From University Lecturer to Chief Academician

Mitsuo Tian is just one of those scholars who don't believe in proofs.

Many scholars have carefully studied Wang Hao's proof, except for a very few scholars who understood all of it, most of them did not understand it.

There are a few logical analysis, they all feel a little awkward, it seems a little unreasonable, but they have no way to say what is unreasonable.

To put it bluntly, I just didn't understand.

In fact, it is also very normal. There is a saying that is good, there are specializations in the art industry.

This is especially true in scientific research.

Few mathematicians can develop in an all-round way. Most of them focus on one or two disciplines, and they only have a little understanding of other sub-disciplines. Even the top international mathematicians are not as good as an excellent Ph.D. when they encounter unfamiliar subjects.

Wang Hao's proof is mainly a parameter argument, that is, to expand the limit of conventional values ​​to infinite values ​​in the previous proof.

The core of it is logical argumentation, which involves the content of complexity theory. Combining complexity theory with equation calculation and analysis, the requirements for the foundation are relatively high.

It will be very difficult for scholars who have not been engaged in the study of complexity issues to understand the content by themselves.

In the conference hall, many people were discussing the logical issues in the proof process. Interestingly, Luo Dayong quickly became the focus.

Luo Dayong has a deep understanding of Wang Hao's proof, because its core content is the research they conducted together, and the expansion is only to add some follow-up equation analysis and calculation problems.

Many scholars in the venue are constantly discussing related issues.

Luo Dayong also joined the topic, started talking with several scholars, said a few words, and then it became other people listening to him.

Several people gathered around, including a Fields winner.

Luo Dayong explained seriously, "This is an analysis of an N problem, an N problem, not a P problem, and N is just a coefficient."

"N*1 is a separate problem, which can be understood as N P problems. The relationship between the two is multiplicative, not exponential."

"Wang Hao's proof is based on the commonality of the parameters of the equation to study the transformation of the parameters. Part of the content is the analysis of the N problem..."

Luo Dayong said something.

Some people seem to understand after listening to the explanation, but they still don't understand after thinking about it carefully.

Some people just don't get it at all.

Logical problems are often much more complicated than computational problems, and it is not easy to understand even after listening to others.

Wang Hao didn't talk about the problem, because tomorrow is his report, and then we can talk about it together.

He met a lot of people at the venue and got to know a lot of people.

Among them are several well-known mathematicians, including Martin Hale, a top master in the field of partial differential equations, who has made great contributions to the theory of stochastic partial differential equations. He has established a set of feasible regularities for complex equations Structural theory, and won the Fields Medal for related research.

Wang Hao's impression of Martin Haier is that his hair is 'cool', which even made him think of Zhang Zhiqiang.

Martin Haier has an extremely sparse afro head, with all the hair standing on end, as if feeling like an electric shock, but it is so sparse that it seems that the number can be counted.

"In a few years, Zhang Zhiqiang will do the same, right?" Wang Hao rubbed his forehead in thought. He felt that he should pay attention to this problem. Fortunately, his hair hasn't lost its tendency yet.

In addition to Martin Hale, he also met Bruce Pulitzer. They were already familiar, but this was the first time they met.

The first thing Bruce Pulitzer said when he saw Wang Hao was, "I'm here for you, Wang Hao, I'm so happy to see you in advance."

Wang Hao rubbed his hair again, "You must have come here for the thesis, right?"

"Haha~~"

Pulitzer smiled awkwardly, "Of course it's incidental, but you will publish it in Advances in Mathematics, right?"

Wang Hao smiled, "Of course, we are old friends."

Wang Hao chatted with Pulitzer for a few words, and met another very interesting person.

Didier Mayor.

Mayor is a well-known physicist and one of the giants of CERN, but when he came to participate in the NS equation report, some people couldn't understand it.

"I'm also here just for you, Wang Hao." Mayor said, "But it's not NS equations. I don't care about visible physics."

"Then you are...?"

"Your annihilation theory." Mayor said enthusiastically, "I saw it last year, and it sounds very interesting. I think this idea is very good, and there is a certain possibility of existence."

Mayor continued, "I have wanted to come and talk to you for a long time. I hope to know more about it, and I hope to be able to verify its existence."

Wang Hao was interested in what Mayor said, "Do you believe in my theory of annihilation?"

"It's not that I believe it, but that I can't refute it."

Mayor said, "I believe that all the physical theories in the world, as long as they cannot be proven wrong, they may be correct."

"Including string theory, cosmology, big bang theory, etc., I have also seen a theory of calculating the universe. There are many such theories in the world, but only a handful of them can be verified."

"The theory of annihilation, I think it can be verified, but you need to think about the method."

"That's why I came here."

Wang Hao said with a smile, "Your statement is very interesting, but I haven't thought about how to verify it."

"Of course, I knew it a long time ago." Mayor said indifferently, "We can have a good talk on this issue, but today is not suitable, let's wait until after your report is over tomorrow."

"I hope your proof is wrong, and then you can give up those complicated pure mathematics research and come to the paradise of physics. For a mathematical genius like you, theoretical physics is your final destination."

Wang Hao twitched his lips and said, "It's the first time I've heard such affirmation, but thank you."

"You're welcome, come on!"

...

The next day is the day of the report.

In the morning, a large group of mathematicians came to Donggang University, together with the reception and the people in charge of security, it made the vicinity of the conference lecture hall of the Government Affairs Building very lively.

After the mathematicians came to the university, they entered the conference hall one after another and waited.

The reception of Donggang University is still very attentive. Each scholar has a separate seat and table. They not only prepared drinks, but also prepared some snacks for them to eat and wait.

Wang Hao was not in the mood to pay attention to these things. After he came to the conference hall, he went to the back office, and then prepared some materials, and walked towards the conference hall after seeing that the time was almost up.

There are already many people in the conference hall.

Scholars from top universities in China came to listen to the reports, and some even brought students with them, and one-third of the venue was scholars from abroad.

Among them, there are four Fields winners, including Martin Haier, Alessio Figali, Qiu Chengwen and Tao Zhexuan, as well as some winners of Albert and Wolff, such as Tian Junganfu, Louis - Nirenberg et al., each of which can be said to be a top scholar in the field of partial differential equations.

Some of them were talking and laughing, while others were sitting silently.

All are waiting.

The start time of the report is set at 9 o'clock, and the time will last for two and a half hours, and the rest is for question and answer time. If there are more people asking questions, the time will be extended.

Compared with the major problems of the NS equation, the report of more than two hours is very short, but Wang Hao does not need to make a report for too long, because he is only doing calculation analysis and demonstration, expanding the original conventional value range to Unlimited values.

As for the proof of the smoothness of the NS equation solution set, he has already completed it and published it in "New Advances in Mathematics".

That part of the proof does not need to be reported.

This report is not just for scholars to listen to. Donggang University also organized a review meeting, which means that the top scholars who came to listen to the report will form a review meeting to give review opinions on Wang Hao's report, and finally decide whether his paper is passed or not.

The members of the judging committee include nine members including Qiu Chengwen, Tao Terence, Martin Haier, Alessio Figalli, and Tian Jun. The support of so many top scholars in the same field is enough.

Soon, it was nine o'clock.

Wang Hao walked into the venue on time. He first glanced at the audience, and then showed a very flat smile, "Thank you for coming here to listen to my report. This report is a demonstration of the smoothness of the NS equation. Value' extended proof."

"I believe that everyone present should have understood my other paper, which is the proof of the smoothness of the NS equation solution set under conventional values."

"Now it's time to expand the scope of the restriction, the main content of which is a demonstration of computational logic, and this is where the difficulty of this proof lies."

"Yesterday, I heard some people talk about difficulties. Today, I will talk about these in detail."

"If you have questions, you can ask questions at a later time."

Wang Hao's opening remarks were very straightforward. He just said a word of welcome, and then began the content of the report, and the explanation will explain the difficulties in detail.

As for some simple processes, there is no need for special explanations.

Most of the people present are experts in the field of partial differential equations. They have already read Wang Hao's papers, so they don't need to waste time on small problems.

on stage.

Wang Hao went directly to the topic, "From the conventional value to the infinite value, the main influence is the parameter difference."

"Maybe some parameters will be enlarged to infinity, while some parameters are still fixed values, and the calculation logic will change."

"So the first thing I want to demonstrate is that when each parameter takes an infinite value, the commonality of their influence on the equation..."

Wang Hao spoke carefully.

Everyone looked at the stage, including those top mathematicians and some ordinary scholars.

However, most top mathematicians don't need to listen too carefully. At most, they don't understand one or two difficulties.

Tian Junganfu is a winner of Wolfe, so he can naturally be called a top mathematician. He may be the most serious listener among top scholars, because he hopes that Wang Hao's proof is wrong.

This is not only for face, but also for my own research.

As the saying goes, peers are enemies.

Partial differential equations is a large subject direction, including many types of research.

Tian Junqianfu has invested a lot of energy in the NS equation, but he has achieved nothing so far. Whether it is out of jealousy or other ideas, he does not want Wang Hao to complete the proof.

However, the fact does not depend on human will.

What Tian Junqian couldn't understand was gradually explained by Wang Hao, and he found that he could hear clearly, and it seemed much easier to follow along to understand.

"What he said is very similar to that scholar named Dayong yesterday..."

"Why yesterday, I couldn't figure it out at all, but now I can understand it easily?"

Tian Junganfu felt very surprised, and the last thing he wanted was to be able to understand, because understanding meant that the logic of the other party was correct.

Like Tian Junganfu, there were several other scholars, including Martin Haier. Martin Haier also listened to Luo Dayong for a few words, but in the end they were confused.

Hearing Wang Hao's explanation now, the logic is similar to that of the person yesterday, but after thinking about it, he understood it.

why?

"Maybe I listened to it yesterday, and I understood it after listening to it again. This kind of complex problem requires more thinking and listening..."

Martin Hale thought.

Others can only come to similar conclusions. After understanding the difficulty of Wang Hao's explanation, the others are not a problem at all.

Martin Haier realized that he didn't need to listen any more. He had already figured out the other content, so he just raised his legs and looked around at other people. Finally, he found Tao Zhexuan next to him, and he didn't continue to listen carefully.

He suddenly whispered, "Terry, you understand it too? I really didn't expect that the NS equation problem was solved in this way. I thought this problem would last for decades."

Tao Terence laughed, "I didn't think of it either. I have also studied this problem, but I just wanted to use a method to describe it, not to really prove its smoothness, just like the Monge-Abe equation, always Only under certain conditions can a conclusion be drawn.”

"As a result, the more important NS equation problem will be proved faster than the Monge-Abe equation."

Martin Hale said with a smile, "On the Monge-Abe equation, the young people on stage are also experts, and he also made the last relevant research."

"yes."

Tao Zhexuan also sighed and nodded, "He is that kind of elusive genius."

He won the Fields Medal for his research in number theory, and later began to engage in research in other fields, including harmonic analysis, nonlinear partial differential equations, combination theory, etc., and his research spanned multiple branches of mathematics.

Terence Tao also found a problem. When conducting research across multiple fields, it is difficult to focus on one research, because independent thinking may be affected by thinking in other fields.

This is one of the reasons why many mathematicians only focus on a single field of research.

Few mathematicians can research in multiple fields and achieve great results.

The young people on the stage now seem to have broken this law. Number theory and partial differential equations are two different fields, and the correlation is very low. As a result, the other party has achieved amazing results.

Goldbach Conjecture.

NS equation.

These are two different disciplines and there is no question of any correlation.

In just one year, the other party completed two major studies, both of which can be said to be incomprehensible. Tao Zhexuan has always considered himself a genius, and the evaluation of him by the outside world is also the same.

Now looking at Wang Hao on the stage, he realized that he has become very ordinary.

...

In fact, before the report, Wang Hao was a little worried about the report, because his calculation logic was too complicated, and most of the audience did not dabble in complexity theory.

Just like the situation that Luo Dayong encountered yesterday, he explained it carefully for a long time, and few people could fully understand it.

Seeing the reactions of the scholars in the audience, especially several top mathematicians, who began to chat in distracted whispers, he knew that he had succeeded, at least the top scholars had understood.

For a report of a brand new study, it is enough for the scholars involved in the review to understand.

However, Wang Hao still hopes that more people can understand. He continued to analyze the difficulties in the calculation logic and explained some minor difficulties.

He hopes to ensure that at least half of the people can understand.

After explaining for two hours, Wang Hao sorted it out from the beginning, until the final logical analysis, and then entered the calculation content.

At this time, many people knew that Wang Hao's proof had indeed been completed.

Some people even couldn't help but want to applaud in advance, because the follow-up content is not too complicated, and they can understand it even if they study it by themselves.

Wang Hao said it again.

With everyone watching, he carefully completed the rest of the process, and finally wrote a formula on the whiteboard, "So, we can pass the seventh equation, Lemma 2, Lemma 6, and Lemma 11, to get Each parameter of the equation can be infinite without affecting the established proof."

"complete!"

Wang Hao put down the pen in his hand, turned around and faced everyone.

The conference hall was also quiet for a moment.

Wang Hao fiddled with it, and simply repeated, "My proof is over. If you have any questions, you can ask them. The rest is time for answering questions."

At this time, applause broke out from the audience.

The first person to applaud vigorously was Pan Weiguo, followed by Luo Dayong, Zhou Qingyuan, and other familiar people, and then the applause spread slowly and became louder and louder.

Everyone in the audience was not in a calm mood. They witnessed the NS equation problem being proved.

In 1831, Poisson proposed the equation of motion of compressible fluid, which is the origin of NS equation. In the following twenty years, the ns equation has undergone two revisions, and the main function of the equation is to do application-related calculations.

This is a partial differential equation directly related to the application.

Because the NS equation is widely used, the mathematical community has always hoped to verify its stability, that is, to give perfect theoretical support for its application.

It has been more than a hundred years since the question was raised, and countless mathematicians have devoted a lot of energy to research.

until now.

One of the millennial mathematical puzzles, considered a cornerstone of the field of dynamics, has finally been successfully demonstrated.

Everyone had a lot of emotions in their hearts, and the conference hall was completely filled with fierce applause.

This is a historic moment!

(seeking a monthly ticket)

I just found out that there are double monthly tickets~~~ It’s the end of the month, ask for a monthly ticket~~