Research starts with PhD students

Chapter 180 The great god is the great god, incomparable to ordinary people!
At the entrance of Hall 3.

Many scholars were standing scattered around; they arrived a little late and were unable to get a seat.

Some people just come to watch the fun.

The current report is the biggest part of the meeting, and they hope to get the results as soon as possible, but most people think that the report will take a long time.

Zhang Shuo was invited to give a 45-minute report, and the report list in Hall 3 also marked it as 45 minutes. However, when it came to the argument of the singularity of turbulent transition in the NS equations, the report time was not a problem at all.

Even if the report lasts for a whole morning or even a whole day, the organizer, the Mathematical Union, and even other scholars who are going to give reports will not have any objections.

Therefore, many people did not wait at the door of the lecture hall, but stood there scatteredly. Some simply walked around the small square and only came over occasionally to check on the progress.

When the report was in the 50th minute, there was a sudden noisy shout from the door, "The report is almost done!"

"Who said that?"

"So fast?"

People who were standing closer came over immediately, and then heard thunderous applause coming from inside.

The applause grew louder and louder.

It can be heard clearly from the flowerbed in the small square.

Everyone in the square quickly ran over and found that everyone at the entrance of the lecture hall started to applaud, and some people shouted excitedly, "It's done!"

"The proof is complete, applause!"

"Less than an hour, right? So soon?"

A scholar standing at the front turned around and explained excitedly, "I squeezed into the back row to listen a little bit. It used a completely new method, comparing two-dimensional and three-dimensional solution sets."

"anything else?"

"That's all I heard..."

"Are you sure you're done?"

"There's so much applause inside, do you still have any questions? Koncevic and Kapustin are here!"

The last sentence is very convincing.

Maxim Kontsevich is a former Fields Medal winner with a very wide range of research areas; Anton Kapustin focuses on research in the field of partial differential equations, has many academic achievements, and is one of the most influential figures in partial differential equations internationally.

If there were problems with the report, they would have surely spotted them, instead of applauding.

In the lecture hall.

Many people were still clapping excitedly, and those who applauded until the end were several domestic scholars.

For example, a group of people from Soochow University.

Luo Yongjun's palms were numb from clapping, but he was still shouting excitedly, "Did you see that? I told you that Zhang Shuo would be fine. My student! My student!"

Qi Zhixiang, Wang Hui, Sun Xingli and others were also applauding.

They had long known that Zhang Shuo had completed the singularity proof of the turbulent transition of the NS equations, but it was not certain whether the proof was complete. Now it has been confirmed.

This level of research is absolutely the best in the world and is destined to go down in history.

The singularity problem of turbulent transition has always been controversial in mathematics and applied mathematics.

The controversy has lasted for decades.

Because there has been no progress in pure mathematical arguments, many scholars in the field of pure mathematics who study incompressible fluids also assume that there are singularities at the location of turbulence.

Now the controversy can end.

Zhang Shuo used a completely new method to prove that there is no singularity in turbulent transition, and also allowed many mathematicians to see the possibility that the NS equations are regular.

This is of great significance to the field of mathematics and even applied engineering.

If there are singularities at the turbulent position of the NS equation, from a mathematical perspective, we can conclude that the NS equation has many singularities and the equation does not have regularity, which means that the equation is "unstable".

Then there will be problems in using the NS equations for physical calculations and predictions.

For example, predicting flows can lead to multiple outcomes.

Now there is no need to worry, the turbulence transition positions are continuous, and the solution set of the three-dimensional NS equations is likely to be 'all smooth'.

This is one of the important significances of the research.

The applause finally stopped.

Those scholars who stood up also sat back down one after another. Zhang Shuo's report was over, but he still had to answer questions from the scholars. Some people understood everything, but many people still had questions about certain steps.

The question-and-answer session lasted shorter than expected.

The first person to ask a question was Anton Kapustin, who asked a question about function mapping; the second was Maxim Kontsevich, who asked about the use of algebraic geometry methods in the proof.

Subsequently, three more scholars raised questions.

Zhang Shuo answered the questions patiently. After answering the fifth question, no one else stood up.

In fact, the reason is very simple. Because the research involves too broad a range of knowledge, most scholars do not fully understand it. There are too many questions in their minds and they have no way to ask questions.

So when Zhang Shuo was about to leave the stage, a scholar in the first row asked directly, "Professor Zhang Shuo, where and when are you going to publish your paper?"

Someone else asked, “Can you make a copy of the proof? I want to study it slowly when I get back.”

“I haven’t decided to publish it yet.”

Zhang Shuo replied, but agreed to the request to make a copy of the proof, "I can post it online and you can download it yourself, or you can email it to me."

He really hadn't thought about the question.

If he had not been giving a report at the International Congress of Mathematicians, he would not even have thought of publishing the proof of turbulence singularities as a separate achievement.

The singularity problem of the NS equations is a large research project, and I subconsciously thought that I would publish the results once it was completed.

After Zhang Shuo finished his report, he felt a little tired and planned to go back to rest. As soon as he walked out of the lecture hall, he was surrounded by a crowd, including several reporters.

"Hello, Professor Zhang, I am a reporter from Science and Technology News. May I ask..."

"I am a reporter from Huzhou Provincial TV Station. May I ask..."

"I'm a reporter from Hanoi National Television..."

Every reporter rushed to ask questions, and Zhang Shuo also patiently answered a few questions.

After dealing with the reporters, several scholars continued to gather around him. They all wanted to get to know Zhang Shuo. “Professor Zhang Shuo, can you take a photo with me? I want to keep it as a souvenir.”

"Professor Zhang Shuo, what's your email address?"

"Can you give me an autograph? Just write it in this diary. I'm not a fan of celebrities, but my daughter who is in college really admires you..."

"..."

Zhang Shuo was surrounded for half an hour, and he finally got rid of the crowd after saying sorry many times.

Fortunately, the scholars were not fanatical fans. They noticed that Zhang Shuo was indeed a little tired and gave way.

Zhang Shuo went back to the hotel to rest. He did not feel tired from giving the report, but dealing with reporters and other people was very tiring. Fortunately, it was over, and the main work of attending the Mathematicians' Congress was also over. He could then freely listen to other people's reports.

He lay in bed for half an hour, got up and drank a cup of coffee, and felt more energetic. He suddenly remembered that after finishing the report, he promised others that he would upload the proof process to the Internet, so he simply uploaded a copy. Then, he clicked on Weibo and posted a message, "NS Equations: Singularity Argument for Turbulent Transition, interested friends can click the link to download: {link}."

After the message was released on Weibo, many netizens were confused.

Zhang Shuo just won the Fields Medal and there were a lot of reports in the media. Why didn’t he mention the award or anything like that, but suddenly posted a link to the paper?
But this does not affect the following comments, "Congratulations on winning Fields and becoming the number one mathematician in the country!"

“Congratulations on setting the record for the youngest winner of the Phils!”

"Master, you are indeed a master. Your work is truly incomparable to that of ordinary people. After winning the Fields Medal, I will publish a paper to express my happiness..."

"Turbulence singularity argument? As an engineer, I was very shocked. Is this the turbulence I understand?"

"real or fake?"

There are a lot of reports about Zhang Shuo in the domestic media because he won the Fields Medal and was the first scholar in domestic history to win the award.

This is certainly something to write home about.

As for what report Zhang Shuo would give, not many people paid attention to it.

Some media reported some gossip, but no one paid any attention to it. When they saw Zhang Shuo suddenly published a paper, some media still reprinted it, but the comments were similar to the netizens' thoughts. In one sentence, it was -

"The great god is indeed a great god, he is incomparable to ordinary people!"

Soon, public opinion changed.

The first media released the latest news from the International Congress of Mathematicians. In his report in the morning, Zhang Shuo completed the singularity proof of the turbulent transition position of the NS equation and proved that there is no singularity in the transition from laminar flow to turbulent flow.

Most people think that this is just a proof when they hear the news, but anyone who has some understanding of the relevant content will find it very unusual.

That's the NS equation!

The transition from laminar flow to turbulent flow is one of the major issues in the application research of the NS equations.

The proof that there are no singularities in the transition from laminar flow to turbulent flow has further confirmed the smoothness of the solution set of the NS equations. At the same time, it also represents a major progress in the mathematical research of the NS equations.

“This is really remarkable mathematical research!”

"If we rank mathematical research, this research is definitely at the top of the pyramid, and is enough to win various international mathematical awards..."

"So after Zhang Shuo won the Fields Medal, he also achieved another Fields-level achievement?"

"Last time it was the numerical simulation of the NS equation, and now it's the singularity proof of the NS equation at a special position. It can be said that in the field of NS equation research, Master Zhang Shuo is the world's number one!"

"Absolutely the best in the world, no one can compare to him!"

Zhang Shuo's research results have aroused heated discussions in public opinion and also attracted widespread attention from the international mathematics community.

After entering the 21st century, there has been no progress in the pure mathematical proof of the NS equation. The latest research results of the NS equation are more from applied mathematics and physics.

Simply put, it is to use physical experiments to determine the solution of the NS equation in order to understand the solution set of the NS equation under specific values.

The transition from laminar flow to turbulent flow is a very typical physical problem.

Because the transition occurs instantaneously, the solution at the transition point is likely to jump, which means that the NS equation is considered to have a singularity at this position.

Now Zhang Shuo has proved that there is no singularity, which is of great significance to both mathematical and physical research.

In the afternoon, Zhang Shuo appeared at the venue of the Mathematical Congress again. He was still in Hall 3 most of the time. There were always a lot of scholars around him, and the topic they talked about was always about the NS equation.

Anton Kapustin was also sitting next to Zhang Shuo. He also talked about the singularity argument and was very impressed by Zhang Shuo's method. Later, he joked, "I am now glad that I nominated you directly."

“You may not know that some people previously thought that you should be nominated next time because your research has just been completed and its impact is not that great yet.”

"But I and others said that Fields' selection should not be done this way. Considering the impact of research is the practice of the Nobel Committee. Moreover, it is expected that your research will have an impact. The research of other nominees is also not influential."

“It’s not fair.”

Anton Kapustin said with a smile, "The others are probably glad to have nominated you, otherwise our selection might have been questioned."

"Numerical simulation, combined with current research, has solved half of the NS equation problem."

"I think the Clay Institute can consider awarding you the Millennium Mathematical Problem Prize. It is very difficult to prove infinite values ​​in the mathematical direction of the NS equation, and it is almost impossible to find an entry point. You have completed the proof from laminar flow to turbulent flow. Perhaps you can use the same method to prove other conventional value problems."

"This way, we can quickly complete the demonstration of the conventional value-taking part."

Others also nodded and said, "The application of the NS equation is the natural boundary and conventional value. If we can prove the smoothness of the solution set of conventional value under the natural boundary, we have covered all the application problems."

"This is equivalent to completing the proof of the smoothness of the NS equation, and it is not necessary to prove 'infinite values'."

"Thank you."

Zhang Shuo smiled and said, "It would be great if they could pay the bonus in advance, but I still hope to be able to make an infinite value argument."

"If we only use conventional value arguments for problems encountered in physics, the scope of the argument will be very narrow and the proof will be incomplete."

"In many application fields, infinite values ​​are also of great significance. More importantly, this is mathematics, not applied mathematics or physics."

Zhang Shuo's words silenced the others.

This is mathematics, not physics.

Many mathematical researches do not necessarily need to be applied, but the hope is to form a complete theory, to seek to perfect mathematical theory, and to solve more problems with mathematical methods in the future.

The same is true for the mathematical argument of the NS equation.

If the proof problem of the NS equation can be solved, other similar complex partial differential equations can be proved in the same way, and a series of problems can be solved.

At the same time, a methodological theory of partial differential equations can also be formed.

Many scholars who conduct pure mathematical research on partial differential equations are doing this kind of work. It is their accumulation of results that allows the theory to be gradually perfected and used to solve many scientific and industrial problems.

……

The International Congress of Mathematicians lasted for seven days, and Zhang Shuo stayed in Hall No. 3 for the following days.

Hall 3 is the special session on partial differential equations. Many reports and studies have greatly contributed to the proof of singularities of the NS equations.

In just three days, the task progress increased by '3.6%', which is equivalent to nearly 250 scientific research coins. This also shows how high the level of the academic reports of the Mathematicians' Congress is.

Zhang Shuo gained a lot. He won the Fields Award, the highest award in mathematics, completed a report that was recognized internationally, and his task progress was greatly improved.

On the last day, the conference held its closing ceremony.

After watching the Hanoi Dance Troupe singing and dancing, Zhang Shuo, Luo Yongjun, Sun Xingli and others boarded the return flight back to Eastern Suzhou.

This time it’s completely different.

He had just stepped off the plane when he noticed Wang Hui running towards him, calling out breathlessly, "Zhang Shuo! Zhang Shuo!"

Wang Hui walked up to Zhang Shuo, looked him over and gave him a suggestion, "Where's your medal? Do you want to hang it on your chest?"

"what?"

"I suggest you do this."

"why?"

"Did you hear the shouting?" Wang Hui pointed to his ear and reminded with emotion, "There are many people waiting to pick you up, and they are all shouting your name..."

"Now you've really become a star!"

(End of this chapter)