Main lecture hall.
Wang Hao stood on the podium and finished his last speech, "The development of domestic mathematics research is showing an increasingly good trend...
“I believe that in the future, we will definitely be able to catch up with the international level and surpass it!”
He bowed politely to the audience.
The scene was silent for a long time before someone finally clapped. The applause was quite enthusiastic, but it was just a little worse than the applause given to Zhong Mingchu just now.
The scholars in the audience were still very polite. After all, this was the speech of the winner of the Chen Shengshen Mathematics Award, and he was a mathematician who created the history of the minimum age for the award. However, their emotions were very complicated.
Of course they knew that Wang Hao was telling the truth.
Although it sounds strange, Wang Hao has produced so many mathematical results in one year, so it is impossible for him to be stuck on one research for a long time.
Even if two weeks is a bit short, it cannot be more than one month or two months.
Two weeks, one month, two months, there is no difference to them. They can all understand that they have completed the research smoothly and there is no "stuck" problem at all.
Speaking of research being stuck, Zhong Mingchu was very realistic. There has been no progress for six consecutive years.
This is most of the time.
Many scholars were shocked by the remarks just now. They carefully thought about their mathematical research work and found that their prospects were very sad. They seemed to be the ones in the mathematics circle who were just trying to make up for their mistakes.
When thinking deeply, many people kept clapping mechanically and forgot to stop.
Wang Hao heard the applause in his ears. The intensity was not as strong as Zhong Mingchu's speech just now, and he comforted himself that it was enough to get so much applause for his pirated speech.
Later I discovered that the applause continued for a long time without stopping.
Although there weren't many people walking around, they never stopped and couldn't help but smile.
He shook hands with Zhong Mingchu and walked down the stage together.
Zhong Mingchu felt very complicated when he walked with Wang Hao. Not only was his speech plagiarized, but he also suffered a psychological blow. Compared with the young people next to him, he felt like a fool and idiot.
The two still walked off the stage together.
They separated when they reached the aisle. Wang Hao returned to his seat and faced a lot of complicated looks.
Qiu Chengwen looked at Wang Hao sitting down, and he almost wanted to laugh out loud.
He certainly knew that it was difficult for others to understand top mathematicians.
In fact, he didn't find anything strange about Wang Hao's statement that "the research was stuck for two weeks."
He felt it himself.
Looking back on 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. It only took me a few months to complete the research on the "Complete Riemannian Pop Up-Sum Function".
It caused a very strong response at that time.
In the following years, Qiu Chengwen feels incredible when he thinks about it now. He completed various studies smoothly, and those very difficult contents seemed to be easily solved in front of him.
That was the situation at the peak of mathematical research.
Wang Hao is also at this stage now. As long as it is difficult research in the field he is good at, it will be easy for him to complete it.
Young people are full of creativity and ideas, coupled with a solid foundation and super high IQ, they are naturally able to complete various researches.
Of course, this is beyond the comprehension of ordinary people.
Compared with Wang Hao, most of the people present were just ordinary people.
Wang Hao sat in his seat and felt a little uncomfortable when he felt the complicated looks from around him.
At this time, Bill Carr, who was standing next to him, gave him a thumbs up and said in a strange Chinese tone, "What you said just now is really good. I feel the same way."
"Mathematical research is really difficult. Sometimes you have to think about a problem for a long time, especially when doing research on birational geometry. I think I am very good at this direction, but sometimes I can still think about it for a long time on a problem. sky……"
He said and shook his head helplessly.
Wang Hao also sighed and said, "Yes, mathematical research is really difficult. Sometimes I even feel that I am not good at it."
The two people kept complaining about the difficulty of mathematical research, which made the people around them feel more complicated.
Several people regretted applauding Wang Hao just now.
They knew that what the two people said was true to their hearts, and they didn't mean to hurt them, but it was even more hurtful because it was true!
…
The next step is to award the Zhong Jiaqing Mathematics Award. The winners are doctoral students from Donggang University, Sudong University, Xijing Normal University and Gangcheng City University.
Several young doctors were obviously very excited when they came on stage.
This was the most touching moment since the opening ceremony, because they were really excited to receive the Zhong Jiaqing Mathematics Award. Some doctors even turned red in the face, and some shed tears.
They were just studying for a Ph.D., but they won such a prestigious award because of their research.
On the one hand, it is an affirmation of themselves, on the other hand, it can also make them more confident and look forward to future research.
In the morning there was the speech and opening ceremony.
After the awarding ceremony at the opening ceremony, another deputy director of the Mathematical Society came up to give a summary, and then it ended.
A series of reports started in the afternoon, and many people began to look forward to it.
The most anticipated report this time is Wang Hao's report. It is not only expected by those attending the mathematics conference, but also by many top mathematicians in the world.
During lunch, Wang Hao and Birkar sat together. The two communicated more and became familiar with each other, and their relationship felt much closer.
Birkar took a bite and asked Xiang Wang Hao, "How are you preparing for the report? I have been looking forward to it for a long time, and I came here specifically for your report."
Wang Hao said, "I'm fairly well prepared, but I find it difficult to give a report."
"Why?" Bill Carr raised his head in confusion.
"It's not easy to explain!" Wang Hao sighed with emotion.
This was the most complicated report he had ever faced, and he could only excerpt a part for explanation.
It took him a long time to summarize this mathematical method, and the paper was more than fifty pages long, which also involved a lot of logical thinking.
Wang Hao could feel the difficulty, and the report could not last too long. The schedule for the math meeting was three hours, starting at 2:30 p.m.
Under normal circumstances, the meeting ends at half past five or six o'clock.
In other words, the mathematics club arranged for him to give a three-hour report, and the time could be extended if he couldn't finish his explanation.
Wang Hao felt that the time was still too short, and his preparation was only to explain the parts related to the Kakutani conjecture, not all the content.
Even so, it is very difficult, even higher than proving the Kakutani conjecture, because his research is based on methodological ideas rather than logical analysis.
The entire research is to give a general direction of thinking and solution, but specific problems still need to be analyzed in detail, which can be said to be a systematic solution.
After the publication of the proof report and paper of Kakutani's conjecture, the mathematical community began to study the method he mentioned, and they were certain that the research content was a method and idea.
It's like a valid and don't care carry filter.
The effective and irrelevant carry method is a method idea, an algorithm solution direction and idea, rather than a definite calculation logic and program.
Mathematically speaking, for example, it can be understood as 'solving a system of multivariate cubic equations', or 'solving partial differential equations'. One thing they have in common is that there is no definite method for solving it.
Most of the basic content of learning can only provide methodological ideas. It may be able to directly solve some specific problems, or it may not be able to solve them.
This requires a thorough study of methods.
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 or making a report.
Soon, it was afternoon, and the reports in each department had officially begun.
Wang Hao is in the main hall No. 1.
Three reports were arranged in the main hall of No. 1. Wang Hao's report was arranged in the third session. The first two reports were brief and the other was a work report.
Most of the scholars in the main hall are waiting for Wang Hao's report.
The first two reporters had a hard time because few people in the audience were listening attentively. During the process of their presentations, many people could be seen talking in low voices.
Since the 'audiences' in the audience didn't pay the price, the report ended quickly.
As a result, it was Wang Hao's turn ten minutes early.
Wang Hao could only go backstage to prepare in advance. After simple preparations, he walked on stage.
At this time, the main hall was completely different. Scholars from other halls had come over, and it felt like the audience was overcrowded.
Everyone looked at Wang Hao seriously, and some people took paper and pen to take notes.
The reporter also turned his camera over.
Off stage.
Qiu Chengwen and Bill Carr were talking, "I have carefully analyzed Wang Hao's Kakutani conjecture proof. It does contain a method, but it is not easy to find it. It should be like what he said, the proof is just a mathematical method. part of the application."
"This mathematical method should already be Fields-level achievement."
There is no such thing as a Fields-level achievement, because the Fields Medal rewards contributions to mathematics, not a single piece of research.
Qiu Chengwen's obvious meaning is that Wang Hao's contribution to mathematical research is likely to be enough to win the Fields Medal with this mathematical method.
Bill Carr also nodded in approval.
The conversation between the two people was not deliberately hidden from other people. The people around them suddenly became more serious after listening to it. They also wanted to know what Fields-level results were.
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 been written long ago, there is too much content, so I can only excerpt a part of the content related to the Kakutani conjecture for explanation."
"What I'm explaining is a method and its name is "Finding the Mathematical Conversion Method of Infinite Sequences"."
"A simple understanding is how to solve the problem of mathematical changes caused by fixed columns, that is, the analysis problem of infinitization of columns."
"The simplest one is the number 1. Add 1 at every step, and the result is a sequence of natural numbers."
"If it is divided into two steps, the first step is to add 1 and then subtract 1. The result is the set of numbers 1 and 2."
"This sounds very simple, but in fact, it is very complicated. If you take any natural number, add 1 and subtract 1, turn it into multiplying 3 and adding 3, then make a judgment, and then divide by 2, it is a 3x+3 problem. It’s hard to tell if there’s an end to it.”
"What I want to do is study the determination and analysis methods of similar problems."
After Wang Hao finished his opening remarks, he began to explain, "When dealing with this type of problem, we must first think in columns. This is the most important and basic."
"The column formula and the judgment are directly related. We need to analyze the relationship between the two, which involves a classification set problem. Let's take a look at this..."
"..."
Wang Hao just made an opening statement and then slowly advanced into the content, which already made everyone in the audience feel profound.
They followed Wang Hao's explanation and gradually understood it in depth, and they were all very focused.
This also made the report completely silent, with no other sounds at all.
Many people find that all they need to do is get distracted and they may never understand again.
Not only that.
When it comes to more in-depth content, some people start to have trouble keeping up.
Wang Hao explained an algebraic set transformation problem. He completed a series of equations in two or three steps. The speed of his explanation was not fast. He hoped that more people could understand it, but there were still many people who couldn't keep up.
They followed it carefully and thought about it for a while before they finally understood.
At this time, I found that the content of the explanation had reached another place. I could only write down the conclusion with a wry smile, and then try to keep up with the progress of the explanation.
Fortunately, Wang Hao explained it very clearly, and the additional understanding effect of "The Gift of Teaching" also worked, and many scholars were able to keep up.
When the explanation went on for two hours, the difficulty became more in-depth, and naturally it became more difficult to keep up.
Some scholars can no longer keep up and don't even know what Wang Hao is explaining.
They could only smile bitterly and continue to sit, for fear of disturbing other people who were listening carefully.
Later, more people couldn't keep up.
Even if they can't keep up with the speed of the explanation, many people still listen carefully because they feel that this report is very helpful in broadening their thinking.
Many of the mathematical logic and ideas made them feel like they were suddenly enlightened, and many of the exquisite derivation seemed to be helpful to their research.
The report lasted 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 complicated. He hopes that more people can follow it, so the explanation will naturally take longer.
After all the explanations were completed, Wang Hao concluded, "The above is my report. This is also the thinking logic for completing the proof of Kakutani conjecture."
After he finished speaking, he bowed slightly to the audience, and then quickly took a drink of water to supplement.
Many scholars in the audience had not yet reacted. They seemed to be still thinking along with it, and then the applause started slowly.
The applause got louder and louder, and the ceiling of Main Hall No. 1 seemed to be shaken.
Everyone felt very tired, but everyone was applauding because they truly felt that what Wang Hao explained was very meaningful.
Some people have previously questioned rumors that the mathematical methods studied by Wang Hao are more significant than the proof of Kakutani's conjecture.
No one questions it now.
It was clear to everyone that they heard a new, systematic way of thinking about mathematics, and they all felt it was very valuable, and some even found it meaningful to their own research.
There are many scholars in the audience who study analytic number theory, complexity theory, etc., and the feeling is even more obvious.
After listening to the report, they all felt that they had new inspiration and wanted to go back and make a summary, so that they might be able to find a way to complete the research.
When there was a break in applause, many people started discussing, "This method is so meaningful. I just understood half of it, but I still gained a lot."
"Me too, it's indeed the rumored Fields-level achievement!"
"No wonder Wang Hao was able to complete the proof of Kakutani's conjecture. This method is much more important than proving a numerical conjecture."
"But that's not all, what a shame..."
Many people are concerned about the content of the entire paper.
When it comes to question time, few people ask questions about the contents of the report because they know that some contents may not be understood even if they are said again, and each question cannot be explained clearly 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 the full content."
Everyone in the audience immediately looked over.
Wang Hao smiled and said, "I have made an agreement with Academician Wang Liqun of the Institute of Mathematics of the Academy of Sciences that the paper 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 immediately looked at Wang Liqun in the front row.
Wang Liqun is an academician of the Academy of Engineering and is responsible for two major journals of the Institute of Mathematics - "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 SCI searches.
Wang Liqun stood up and waved to the others and said, "Don't worry, everyone, it will be available in the next issue. Professor Wang Hao's paper will be printed and published first."
Everyone else suddenly looked forward to it.
…
After Wang Hao finished his explanation, he chatted with others and went back to the hotel after dinner.
After returning to the hotel, he couldn't wait to start recording.
Others felt that they had gained a lot after listening to his report.
Wang Hao also gained a lot.
【Task 1】
[R&D project name: Research on Navier-Stokes equation (difficulty: S+). 】
[Inspiration value: 34. 】
"The inspiration value has increased by 9 points!" He was still very satisfied with the increase in inspiration value, but the most important gain was in his mind.
The study of NS equations is a systematic and large-scale project, and every progress can be said to be very important.
Now he has some more ideas related to solving NS equation problems.
One of the ideas along the research direction of approximate value solution made him feel a little confused and puzzled.
He felt that he had almost achieved the ultimate in the approximate solution of the NS equation. He developed a universal substitution equation method for projects. The approximate value he obtained proved to be very close to the exact bound, and the degree of approximation exceeded previous methods.
Now he suddenly felt that what he had done was far from enough, and it seemed that he should go further and make the approximate value infinitely close to the exact solution.
“If we can get infinitely close to the exact solution, why not find the exact solution directly?”
"And some NS equations may not have exact solutions. This is a difficult problem in mathematics in the world. How can it be infinitely close to the exact solution?"
Wang Hao was sure that his idea was correct, but there was a contradiction between his idea and logical judgment.
This is what he gained.
"This problem must be solved. It will definitely be of great help to the study of NS equations..."
(Ask for monthly ticket)
