Research starts with PhD students

Chapter 206 Report End! This is the level gap
Anton Kapustin is not the only scholar to comment on the paper.

Several other top mathematicians also expressed their views on the paper. They commented on its content. Some were amazed, some were puzzled by some detailed arguments, and some discussed Zhang Shuo's level and lamented that he was born to solve the NS equations.

In the field of mathematics, Zhang Shuo has been associated with the ns equation because several of his research results are related to it.

It includes numerical simulation of ns equation, proof of bounded value of Ns equation, and now proof of infinite value.

One step, another step.

From computational mathematics to the perfect proof of pure mathematics, he is about to win the most shining crown in the field of mathematics.

There are many discussions in the public opinion. "I really want to know whether Zhang Shuo has solved the NS equation problem!"

"Many professional scholars have expressed their views, but no one can be sure, including those overseas scholars."

"So far, there is still no result?"

"It seems that some scholars believe that they have completed the proof, but they are not completely sure."

"We still have to read the report. Zhang Shuo will be giving a report at the Chinese Mathematicians Conference soon. This year's conference seems to be held in Xijing."

"It is indeed Xijing, the conference center of the Science and Technology Industrial Park. Preparations are already being made there."

"I was just thinking of going to Xijing for a tour, so I can get a close look at the academic demeanor of Master Zhang Shuo."

Amid heated discussions in public opinion, time quickly arrived at the day of the Chinese Mathematicians Conference.

Many media outlets came to Xijing Science and Technology Industrial Park, hoping to interview Zhang Shuo or to know the results of the report first.

This academic report has a huge impact and is related to a major mathematical problem of the millennium.

If the report is passed, then another Millennium Mathematical Problem will have been solved, and the solver will be a Chinese mathematician.

That is quite an achievement!

This year's Chinese Mathematician Conference is co-organized by Xijing Jiaotong University, Xijing University of Science and Technology and Xijing Science and Technology Industrial Park, and the venue is located in the conference center of the Science and Technology Industrial Park.

The city of Xijing attached great importance to this conference, and senior officials attended the conference in person. They welcomed scholars from home and abroad, and also welcomed them to visit various places in Xijing.

In the morning, there is the opening ceremony.

More than a thousand scholars from all over the world gathered in the main hall of the conference center.

The opening ceremony was the same as the International Congress of Mathematicians. After a brief opening speech, it was time for the awards ceremony. The conference presented a total of three awards, including the ICCM Mathematics Award, the Chern Award and the ICCM International Cooperation Award.

Among them, the ICCM Mathematics Award (formerly the Morningside Mathematics Award) is known as the "Chinese Fields Medal" and is the highest award in the world's Chinese mathematics community. It recognizes Chinese mathematicians under the age of 45 who have made outstanding achievements in basic mathematics, applied mathematics and have contributed to the development of mathematics.

At the opening, Zhang Shuo invited us to sit in the first row.

When it came to the award ceremony, the first awards given out were the ICCM International Cooperation Award, the ICCM Silver Award, etc. Many scholars whose names were called came on stage to receive their awards.

Among them were scholars from China and abroad. Zhang Shuo was also invited to be the award presenter to present an award to a professor from Tongzhi University.

This is a brand new experience.

Although I just took the certificate and medal and walked over to hand them to the award-winning professor, I still felt very good when I saw how nervous and excited he was.

The last award was the ICCM Mathematics Award. Qiu Chengwen announced the winner, "The winner of this year's ICCM Mathematics Award is Professor Zhang Shuo from Soochow University."

"He has made great contributions in the fields of pure and applied mathematics. In the field of computational mathematics, he completed a general algorithm for complex partial differential equations, which greatly simplified calculations in the field of applied engineering."

"At the same time, he completed the numerical simulation of the NS equation, which greatly simplified the amount of calculation, made the results more accurate, and solved the problem of chaos theory."

"In the direction of pure mathematics..."

Qiu Chengwen introduced a lot of content, which were all Zhang Shuo’s achievements in the field of mathematics.

When Zhang Shuo heard his name called, he stood up and was a little surprised. He had never thought that he would win the award. Winning the award was nothing, but there was no advance notice, so it felt sudden.

After Qiu Chengwen finished his introduction, the audience burst into warm applause.

Zhang Shuo took a deep breath and walked up to the podium. He stood there with a smile on his face, waiting for the guests to present him with certificates and medals.

Qiu Chengwen returned to the stage.

He sat on the side of the first row, next to his old friend Rost Brand.

There are many foreign scholars attending this Chinese Mathematicians Conference, and they are all very well-known scholars. Their purpose of attending the conference is to listen to Zhang Shuo's report on the demonstration of the ns equation on the spot.

Most people also paid attention to Zhang Shuo’s report.

The same goes for Rost-Brand. He came to the meeting to give a report, and the approval of the report would mean that the NS equation problem had been solved.

This is a very serious matter.

After Qiu Chengwen sat down, Rost-Brand immediately couldn't help asking, "Have you read the paper? What do you think? Is the proof complete?"

“I haven’t read it all.”

Qiu Chengwen shook his head. "Some of the logical arguments are too complicated and difficult to understand on my own. I did some research, but then I gave up and decided to wait for the report."

"What do you think?" Rost-Brand asked.

Qiu Chengwen smiled and said, "I believe there will be no problem. Zhang Shuo has always been like this. He can always bring surprises to people."

Rost-Brand nodded thoughtfully.

Suddenly, a voice came from behind, "Rost, I've been telling you not to dwell on this. We just need to come here and wait for the report."

They both turned around and saw Professor Charles Fefferman who came with Rost Brand.

Professor Charles Fefferman is a very famous scholar.

He was a child prodigy since childhood. He published his first scientific paper at the age of 15, obtained a double bachelor's degree in mathematics and physics at the age of 17, received a Ph.D. in mathematics from Princeton University at the age of 20, and was appointed a professor at the University of Chicago at the age of 22, making him the youngest person to be appointed a professor at an American university.

Just two years later, he was hired as a professor at Princeton University, and then won the Alan Waterman Award and the Fields Medal.

Charles Fefferman was in his seventies and his energy was not as good as when he was young. He devoted most of his time to education, but he always paid attention to the problem of ns equations.

The ns equation problem is directly related to him.

In 2000, the Clay Institute held a mathematics conference and announced seven mathematical problems, namely the seven great mathematical problems of the millennium. Among them, the NS equation problem was the one that Fefferman explained on stage. He had always hoped that the NS equation problem could be solved.

Charles Fefferman said seriously, "I have also read the report and I am also unsure, but I hope it is complete."

"If it succeeds, I mean if the proof is complete, I want to thank him, from the bottom of my heart..."

Qiu Chengwen smiled and said, "I definitely will."

Rost-Brand said, “I hope that’s right. This is not only a solution to the problem, but also a huge boost to mathematical research.”

"Let us wait together for tomorrow..."

……

Many scholars are waiting for tomorrow.

There are a large number of participants in the Conference of Chinese Mathematicians, including many internationally renowned scholars, seven Fields Medalists, and many top scholars will give reports.

Even so, many people are still looking forward to tomorrow because Zhang Shuo's report is the finale.

Finally, the second day arrived.

Zhang Shuo's report was arranged in a smaller conference hall, which is more convenient for giving difficult mathematics reports.

The venue can accommodate three to four hundred people. Because there are so many people who want to listen to the report, the organizers simply "reserve seats" for top scholars in advance.

Top scholars are the main force in reviewing the reports. Most of the others are just there to join in the fun and have no chance of understanding all the content. If they want to enter the venue to listen to the reports, they can only come in advance to reserve seats in the back row.

If the seats in the back row are also full, you can only stand in the empty space at the back or in the aisle.

Some people even crowded at the door. They had no intention of entering the venue to listen to the report, they just wanted to know the results first.

Zhang Shuo, Luo Yongjun and Li Weihua were waiting together in the lobby of the venue.

They sat at a small round table.

Li Weihua glanced at the door calmly, obviously looking very nervous.

Luo Yongjun joked, "Why are you so nervous? I'm the first one to go on stage!"

Li Weihua didn't care about Luo Yongjun's ridicule at all, but retorted, "This is the demonstration of the ns equation, the millennium mathematical conjecture! Is it normal for me to be nervous?" "It will be better if I experience more big scenes!"

Luo Yongjun was sharing his experience with a smile, but his rapid breathing made it clear that he was nervous. Just like Li Weihua said, this was a demonstration of the ns equation.

Of course I'll be nervous when I'm the first one on stage.

"Don't worry."

Zhang Shuo smiled and said, "Teacher Luo, I will start the article and go up with you. You just need to give a general introduction and talk about the process of the proof."

"I'm not nervous, not at all!" Luo Yongjun quickly corrected.

Zhang Shuo chuckled nonchalantly, then said to Li Weihua, "Teacher Li, you are explaining the first part, which is not difficult. Just explain the key points in detail."

Li Weihua nodded seriously, "Don't worry, I didn't go to bed until 3 o'clock last night. I read it over and over again many times. I can memorize whatever you say by then!"

Zhang Shuo nodded slightly and waited for the show to start.

The research was done by three people together, and the report was also done by three people together. It was not for the purpose of dividing the credit or anything like that, but mainly because the paper was more than 80 pages long, with complex and difficult content. It would conservatively take three hours to present.

After such a long time, Zhang Shuo also felt a little scalp tingling.

So they divided the work, Luo Yongjun and Li Weihua spoke for more than an hour at the beginning, while Zhang Shuo was responsible for the complicated part at the end and also did the final finishing touches.

Under the attention of the whole audience, there was finally movement backstage. Zhang Shuo and Luo Yongjun walked onto the stage together, and a clear title appeared on the screen - Proof of the smoothness of the solution to the Navier-Stokes equation.

At this time, the venue automatically became quiet.

Everyone stared at Zhang Shuo who walked to the center of the stage. He placed the information on the table and then spoke seriously, "Water flowing out of the tap, airflow over the wings of an airplane, or the ever-changing ocean currents, etc., all of these can be described and analyzed using the NS equation."

"From a physical point of view, the equations described work well, but from a mathematical point of view, their rationality is uncertain. We always want to know whether there are some cases where the operation will fail? In other words, will the equations produce uncertain or wrong answers?"

"The Ns equation has a history of 200 years, but the mathematical problems it generates have never been completely solved."

“Mathematics is a rigorous discipline and we cannot use the word ‘uncertain’ to describe a problem.”

"And now, we will give the answer to the NS equation problem!"

After a brief opening statement, the report got into the main topic.

Zhang Shuo gave the time to Luo Yongjun.

Luo Yongjun gave the initial explanation, which was a general summary of the report, that is, an explanation of how the whole was done.

The explanation of this part is still very important.

Scholars who understand the paper naturally know the proof process, but many scholars do not understand the paper or do not have the time to read it.

Only through the explanation did they understand the overall proof process and the methods used in the proof.

The next person to come on stage was Li Weihua, who gave the first part of the explanation.

The first part discusses the parameter analysis problem of infinite numerical substitution. After analyzing the parameter problem, we can sort out the logic of the subsequent argument.

This part of the explanation took nearly an hour.

Then Zhang Shuo spoke.

Zhang Shuo was the main speaker. He explained the difficult parts of the paper, that is, the most difficult parts to understand. The logic of these parts was very brain-burning, and many people felt they couldn't understand them even after listening to them.

When Zhang Shuo was giving a lecture, the audience listened most attentively. Even the scholars in the front row stared at the content on the screen and listened very carefully, fearing that they would miss any details.

"We can determine a set of parameters by combining the previous parameter argumentation part with the current conclusion."

"Within this set, the boundary function..."

"Set the vector field to..."

"Finally we get a continuous mapping... We can find that..."

……

In the audience, front row.

Qiu Chengwen, Anton Kapustin, Rost Brand, everyone listened very carefully.

They have all studied the thesis, so when Luo Yongjun and Li Weihua were explaining it, they all felt very relaxed because they were all understandable parts.

What Zhang Shuo said is the key.

Those parts that seemed obscure and logically very difficult were difficult for them to understand on their own, so they came to listen to the report carefully.

After listening to Zhang Shuo's explanation, some things that I didn't understand suddenly became clear to me.

After listening to a section of the content, Qiu Chengwen exhaled lightly and said to Rost-Brand, "So that's how it is. I never understood this part."

"Yeah, it's amazing."

Rost-Brand made a light comment, and then heard Fefferman's dissatisfied voice behind him, "Don't talk, listen carefully!"

"Uh~~~"

Rost-Brand and Qiu Chengwen looked at each other awkwardly.

The report on the stage continued.

After Zhang Shuo talked about several difficult points in succession, he continued to sort out the final part.

He has a deep understanding of the research, clear logic, and his explanation process is very smooth.

His tone became faster and faster.

When the boundary function argument is completed and then connected to the initial parameter argument, the conclusion of the 'finite value argument' can be substituted to prove that the solution at any position exists, is unique, and is smooth.

This is the final part.

It was already past 12 o'clock. Normally, the meeting would have entered the lunch break, but no one left the venue and everyone continued to stare at Zhang Shuo on the stage.

Some scholars in the front row already had relaxed smiles on their faces.

For example, Charles Fefferman.

Charles Fefferman's eyes sparkled, and he didn't need to listen any further, as he was sure that the NS equation problem had been solved.

The same is true for Qiu Chengwen and Rost-Brand.

Anton Kapustin had already made up his mind earlier. He stood on tiptoes with ease and said to Bennys beside him, "Are you still listening? Is there anything else?"

Bennis continued to stare for a long time, and said depressedly, "There are two things I still don't quite understand."

"This is the difference in level, haha." Anton Kapustin sneered.

Bennis said unhappily, "If it's algebraic geometry, even ten of you wouldn't be a match."

"I won't attend the lecture on algebraic geometry either."

"..."

Bennis realized that he had lost the argument, so he simply asked, "Now that you understand everything, how is it?"

"Of course, it's just as you thought."

Anton Kapustin's expression also became solemn. He exclaimed seriously, "The NS equation problem has been solved!"

"very perfect!"

As soon as he finished speaking, the stage remembered the final ending, "At this point, it is obvious that the solution of the Nastok equation exists at every position, and it is smooth!"

As soon as the words fell, the meeting room fell silent.

Anton Kapustin was the first to stand up and clapped vigorously.

The scholars in the front row also stood up and applauded. Their applause seemed to have a driving force, causing everyone in the audience to stand up and applaud loudly.

The applause was so loud and long that it could be heard even in the square outside the conference hall.

From this moment on, the ns equation problem has been completely solved!
(End of this chapter)