Mikio Tian is just one of those scholars who doesn't believe in proof.
Many scholars have carefully studied Wang Hao's proof. Except for a very few scholars who have understood it all, most of them have not understood it.
Some of the logical analysis seemed a bit awkward to them and seemed a little unreasonable, but they couldn't tell where it was unreasonable.
To put it bluntly, I just didn’t understand it.
In fact, it is quite normal. There is a saying that goes well, there are specialties in the art.
This is especially true in scientific research.
Few mathematicians can develop comprehensively. Most of them focus on one or two subjects and only have a slight understanding of other branches. Even the top international mathematicians are not as good as an excellent PhD in unfamiliar subjects.
Wang Hao's proof is mainly a parameter argument, which is to expand the limit of conventional values in the last proof to infinite values.
The core of it is logical argument, which involves the content of complexity theory. Complexity theory combines equation calculation and analysis, and the requirements for basics are relatively high.
For scholars who have not engaged in research on complex issues, it will be very difficult for them to understand the content 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 only involves adding some subsequent equation analysis and calculation issues.
There are many scholars in the venue now, constantly discussing related issues.
Luo Dayong also joined the topic and started talking with several scholars. He said a few words, and then others listened to him.
Several people gathered around, including even a Fields winner.
Luo Dayong explained very seriously, "This is an analysis of the N problem. The N problem is not a P problem. 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 equation parameters to study the transformation of parameters. Part of the content is the analysis of the N problem..."
Luo Dayong said something.
Some people seem to understand it after listening to the explanation, but they still don't understand it when they think about it carefully.
Some people just don't understand it at all.
Logical problems are often much more complicated than calculation problems. Even if you listen to others explain them, it is not easy to understand them.
Wang Hao did not talk about the problem, because his report would be tomorrow, and we could just talk about it together then.
He met and got to know many people at the venue.
Among them are several well-known mathematicians, including Martin Hare, a top master in the field of partial differential equations. He has made great contributions to the theory of stochastic partial differential equations. He 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 was that his hair style was very 'cool', which even reminded him of Zhang Zhiqiang.
Martin Haier has an extremely sparse afro, all of which stands on end. It feels like an electric shock, but it is so sparse that you can count the number.
"In a few years, Zhang Zhiqiang will be like this, right?" Wang Hao thought and touched his forehead. He felt that he should pay attention to this problem. Fortunately, his hair has not become thinner yet.
In addition to Martin Hale, he also met Bruce Pulitzer. They were already familiar with each other, but this was the first time they met.
The first thing Bruce Pulitzer said when he met Wang Hao was, "I'm just here for you, Wang Hao. I'm so happy to see you in advance."
Wang Hao rubbed his hair again, "You are here for your thesis, right?"
"Haha~~"
Pulitzer smiled awkwardly, "Of course that's just incidental, but you will publish it in New Advances in Mathematics, right?"
Wang Hao smiled and said, "Of course, we are old friends."
Wang Hao chatted with Pulitzer for a while and met another very interesting person.
Didier Mayor.
Mayor is a well-known physicist and one of the giants of the European Organization for Nuclear Research, but when he came to attend the lecture on the NS equation, some people were confused.
"I'm here specifically for you, Wang Hao." Mayor said, "But it's not the NS equation. 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 it has 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 verify its existence."
Mayor's statement made Wang Hao interested, "Do you believe my annihilation theory?"
"It's not that I believe it, but that I can't refute it."
Mayor said, "I believe that all physical theories in the world, as long as they cannot be proven to be wrong, are probably 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, can be verified, but we just need to think about the method."
"That's why I'm here."
Wang Hao smiled and said, "Your statement is very interesting, but I haven't thought about how to verify it yet."
"Of course, I have known it for a long time." Mayor said nonchalantly, "We can have a good talk on this issue, but today is not the right time. 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 mathematical studies 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, "This is the first time I've heard such an affirmation, but thank you."
"You're welcome, come on!"
…
The next day is the day of reporting.
In the morning, a large group of mathematicians came to Donggang University. Together with the receptionists and people responsible for security, the area near the conference lecture hall of the Government Affairs Building became very lively.
After the mathematicians arrived at the university, they entered the conference hall and waited.
Donggang University's reception is very attentive. Each scholar has a separate seat and table. They not only prepare drinks, but also some snacks for them to eat while waiting.
Wang Hao was not in the mood to pay attention to this. After arriving at the conference hall, he went to the office at the back. Then he prepared some information and looked at the time before walking to the conference hall.
There are already many people in the conference hall.
Scholars from all the top universities in the country came to listen to the lectures, and some even brought their students. One-third of the venue was composed of 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 Wolf awards, such as Tian Jun Mikio and Lewis -Nirenberg et al., each of whom 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.
Everyone is waiting.
The start time of the report is set at nine o'clock, and it will last for two and a half hours. The rest is the question and answer time. The more people ask questions, the longer the time will be.
Compared with the major issues of the NS equation, a report of more than two hours is very short. However, Wang Hao does not need to give a long report because he is only doing calculations, analysis and demonstrations, expanding the original conventional value range to Infinite value.
As for the proof of the smoothness of the solution set of NS equations, he has already completed it and published it in "New Advances in Mathematics".
That part of the certification does not need to be reported.
Not only scholars came to listen to this report, Donggang University also organized a review meeting, that is, the top scholars who came to listen to the report formed a review meeting to give review opinions on Wang Hao's report, and finally decided whether his paper passed or not.
The members of the jury include nine members, including Qiu Chengwen, Terence Tao, Martin Haier, Alessio Figali, and Mikio Tian. The support of so many top scholars in the same field is enough.
Soon, the time came to nine o'clock.
Wang Hao walked into the venue on time. He first glanced at the audience, and then showed a very calm smile, "Thank you everyone for coming here to listen to my report. This report is about the smoothness demonstration of the NS equation." An extended proof of 'regular value'."
"I believe that everyone here should have already understood my other paper, which is the proof of the smoothness of the solution set of NS equations under conventional values."
"Now we are expanding the scope of restrictions, and the main content is the argument about computational logic. This is also the difficulty of this proof."
"Yesterday, I heard some people talking about the difficulties. Today, I will talk about these details in more detail."
"If you have any questions, you can ask them at a later time."
Wang Hao's opening remarks were very direct. He just said welcome and then started the content of the report. He also explained the difficulties in detail in the briefing session.
As for some simple processes, no special explanation is needed.
Most of the people present are experts in the field of partial differential equations. They have already read Wang Hao's paper, so they don't need to waste time on small problems.
On stage.
Wang Hao went directly to the topic, "The main impact of expanding from conventional values to infinite values is the difference in parameters."
"Perhaps 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 impact on the equation..."
Wang Hao spoke carefully.
Everyone looked at the stage, including the top mathematicians and some ordinary scholars.
However, most top mathematicians don't need to listen too carefully. They don't understand at least one or two difficult points, and they don't understand anything, so naturally they don't need to take it too seriously.
"Treading on the Stars"
Tian Jun Mikio is a Wolf winner and can naturally be called a top mathematician. He may be the most serious among the 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 area that includes many types of research.
Tian Jun Mikio has invested a lot of energy in the NS equation, but has achieved nothing so far. Whether it is out of jealousy or other ideas, he does not hope that Wang Hao can complete the proof.
However, facts are not subject to human will.
What Tian Jun Mikio couldn't understand was slowly explained by Wang Haozhen, and he found that he heard it very clearly, and it seemed much easier to follow and understand.
"What he said was very similar to the scholar named Dayong yesterday..."
"Why was it that I couldn't understand it at all yesterday, but now I can understand it easily?"
Tian Jun Mikio felt very surprised, and the last thing he expected was to understand, because understanding meant that the other party's logic was correct.
There were several other scholars who felt the same way as Tian Jun Mikio, including Martin Haier. Martin Haier also listened to Luo Dayong for a few words, but he was completely confused.
Now that I heard Wang Hao's explanation, the logic was similar to that of the person yesterday, and I finally understood it after thinking about it.
why?
"Maybe I listened to it once yesterday, and then I understood it after listening to it again. This kind of complex problem requires more thinking and listening..."
Martin Hale thought.
Others can only draw similar conclusions. After understanding the difficulties explained by Wang Hao, the rest is not a problem at all.
Martin Haier realized that he didn't need to listen anymore. He had already figured out the rest of the content, so he simply crossed his legs and looked around at the others. Finally, he found that Terence Tao next to him did not continue to listen carefully.
He immediately whispered, "Terry, do you understand it? I really didn't expect that the NS equation problem was solved like this. I thought this problem would continue for decades more."
Tao Zhexuan smiled and said, "I didn't expect it either. I have also studied this issue, but I just wanted to use a method to describe it, rather than really proving its smoothness, just like the Monge-Abe equation, which always A conclusion can only be drawn under certain conditions.”
"As a result, the more important NS equation problem will be proved faster than the Monge-Abe equation."
Martin Haier smiled and said, "On the issue of the Monge-Abe equation, the young man on the stage is also an expert. He also made the last relevant research."
"yes."
Tao Zhexuan also sighed and nodded, "He is the kind of genius who is hard to fathom."
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, combinatorial theory, etc. His research spanned multiple branches of mathematics.
Tao Zhexuan also discovered a problem. When conducting research across multiple fields, it is difficult to focus on one research, because thinking alone 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.
There are few mathematicians who can conduct 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, both parties have achieved amazing results.
Goldbach Conjecture.
NS equation.
These are two different disciplines and are not related in any way.
In just one year, the other party has completed two major studies, both of which can be said to be incomprehensible. Tao Zhexuan has always believed that he is a genius, and the outside world also evaluates him in the same way.
Now looking at Wang Hao on the stage, he found that he had become very ordinary.
…
In fact, before giving the report, Wang Hao was a little worried about the report because his calculation logic was too complicated, and most of the people in the audience had no knowledge of complexity theory.
Just like the situation Luo Dayong encountered yesterday, he explained it carefully for a long time, but few people could fully understand it.
Seeing the reaction of the scholars in the audience, especially several top mathematicians, who all started chatting in low voices to distract themselves, he knew that he had succeeded. At least the top scholars had understood.
For a report on a new study, it is enough that the scholars involved in the review understand it.
However, Wang Hao still hopes that more people can understand it. He continues to analyze the difficulties in calculation logic and also explains some minor difficulties.
He wanted to make sure that at least half of the people could 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 subsequent content is not too complicated and can be understood even if you study it yourself.
Wang Hao said it again.
With everyone watching, he carefully completed the remaining process, and finally wrote a formula on the whiteboard, "So, through the seventh formula, as well as Lemma 2, Lemma 6 and Lemma 11, we get Each parameter of the equation can be taken to infinity without affecting the established proof."
"complete!"
Wang Hao put down the pen in his hand and turned around to face everyone.
The conference hall was also quiet for a moment.
Wang Hao fiddled with it for a while and simply repeated it, "My proof is over. If you have any questions, you can ask them. The rest is Q&A time."
At this time, the audience burst into applause.
The first person to applaud vigorously was Pan Weiguo, followed closely by Luo Dayong, Zhou Qingyuan, and other familiar people. Then the applause slowly spread and became louder and louder.
Everyone in the audience was not calm. They witnessed the NS equation problem being proved with their own eyes.
In 1831, Poisson proposed the equation of motion for compressible fluids, which is the origin of the NS equation. In the following twenty years, the ns equation has been revised twice, and the main function of the equation is to perform application-related calculations.
This is a partial differential equation that is directly relevant to applications.
Because the NS equation is widely used, the mathematical community has always hoped to verify its stability, that is, to provide complete theoretical support for its application.
It has been more than a hundred years since the problem was raised, and countless mathematicians have invested a lot of energy in research.
until now.
One of the millennium mathematical puzzles, considered a cornerstone of the field of dynamics, has finally been successfully proven.
Everyone had a lot of emotions in their hearts, and the conference hall was completely filled with fierce applause.
This is a historic moment!
(Ask for monthly ticket)
