly.

The outside world knows that Soochow University is going to hold a seminar on nonlinear partial differential equations, and Zhang Shuo is likely to attend the meeting and even serve as a judge.

Many doctoral students, postdoctoral fellows, and even associate professor-level mathematical scholars directly submit their research to the seminar.

At the same time, many professors who were not invited applied to attend the conference. They definitely came to attend the conference because of Zhang Shuo.

Either for the study of numerical simulation of NS equations or for the study of discrete analysis of fermion Hubbard model. In short, the seminar was a hit.

Zhang Shuo had no other choice. "How about this? I won't be a judge anymore. You can tell everyone that I was not there during the seminar?"

"Uh~~~"

Tan Youming thought about it and said, "Forget it. It's actually good to have more people participating. We can just treat it as a small academic conference."

"You coming as a judge will also help boost the reputation of the School of Mathematics. We'll see what happens when the time comes."

"I'll talk to other professors and see what to do..."

……

In fact, the person in charge of the seminar was not Tan Youming, but Qi Zhixiang.

Tan Youming's main area of ​​research is harmonic analysis, not nonlinear partial differential equations, and he does not usually attend academic seminars in the field of nonlinear partial differential equations.

But he is the dean of the School of Mathematics.

When problems arose during the meeting, Qi Zhixiang reported them to him. In addition, other academicians applied to attend the meeting, so Tan Youming would definitely pay attention to the meeting work.

Zhang Shuo didn't care about these. He was invited to serve as a judge for the seminar. When the time comes, he will just have to attend the meeting. As for other problems that arise, let the person in charge of the meeting worry about it.

He continued with his normal life.

Sun Xingli still often comes to Zhang Shuo's office. After he officially joined Chen Tianze's research group, he is no longer as relaxed as before. Even when he comes to Zhang Shuo's office, he always has documents in his hands, as if he is ready to study and think at any time.

His explanation was, "When I met Professor Chen, he would definitely think I was serious when he saw what I was holding!"

"That's the kind of person I am. Now that I've joined the project, I have to do my best."

Zhang Shuo asked, "Any progress?"

Sun Xingli laughed out loud. "What progress can this kind of research make? Anyway, I will do whatever you ask me to do. We just need to hold a meeting once a week to discuss it."

"There is no future in studying Riemann functions and Riemann primes. When I think about these problems, I can't help but think about the marginal prime proof of square numbers."

"It seems that you are still suitable for research in the direction related to Zhou's conjecture." Zhang Shuo commented.

"I think so."

Sun Xingli suddenly opened the folder and took out a piece of manuscript paper and handed it to Zhang Shuo. "But I haven't been thinking about researching these days. I've been thinking about this. Take a look."

Zhang Shuo took a quick glance and found a bunch of numbers on it.

"Mersenne primes?"

"of course not."

Sun Xingli laughed and said, "You didn't understand, right?"

Zhang Shuo took a closer look and found that he really couldn't understand it. It was just a long string of numbers. What else could it be but Mersenne primes?

telephone number?

"The winning numbers of the Hong Kong Mark Six Lottery!" Sun Xingli gave the answer.

“…I didn’t expect this.”

Sun Xingli continued with a smile, "Xiaohong also bought a house, you also bought a house, and I also plan to buy a house, but it's very expensive, so I was wondering if I could do some research and then win a big prize. Now the prize pool has rolled up to nearly 200 million."

He picked up a pen and paper and started writing on the table, explaining, "This is not illogical research. We are studying mathematics and we want to find patterns."

"There are people in the world who specialize in analyzing lotteries and then win prizes."

“I want to find some patterns, too.”

"These are just the recent winning numbers. I have saved all the numbers I could find on my computer and analyzed them using statistical methods."

"Although in theory the probability of each number appearing is the same, I found that there are still deviations in the probability. It's like studying whether a number is prime. The probability of it being prime is related to the distribution of prime numbers."

"For example, if the number is small, the probability of it being prime is greater, and if the number is large, the probability is smaller."

"The winning numbers are random, but theoretically, the numbers in each position have the same probability of appearing. So after doing statistical analysis, if the frequency of occurrence is low, then the probability of appearing next time will naturally be greater..."

Sun Xingli said a lot of things in succession.

Zhang Shuo shook his head and said, "It's like tossing a coin. If you toss it again, the probability of heads or tails is still the same."

"However, what you said about the overall and single-occurrence probabilities does make a little sense. Analytically, I think we should not only analyze the overall situation, but also conduct research in sections."

“For example, we can make a function curve of the frequency of digital appearance in stages to study it.”

Sun Xingli thought about it and nodded, "Well, log in with your computer and I'll retrieve the data."

"Let's study it together."

After Sun Xingli retrieved all the data, they began to study the numbers.

At first, we conducted overall statistical research, then conducted statistical research in stages, and later we simply made function curves.

Zhang Shuo even created a task——

[Research project name: Mathematical rules of the winning numbers of Mark Six Lottery (Difficulty: E). ]

The difficulty level is only E, which means there is no innovative content.

In the absence of innovative content, even if the research is completed, it is only an "analysis" that can be analyzed using other methods, just like solving a math problem in many ways.

Zhang Shuo and Sun Xingli conducted various analyses together, with only one research goal - to obtain the most likely numbers to appear in the next few draws using mathematical and "non-mathematical" methods.

When Luo Yongjun entered the office, he saw Zhang Shuo and Sun Xingli discussing numerical problems together. There was a pile of mathematical manuscripts on the table, and there were also several manuscripts on the floor.

He picked one up and took a look at it, and found that it was a complex plane curve graph with several functions next to it.

He asked puzzledly, "What are you studying? Why can't I understand it?"

"Is it so complicated? What kind of function is this? I have never seen a similar curve before."

Zhang Shuo and Sun Xingli turned their heads to look over there.

Sun Xingli explained, "We are studying the most likely winning numbers for the next few draws of Hong Kong City Mark Six Lottery."

Zhang Shuo said, "Teacher Luo, do you want to study this together? You have a deep understanding of linear differential equations. Can you help us look at these equations and see if there are any common points?"

"……No."

Luo Yongjun pulled the corners of his mouth hard, and after a long while he managed to squeeze out a sentence, "I'm not good enough. You should do this kind of high-end research on yourselves."

(End of this chapter)