Research starts with PhD students

Chapter 116 We would like to do this, but the problem is that we don’t have the ability!
Liu Jian, Zhang Chunyang and Xu Jun witnessed the discovery of the "billion-digit prime number" with their own eyes, learned about Zhang Shuo's research progress, and brought back a research-related manuscript.

Everyone felt that they had gained a lot.

But in reality, they did not achieve their goal.

They hope to learn about the research progress and support the project on behalf of the Bureau of Science, Technology and Industry, which means providing financial sponsorship for the project.

One is to show that the Bureau of Science, Technology and Industry attaches great importance to computational mathematics and applied mathematics.

In addition, I also hope to have a good relationship with Zhang Shuo. Computational mathematics and applied mathematics are directly linked. Although Zhang Shuo is young, he has already achieved many results in computational mathematics and can definitely be called one of the best scholars in the field of computational mathematics in China.

Such young scholars can definitely play a huge role in major engineering research.

Unfortunately, Zhang Shuo has already completed his research and obviously does not need any financial support, let alone building a team.

"This is not a pity, it's just that their level is high!"

On the way back, Liu Jian said with emotion, "Such research cannot be completed by a team alone, but he has obviously made great progress."

“There is no unified standard for completion, but his progress is definitely much higher than that of Li Jianfeng’s team at the Donggang Mathematics Center.”

"This will be an achievement worthy of an international mathematics award. No wonder even Teacher Li takes it seriously. The key is..."

"He's only 25!"

Liu Jian's words silenced the other two. They thought about the process of meeting Zhang Shuo and felt a lot of emotions in their hearts.

All three are well-known scholars in the country.

They have produced many research results, published many papers, participated in many mathematics conferences, and have some influence in the field of applied mathematics.

At the same time, I have also met many young talents.

Zhang Shuo is different.

During the conversation, they found that Zhang Shuo was very confident and mature. Every sentence he said hit the key point and he even dominated the discourse.

But why?

"He was only 25 years old, which was the age when he started his doctorate. He completed his doctorate in just one year and has done so many researches..."

"I won't talk about computational mathematics. I don't understand the physical algorithms either, but the Jebov conjecture and the numerical simulation of the NS equations..."

“I don’t even dare to think about it!”

Zhang Chunyang smiled bitterly and said, "Look at us, we are in our 40s and 50s, but we only have the title of professor."

“Mathematics is really the domain of the young!”

“I have always believed that in the field of partial differential equations, experience accumulation is more important than talent, but the most advanced fields still rely on young people.”

They sighed together for a long time.

Liu Jian suddenly asked, "If there is no problem with the research, the Science and Technology Industry Bureau should start a research project on aerodynamic simulation programs, right?"

"Will Zhang Shuo be invited to participate then?"

Xu Jun nodded and said, "I think so. This kind of research is very important and will be used in both aerospace and aviation, but Zhang Shuo may not be interested."

"I heard that the Second Hospital has a general algorithm project, and Zhang Shuo just reluctantly agreed to be a specially hired expert. In fact, he doesn't participate in the work at all."

"Why? Aren't you interested in this kind of project?" Zhang Chunyang asked puzzledly.

Liu Jian laughed, "I have heard of this. Zhang Shuo said that he is not interested in non-innovative research."

“Isn’t it non-innovative research to make algorithms based on the results?”

Zhang Chunyang sighed, "It's really amazing that you can say such a thing!"

Xu Jun also said, "If I were 20 years younger, I might want to say the same thing, but... I definitely can't do it!"

"Hahaha--"

They laughed together.

……

After Xu Jun and the other two left, Zhang Shuo began to organize the manuscript materials.

The name of the paper he was going to publish was called "Numerical Simulation of the NS Equation". The title was simple and direct, but the only thing about it was that it was "too grand", as if it included both the numerical solution and computer simulation of the NS equation.

In fact, the title is just right.

His research is on numerical simulation of NS equations. Part of the paper is theory, and the other part is mathematics and computer methods. Institutions or teams in related fields can conduct research according to his theoretical direction.

While sorting out the materials, Zhang Shuo was also thinking about the next research question.

For example, whether it is necessary to prove the solution of the Ns equation from a purely mathematical perspective.

This is the content of the seven great mathematical conjectures of the millennium.

He tried to establish a task and found that the research on numerical simulation also had a direct impact on pure mathematical arguments.

【Task 1】

[Research project name: Demonstrate the existence and smoothness of solutions to the NS equation (Difficulty assessment: A). ]

【Progress: 3.970%.】

Although the progress is less than 4%, considering that the research requires up to 9000 scientific research coins, the progress of less than 4% is also very high.

"Nine thousand research coins..."

"With this difficulty, you will definitely run into a lot of problems. Each purchase of progress will cost you 90 research coins."

"There are still too few scientific research coins!"

When compared with the high-difficulty research, it feels like the scientific research coins are not enough.

The last research was to find billion-digit prime numbers. Not only did I not earn any research coins, I also lost a total of 11. It hurts to think about it.

Of course, the research earned me fame, and there was also a $15 bonus to follow, so the expense and benefits were still worth it.

Zhang Shuo put down the materials, sat down to rest, and turned on the news to read the media opinions.

The discovery of billion-digit primes has a huge impact.

The media coverage was even more heated than the proof of the Gerbov conjecture, probably because the new discovery made history.

Before this, no Chinese had discovered Mersenne primes.

What has been discovered now is a new Mersenne prime, and it is also the first 'billion-digit prime number', which will surely be recorded in the history of prime number research.

"The discovery of billion-digit prime numbers is of great significance in promoting prime number research."

"The new prime number record may last for a decade or more. The Mersenne primality test of more than 100 million digits requires a huge amount of calculation for each digit."

“If you want to break this record, you either need to invest a lot of computing resources or wait for explosive improvements in computing technology…”

"The former is very difficult. No organization will invest so much computing resources to calculate Mersenne primes. The gain is not worth the loss."

“The latter might require a quantum computer?”

Foreign media also have a positive attitude towards the new discovery. The well-known media "Science News" believes that the discovery of new Mersenne primes will be one of the most important inventions this year.

Invention, not research.

The discovery of Mersenne primes can be classified as an 'invention'.

The significance of this discovery is significant, including promoting the study of number theory.

Mersenne primes are an important part of number theory research. Its exploration helps mathematicians understand the properties of prime numbers and promotes the development of number theory.

In addition, some of the discovered prime numbers have been used for encryption or other application tasks, and the discovery of billion-digit prime numbers will also expand the application in this field.

Among the extensive media coverage, people from Soochow University also accepted interviews from reporters.

For example, Dong Hao, director of the Computer Structure Laboratory.

Dong Hao said that the laboratory fully supports the work of finding Mersenne primes and will invest more computing resources in the search for Mersenne primes in the future.

During the interview, he showed confidence and seriousness, displaying the demeanor of a professor at Soochow University, and received a lot of praise.

However, Sun Xingli described Dong Hao in a completely different way. He came to Zhang Shuo's office and told a piece of gossip, "I don't know what Director Dong Hao of the Structural Laboratory was thinking, he actually went through the trash cans and quarreled with the garbage collector, but when asked what he was doing, he just wouldn't tell me."

"This is an interesting matter. Many people said that Dong Hao might have been too excited after the interview. This was his first interview with a major media."

Zhang Shuo pursed his lips and thought for a moment, "Maybe I'm too excited."

The two chatted for a few minutes, and then Sun Xingli brought up another topic, "Our research will be published soon, in the new issue of Acta Mathematica Sinica."

"Jebov's conjecture?"

"Of course." Sun Xingli looked at Zhang Shuo in confusion. "Aren't you excited? A paper was published in the Journal of Mathematics!"

"Hasn't it been confirmed long ago?" Zhang Shuo asked in confusion.

Sun Xingli fell silent after hearing this.

He thought about it carefully and it was normal. For ordinary scholars like them, it would only be a few times in their lifetime to publish a paper in the four major mathematics journals.

It can even be said that it is good to happen once in a lifetime.

This is the pinnacle of academic career!
For Zhang Shuo, he has published in several top journals within a year, including two in the four major mathematics journals, including "New Advances in Mathematics" and "Annals of Mathematics".

Now there is just one more "Journal of Mathematics", which doesn't seem to be a big deal.

“You’re almost taking over all four major journals!”

Sun Xingli suddenly realized, "If you can publish a paper in the Journal of the American Mathematical Society, you will have achieved the Grand Slam of the four major journals."

“This is also a great achievement!”

Zhang Shuo nodded thoughtfully. He was just thinking about which journal to publish "Numerical Simulation of NS Equations". All four major mathematics journals?

This suggestion seems interesting!
"It's something you can consider..."

"You really want to!" Sun Xingli said with a smile, "I'm just saying it."

"As far as I know, there is a mathematician in China who has published papers in the four major journals. She is a female mathematician named Zhu Liangbi. She is very impressive."

"If you can do that, it might be the second one."

……

Zhang Shuo stayed in the office for several days in a row, sorting out his research manuscripts.

The difficulty level of numerical simulation of NS equation is level B, but because it involves mathematical and computational methods, the manuscript content is very large. Add to that some graphics and other important information on the computer, and a simple summary will result in more than one hundred pages of content.

There is so much content that it takes up a huge stack on the table.

Some of the key methods and calculation contents still need additional steps and materials, and the final paper may be longer.

“Should we reduce the content?”

"Some unnecessary processes and steps, or calculation examples involved, will not be published?"

"Also, reviewing is a big problem. There are so many..."

It is not difficult to understand the research, but the main problem is that there is too much content, so the review will be complicated.

It is better to report so much content to a mathematics institution rather than submitting the paper directly. Another way is to submit it in parts.

Send out one part first, then another part, and publish the content in several parts.

"Anyway, it's not a repetitive study, so you don't have to submit just one paper. You can submit it separately."

“It would be nice to have a few more papers…”

When Zhang Shuo was still sorting out thesis materials, Qiu Zhichao called and asked if he was in the office. Not long after he hung up the phone, Qiu Zhichao and Academician Zhou Gang came to his door.

Behind them was a group of people, including Gao Xiaohong, Tan Youming, Qi Zhixiang, Luo Yongjun and Sun Xingli.

After a group of people entered the office, Zhou Gang, Qiu Zhichao, and Tan Youming sat on the sofa, and the others could only stand by.

They didn't care because they just came to watch the fun.

In fact, it was Qiu Zhichao and Zhou Gang who went to find Zhang Shuo. After entering the research institute building, they chatted enthusiastically with Tan Youming and then went up together.

Sun Xingli and Luo Yongjun found out that several people were going to Zhang Shuo's office, so they rushed over to see what was going on.

Zhou Gang and Qiu Zhichao felt a little awkward sitting down, but they couldn't ask others to leave, after all, they were on the territory of the High Court.

After waiting for a long time, Qiu Zhichao finally spoke, "Professor Zhang, let's be frank. We want to invite you to join our project and help with some mathematical calculation and analysis work."

Zhang Shuo asked doubtfully, "What project?"

"Fermion single-band superfluidity in optical lattices." Qiu Zhichao said a very professional name, and most of the people present were confused.

Zhang Shuo was also a little confused. He paused for a long time and asked tentatively, "Is it related to the Fermion Hubbard model?"

This time it was Qiu Zhichao's turn to be surprised.

Zhou Gang was also surprised and asked subconsciously, "You know?"

"I've heard of it." Zhang Shuo shook his head. "That's just what I've heard of it. I don't understand it. You should find a professional."

"You are a professional!"

Qiu Zhichao affirmed, "Who is more professional than you in the field of computational mathematics?"

Sun Xingli subconsciously looked at Luo Yongjun, then curled up the corner of his mouth into a subtle smile, which made Luo Yongjun feel offended.

Qiu Zhichao explained, "Our research is part of the study of the fermion Hubbard model, but the research has been stagnant for several months. The main experiment is difficult and ordinary experiments have no results."

“The data is too complex, and analysis and calculation are both big problems. In addition, there may be a lack of consistency between the theoretical and calculated results.”

"We have no other choice, so we come to you for help..."

What Qiu Zhichao said and introduced again was equivalent to providing a popular science lecture to everyone present.

The fermion Hubbard model, a model proposed by physicist John Hubbard, is one of the representative physical models describing high-temperature superconducting materials.

The fermion Hubbard model is a simplified model that describes the laws of motion of electrons in a crystal lattice. It is considered to be a core physical model that has the potential to explain the mechanism of high-temperature superconductivity, a problem that has plagued the physics community for nearly four decades.

Once its physical mechanism is understood, it will be possible to design, produce and apply new high-temperature superconducting materials on a large scale, and have a transformative impact in areas such as power transmission, medicine, and supercomputing.

Obviously, the fermion Hubbard model is very difficult to study.

Solving the fermion Hubbard model has always faced huge challenges. First, the model has no strict analytical solution in two and three dimensions. Second, the computational complexity is very high, and even classical supercomputers cannot perform effective numerical simulations.

For example, using classical computing to simulate the motion of 300 electrons would require storage space of the order of 2 to the 300th power, which is more than the total number of atoms in the known universe.

So the scientific community came up with a simple and crude solution - quantum computing!
Quantum computers have developed to the second stage, which is to use the particularity of quantum computing to solve important scientific problems such as the fermion Hubbard model.

'Optical lattices realize fermion single-band superfluidity' is one part of the research on solving the fermion Hubbard model with quantum computing.

This research belongs to the category of quantum computing, is related to the fermion Hubbard model, and is also related to the study of high-temperature superconductivity mechanisms. It is indeed very important.

Zhang Shuo has not conducted research on high-temperature superconductors, nor is he familiar with the fermion Hubbard model, but he is somewhat puzzled by the research method of "physical brute force" to solve computational problems.

After Qiu Zhichao finished explaining, he asked with doubt, "Solving the fermion Hubbard model with quantum computing is a bit like using the DNS method to solve the NS equation numerical simulation problem. Is that right?"

Qiu Zhichao and Zhou Gang looked at each other and nodded together, "Yes, they are a bit similar."

The DNS method uses a huge amount of calculation to solve the numerical simulation problem of the NS equations.

Quantum computing research on the fermion Hubbard model also relies on the ultra-high performance of quantum computing. However, because quantum computing technology is far from mature, solving single-direction academic and scientific research problems requires single-direction research.

Zhang Shuo continued to ask, "Why don't you try to solve the problem mathematically?"

“For example, simply studying and improving the fermion Hubbard model.”

"For example, studying the computational effort of simplifying numerical simulations of the Fermion Hubbard model?"

Zhou Gang and Qiu Zhichao looked at each other, not knowing what to say for a moment.

Why not use mathematical methods to solve the problem?
They thought, the problem is...

I don’t have that ability!

(End of this chapter)