Main Lecture Hall.

Wang Hao stood on the podium and finished the last sentence, "The development of mathematical research in China is showing a better and better trend......

"I believe that in the future, we will definitely be able to catch up with the international level and achieve transcendence!"

He politely bowed slightly to the audience.

The scene was silent for a long time, and finally someone applauded, and the applause was quite warm, but it was a little worse than the applause given to Zhong Mingchu just now.

The scholars in the audience were still very polite, after all, it was the testimonial of the winner of the Chern Prize in Mathematics, and he was a mathematician who created the history of the lowest age of the award, but their feelings were very complicated.

Of course, they knew that Wang Hao was telling the truth.

Although it sounds weird, Wang Hao has come up with so many mathematical results in a year, and it is impossible to get stuck on a research for a long time.

Even if two weeks is a bit short, it can't be more than a month or two.

Two weeks, one month, two months, there is no difference for them, it can be understood that the research was completed smoothly all the way, and there is no problem of 'stuck' at all.

Speaking of the research being 'stuck', Zhong Mingchu said that it was very realistic, and there has been no progress for six consecutive years.

That's the case, for the most part.

Many scholars have been struck by what they have just said, and they have carefully reflected on their mathematical research work, and find that they have a very sad prospect, and they seem to be the one who is indiscriminately filling up in mathematical circles.

When I think about it deeply, many people keep clapping mechanically, forgetting to stop.

Wang Hao heard the applause in his ears, the intensity was not as strong as Zhong Mingchu's testimonial just now, and he comforted himself that 'pirated testimonials, it is okay to get so much applause'.

Later, it turned out that the applause lasted for a long time without stopping.

Although there are not many sparse pulls, they have never stopped, and the corners of their mouths can't help but smile.

He shook hands with Zhong Mingchu and walked towards the stage together.

Zhong Mingchu and Wang Hao walked together in a very complicated mood, not to mention that his testimonial was plagiarized, but also suffered a psychological blow, compared with the young man next to him, he felt like a stupid and stupid person.

The two still walked off the stage together.

When they got to the aisle, they separated, Wang Hao returned to his position, and faced a lot of complicated eyes.

Qiu Chengwen watched Wang Hao sit down, and he wanted to laugh a little.

He certainly knew that it was difficult for others to understand the top mathematicians.

In fact, Wang Hao said that 'the research was stuck for two weeks', and he didn't think it was strange.

He felt the same way himself.

When I was young, I was invited to be an associate professor at the State University of New York at Stony Brook at the age of 23, and it took only a few months to complete the research on "Complete Riemannian Pop Upregulation Functions".

At that time, it caused a very strong reaction.

In the following years, Qiu Chengwen now feels incredible when he thinks about it, he has completed all kinds of research smoothly, and those very difficult contents seem to be easy to solve in front of him.

That was the case at the peak of mathematical research.

Now Wang Hao is also at this stage, as long as it is in the field he is good at, difficult research will be easy for him to complete.

Young people are full of creativity and ideas, combined with a strong foundation and a high IQ, and they are naturally able to complete all kinds of research.

Of course, this is incomprehensible to ordinary people.

Compared with Wang Hao, most of the people present were just ordinary people.

Wang Hao sat in his position, feeling the complicated eyes around him, and he felt a little uncomfortable.

At this time, Birkar next to him gave him a thumbs up and said in a somewhat strange Chinese tone, "Your testimonial just now is really good, I feel the same way." ”

"Math research is really hard. Sometimes I have to think about a problem for a long time, especially when I do the study of double rational geometry, I think I am very good at this direction, but sometimes I can still think about a problem for a few days......"

He shook his head helplessly.

Wang Hao also sighed and said, "Yes, mathematical research is really difficult, and I sometimes even feel that I can't do it at all." ”

The two of them kept complaining about the difficulty of mathematical research, which also made the feelings of the people around them more complicated.

A few people regretted applauding Wang Hao just now.

They knew that the two of them were talking from their hearts, and they didn't mean to hit them, but it was because it was true that it was even more shocking!

……

Next is the presentation of the Zhong Jiaqing Mathematics Prize, which was awarded to doctoral students from Donggang University, Sudong University, Xijing Normal University and Gangcheng City University.

Several young doctors were visibly excited to take the stage.

This is the most touching moment since the opening ceremony, because they are really excited to win the Zhong Jiaqing Mathematics Award, some doctors even blush, and some shed tears.

They were just studying for a PhD, and because of their research, they won such a prestigious award.

On the one hand, it is an affirmation of themselves, and on the other hand, it can also make them more confident and look forward to future research.

The morning was the speech and the opening ceremony.

After the award ceremony of the opening ceremony, the vice director of the Mathematics Society went up to make a summary, and then it ended.

A series of presentations began in the afternoon, and many people began to look forward to it.

The most anticipated report this time is Wang Hao's report, which is not only expected by those who attend the mathematics conference, but also by many top mathematicians in the world.

At lunchtime, Wang Hao and Bill Carl sat together, and the two communicated more and became familiar with each other, and the relationship felt a lot closer.

Bilkar took a bite and asked Wang Hao, "How did you prepare the report?" I've been looking forward to it for a long time, and this time I'm here specifically for your report. ”

Wang Hao said, "The preparation is quite sufficient, but I feel that it is difficult to make a report." ”

"Why?" Bilkar looked up in some confusion.

"It's not easy to explain!" Wang Hao sighed.

This is the most complex report he has ever faced, and he can only take a part of it for explanation.

It took him a long time to summarize this mathematical method, and the paper was written in more than 50 pages, which also involved a lot of logical thinking.

Wang Hao could feel the difficulty, and the report could not be too long, the arrangement of the mathematics meeting was three hours, starting at half past two in the afternoon.

Normally, at half past five, six o'clock, the meeting is over.

In other words, the arrangement of the math club is to let him give a three-hour report, and the time can be extended appropriately if the explanation is not finished.

Wang Hao felt that the time was still too short, and his preparation was only to explain the part related to the Kakutani conjecture, not the whole content.

Even so, it is very difficult, even higher than the proof of the Kadotani conjecture, because his research is a methodological idea, not a logical analysis.

The whole research is to give a general direction of thinking and solution, but the specific problem still needs to be analyzed in detail, which can be said to be a systematic solution.

After the proof report and paper of Kakutani's conjecture were published, the mathematical community has studied the method he is talking about, and they can affirm that the research content is a methodological idea.

It's like a valid vs. irrelevant carry filter.

The effective and irrelevant carry method is a method idea, a solution direction and idea of an algorithm, rather than a certain calculation logic and program.

Mathematically, for example, it can be understood as 'solving a system of multivariate cubic equations' or 'solving partial differential equations', both of which have a common feature that there is no definite way to solve them.

Most of the basic content can only provide methods and ideas, and it may be possible to directly solve some specific problems, or it may not be able to solve them.

This requires a thorough study of the methodology.

Now Wang Hao's research methods are the same, he feels that his research methods can be published in a book, rather than simply writing a paper and making a report.

Soon, in the afternoon, the reports of the various offices had officially begun.

Wang Hao is in the No. 1 main hall.

There are three reports arranged in the No. 1 main hall, Wang Hao's report is in the third place, the first two reports are short, and one is a work report.

Most of the scholars in the main hall were waiting for Wang Hao's report.

The first two reporters were very uncomfortable, because there were not many people in the audience listening carefully, and during the process of their reports, you could see that many people were whispering.

Since the 'audience' in the audience didn't pay for it, the report ended quickly.

As a result, when it was Wang Hao's turn, it was ten minutes earlier.

Wang Hao could only go backstage in advance to prepare, and after simple preparations, he went on stage.

At this time, the main hall was completely different, and scholars from other halls had come, and they felt that the audience was overcrowded.

Everyone looked at Wang Hao seriously, and some people took paper and pens and prepared to make records.

The reporter also turned the camera on.

Offstage.

Qiu Chengwen and Bill Carr were talking, "I have carefully analyzed Wang Hao's Kakutani conjecture to prove that there is indeed a method in it, but it is not easy to find out, it should be like he said, proof is only a part of the application of mathematical methods." ”

"This mathematical method should already be the result of the Fields level."

There is no Fields level of achievement, because the Fields Medal rewards contributions to mathematics, not for a single piece of research.

Qiu Chengwen's meaning is obvious, that is, Wang Hao is likely to win the Fields Medal in terms of his contribution to mathematical research with this mathematical method.

Bill Carr nodded approvingly.

The conversation between the two was not deliberately hidden from others, and the people next to them suddenly became more serious after listening to it, and they also wanted to know what was the result of the Fields level.

At this time, Wang Hao stood in the middle of the podium and said seriously, "I have been preparing for this report for a long time. ”

"Although the paper has already been written, there is too much content, so I can only take a part of the content related to the Kakutani conjecture to explain."

"What I'm going to talk about is a methodological idea, and it's called 'Finding the Infinite Columnar Mathematical Transformation'."

"The simple understanding is how to solve the problem of mathematical changes brought about by fixed columns, that is, the infinite and infinite analysis problems of columns."

"In the simplest, the number 1, add 1 to each step, and the result is a series of natural numbers."

"If it's divided into two steps, the first step is to add 1 and subtract 1, and you get a set of numbers 1 and 2."

"It sounds very simple, but in fact, it is very complicated, if you take any natural number, add 1, subtract 1, become multiply 3 plus 3, and then make a judgment, and then divide by 2, it is also a 3x+3 problem, it is difficult to judge whether there is an end."

"What I want to do is to study the identification of similar problems and how to analyze them."

After Wang Hao finished his opening remarks, he began to explain, "When dealing with this kind of problem, we must first think in columns, which is the most important and the most basic. ”

"And columnar expressions are directly related to judgments, and we want to analyze the relationship between the two, which involves a problem of categorical sets, let's look at this ......"

“……”

Wang Hao just said an opening remark, and then slowly advanced to the content, which already made everyone in the audience feel profound.

They followed Wang Hao's explanation, slowly carried out in-depth understanding, and they were all very concentrated.

This also made the report sound quiet, not even a little other.

Many people have found that they only need to be distracted, and they may not understand it again.

And that's not all.

When it comes to getting deeper into the content, some people start to lose track.

Wang Hao explained the problem of algebraic set transformation, two or three steps of jumping, and completed a column, the speed of his explanation is not fast, is to hope that more people can understand, but there are still many people who can't keep up.

They thought about it carefully, and after thinking about it for a while, they understood.

At this time, I found that the content of the explanation had reached another place, so I could only write down the conclusion with a wry smile and try to keep up with the progress of the explanation.

Fortunately, Wang Hao's explanation is very clear, and the comprehension effect of the bonus of "The Gift of Teaching" also plays a role, and many scholars can still keep up.

When the explanation reached two hours, the difficulty was a little deeper, and it was even more difficult to keep up.

Some scholars can't keep up at all, and they don't even know what Wang Hao is explaining.

They could only continue to sit with a wry smile, for fear of disturbing the other people who were listening carefully.

Later, there were more people who couldn't keep up.

Even if they can't keep up with the speed of the explanation, many people are still listening carefully, because they feel that this report is very helpful for expanding their thinking.

A lot of mathematical logic and ideas made them feel like they had a sudden realization, and a lot of exquisite deductions also seemed to be helpful for their own research.

The report was spent three and a half hours in a quiet atmosphere.

Wang Hao is still 'dragging the hall'.

This is mainly because the content of the report is too complex, and he hopes that more people will follow suit, so naturally the explanation will take longer.

After all the explanations were completed, Wang Hao made a concluding remarks, "The above is my report, which is also the thinking logic for completing the proof of the Kakutani conjecture. ”

After speaking, he bowed slightly to the audience, and then quickly took a sip of water to replenish it.

Many scholars in the audience hadn't reacted yet, and seemed to be thinking about it, and slowly applause rang out.

The applause grew louder and louder, and the ceiling of the No. 1 main hall seemed to be shaken.

Everyone felt tired, but everyone was applauding, because they really felt that what Wang Hao explained was very meaningful.

Some people have questioned the rumors that the mathematical method studied by Wang Hao is more significant than the proof of the Kakutani conjecture.

Now no one questions it.

It was clear to everyone that they had heard a new, systematic approach to mathematical thinking, and that they all felt very valuable, and some even found it meaningful for their research.

There are many scholars in the audience who study analytic number theory and complex theory, and the feeling is even more obvious.

After listening to the report, they all felt that they had new inspiration, and they wanted to go back and make a summary, and maybe they could find a way to complete the research.

When the applause was interrupted, many people also discussed, "This method is so meaningful, I just understood half of it, but I still gained a lot." ”

"Me too, worthy of the rumored Fields-level achievement!"

"No wonder Wang Hao was able to complete the proof of the Kakutani conjecture, this method is much more important than proving a number conjecture."

"But that's not all, it's a shame......"

A lot of people are concerned about the whole paper.

When it's time to ask questions, few people ask about the content of the report, because they know that some of the contents, even if they say it again, they may not necessarily understand it, and for every question, it is not possible to explain it in one or two sentences.

A professor from Capital University stood up and asked, "Professor Wang, can you tell me when this paper will be published?" I want to see it all. ”

Everyone in the audience immediately looked over.

Wang Hao said with a smile, "I have confirmed with Academician Wang Liqun of the Institute of Mathematics of the Academy of Sciences that the papers will be published in the journal of the Institute of Mathematics." ”

"You can ask Academician Wang Liqun for the specific publication time."

A group of people suddenly looked at Wang Liqun in the front row.

Wang Liqun is an academician of the Chinese Academy of Engineering and is responsible for two major journals of the Institute of Mathematics, Acta-Acta Mathematica and Acta-Mathematica-Sinica.

The former is a Chinese mathematics journal, and the latter is an English mathematics journal, which is also included in the SCI index.

Wang Liqun got up and waved at the others, and said, "Don't worry, the next issue will be available, and Professor Wang Hao's paper will be published first." ”

Everyone else was looking forward to it.

……

After Wang Hao finished the explanation, he greeted the others and went back to the hotel after dinner.

When he got back to the hotel, he couldn't wait to start taking notes.

The rest of the people listened to his report and felt that they had gained a lot.

Wang Hao also gained a lot.

[Task 1]

[R&D project name: Navier-Stokes equation research (difficulty: S+).] 】

[Inspiration: 34.] 】

"Inspiration has risen by 9 points!" He's happy with the growth of inspiration, but the most important takeaway is in his head.

The study of the NS equation is a systematic project, and every progress can be said to be very important.

Now he has some more ideas related to solving the NS equation problem.

One of the ideas of following the approximation to solve the research direction made him feel a little confused and puzzled.

He felt that he had almost reached the extreme in solving the approximation of the ns equation, and had developed a general alternative equation method for projects, and the approximation proved to be very close to the exact bounds, and the approximation exceeded the previous methods.

Now he suddenly felt that he had not done enough, and it seemed that he should go one step further and make the approximation infinitely close to the exact solution.

"If you can get infinitely close to an exact solution, why not just find the exact solution?"

"And some NS equations, there may not be an exact solution, this is the world's mathematical problem, how to get infinitely close to the exact solution?"

Wang Hao was sure that his thoughts were correct, but there were contradictions between his ideas and logical judgments.

That's what he learned.

"This problem must be solved, and it will definitely be of great help to the study of the NS equation......

(Ask for a commuter pass)