From University Lecturer to Chief Academician

The research on the NS equation has reached the final sprint stage.

This research lasted for nearly a year, and every progress in the middle is a result, some in theory and some in application.

When it came to the final stage, his mentality was very calm, because it felt logical.

The sprint stage this time is also different from the previous ones.

At the end of some of the previous research, you will encounter some unreasonable problems, and it is not easy to sell it at the close of the door.

Now I feel that everything has been figured out, but there are some details of the argument that need to be carefully considered.

"Probably because the accumulation is enough, the previous proofs have been completed, and the rest is just sorting out the complex calculation logic."

Wang Hao thought about it.

The preliminary proof of the research is "the smoothness of the solution set of NS equations under the normal range of values". Progress".

Now it is connecting the previous demonstrations, and expanding the range of values ​​to infinity requires a detailed sorting out of the range of values ​​and calculation logic.

There is not much work left.

Wang Hao didn't just do research, he just spent 3 to 5 hours a day thinking and recording, and wanted to slowly improve the relevant arguments.

"According to this progress, it will take about half a month."

Wang Hao thought, "The completed argument no longer needs to be revised repeatedly, and when the argument is completed, there is no need to make a summary."

"At that time, there should be no problem."

The research on the NS equation has lasted for a year, and I am looking forward to it being completed soon.

at the same time.

Osaka City, Japan held an academic conference on the theory and application of nonlinear partial differential equations advocated by the International Mathematical Society.

Often similar conferences are attended by a large number of mathematicians from their own country, while the number of scholars from other countries is relatively small.

This meeting was a little different.

The organizer invited many well-known experts in the field of partial differential equations, including Princeton University, Stanford University, Oxford University, etc., and relevant scholars participated.

Among them are very famous ones including Italian mathematician Alessio Figalli, Austrian mathematician Martin Heier and Japanese mathematician Toshi Mikio.

The first two are Fields winners, and the last one is Wolff winner.

Domestic scholars in related fields also participated, such as Yuan Peizhi from the Institute of Mathematics of the Academy of Sciences, Shao Enqi from Capital University, and so on.

The study of nonlinear partial differential equations is a very important direction in the field of mathematics, and there are more than a dozen related topics proposed by the conference.

Research related to the NS equation is also one of the topics.

The research in this direction is highly valued, and the number of interested scholars is also the largest. One of the important reasons is that the smoothness of NS equations under conventional values ​​has been proved.

Top mathematicians pay more attention to theoretical research, and Wang Hao's proof of the smoothness of the NS equation was discussed at the meeting.

The relevant discussion is not his proof process, but to expand with his proof to find ideas for solving NS equation problems.

Many people have expressed their opinions.

Most scholars believe that Wang Hao's proof thinking cannot cover all values, that is, according to his thinking method, it is impossible to complete all the proofs.

Professor Masao Nakamura of Waseda University in Japan explained the reason in the report, "Including Chen Jingrun of Goldbach's conjecture, including Brooke-Jelson of Gushan-Shimura's conjecture, etc., a series of major mathematical problems in the past have completed the weakening proof Scholars have not been able to perfect the proof."

"Wang Hao used a method of value analysis in the process of proving the smoothness of the NS equation solution set under conventional values."

"This method can be said to be tricky, and because of this, it is impossible to continue the argument that the complexity expands to infinity."

Masao Nakamura's point of view has been recognized by many scholars.

However, there are also some people who are noncommittal, such as the young Fields winner Alessio Figalli, who believes that mathematics cannot make relevant inferences based on past experience.

His research is also involved in the field of partial differential equations, but he thinks that his level is not as good as that of Wang Hao, and he can know it only by looking at the results.

When the level has not caught up with others, it is simply stupid to evaluate other people's proofs based on past experience.

Mathematics, not history.

Each study is independent, what is the point of summarizing experience from the so-called "historical"?

Yuan Peizhi from the Institute of Mathematics of the Academy of Sciences also expressed his opinion. He believes that 'someone who can complete the proof of the ns equation within a few years must be Wang Hao', "Wang Hao's understanding of the ns equation is already the best in the world. gone."

Yuan Peizhi admired Wang Hao very much.

Scholars from other countries are just listening, and they have no way to refute Yuan Peizhi. After all, Wang Hao has completed the proof of the smoothness of the NS equation solution set under the normal range of values.

In this area of ​​research, there is no right to speak without internationally shocking results.

Wang Hao's discussion was just an episode.

The follow-up of the topic is to study how to continue to demonstrate the equation, and many scholars have expressed their opinions and ideas.

Related topics lasted for more than two hours.

The meeting lasted for three days. After the meeting was over, the sponsor, Japan Shimada Jingpu Company, announced a big news--

The smoothness of NS equation solution set is very important to promote the development of mathematical theory. The company decided to spend 400 million yen to reward mathematicians who solve NS problems.

...

Xihai University.

Wang Hao is still living a normal life, but takes a certain amount of time every day to do research, and the progress is still very smooth, 90% of which has been completed.

When he was going to eat in the restaurant, he happened to bump into Zhou Qingyuan, and walked over with the plate.

Zhou Qingyuan shared a piece of news with him, "Did you know? There is a company in Japan that announced that it will give out 400 million yen to reward mathematicians who solve NS equation problems."

He smiled and said, "This reward, I think you have a good chance."

Wang Hao was taken aback when he heard that, "Isn't the Millennium Mathematical Conjecture a bonus from the Clay Institute?"

"This is the latest."

Zhou Qingyuan shook his head and said with a smile, "The sponsors decided on the Japan Partial Differential Equations Conference just now, probably as a means of publicity, and it is difficult for someone to complete such a major issue after a few years or decades. "

As he spoke, he suddenly asked, "I see that your paper airplane folds very well, right? That should be a research, it's really amazing, have you been continuing related research recently?"

"It's been going on."

Wang Hao replied, and asked, "This kind of reward just announced, if I finish the research soon, will they award the reward?"

"of course."

Zhou Qingyuan said, "As long as they say it publicly, someone who completes the certificate will definitely give a bonus. 400 million yen sounds like a lot, but in fact it is only 20 to 30 million yuan. It is impossible for a large company to damage its reputation for this money."

"Right."

Wang Hao suddenly looked forward to it.

"By the way, how is your research?" Zhou Qingyuan asked.

"Isn't it going to be soon?"

Zhou Qingyuan was taken aback when he heard that, "Soon?"

"kindness."

Seeing Wang Hao nodding his head, he was a little excited, "Come on! If you can complete this research, it will be amazing."

"Thanks."

Wang Hao was also looking forward to it. When he heard that he could get an extra bonus of more than two million US dollars, his sense of anticipation became even stronger.

After eating, he hurried back to the office.

Zhou Qingyuan sat in a daze. He had great trust in Wang Hao. Since Wang Hao said he would finish the research soon, it must be very soon.

How fast?

"It should be completed in a few months, right? Half a year? Four months?"

He thought about it.

...

Wang Hao entered the state of 'retreat'.

He plunged into the office of the Mason Number Lab and put a 'Do Not Disturb' sign on the door.

The others looked a little dazed and started discussing, "How long do you think Mr. Wang will stay inside this time?"

"It was more than a week last time, no, it's been half a month!"

"Last time it seemed to be Goldbach's conjecture. What is the study this time?"

"He also asked me to bring dinner tonight. It must be a major study. I guess it's the NS equation?"

"It must be related to the NS equation, but I don't know what kind of research it is. He made a paper airplane last time, and this time he made a bigger one?"

"……possible?"

They all guessed wrong.

Wang Hao is indeed 'retreating', but his 'retreat' is only for one day. To be precise, he entered the office in the afternoon and came out the next morning.

seven o 'clock.

Qiu Hui'an was the first to arrive at the laboratory. He saw Wang Hao just as he got out of the elevator, and asked in surprise, "Mr. Wang, why did you come out?"

"Can't I come out yet?" Wang Hao stretched his waist and asked back.

"No, that's not what I meant." Qiu Hui'an hurriedly waved his hands, "Aren't you doing research?"

"Yeah, it's done."

Wang Hao nodded and said, "By the way, wait a minute, you go to the Academic Affairs Building, help me find Director Zhu Jianrong, and ask him to come to the laboratory."

He simply shook his head, "Forget it, I'll go there by myself."

After speaking, he walked out.

The campus was already very lively in the early morning. He first went to the playground for a couple of laps, and then went to the restaurant for breakfast in a leisurely manner.

At this time, it was almost eight o'clock, so I simply went to the teaching affairs building.

When it was time to call the Academic Affairs Building, he happened to see Zhu Jianrong walking over, and Wang Hao stopped him immediately, "Director Zhu, wait."

"Professor Wang?" Zhu Jianrong waited for Wang Hao and asked, "Are you looking for me?"

"Go in and talk."

Wang Hao and Zhu Jianrong went to the Science and Technology Department of the school, and when they entered the office, they directly explained their intentions, "I have a research result, let me talk to the school, and see if the school can cooperate to announce it?"

Zhu Jianrong was stunned for a moment, and then he was a little moved.

Before Wang Hao completed a lot of results, but many of them were published in journals, and the school only got to know the news.

Reported in advance now?

So touching!

He hurriedly asked, "What results? No problem, as long as it is your research, the school will cooperate 100%."

Wang Hao nodded, "NS Equation."

"What?" Zhu Jianrong thought he had heard wrong.

"NS equation." Wang Hao said it again and explained, "This time it is a perfect proof. It is a demonstration of the smoothness of the NS solution set for all values, but the part of the proof is carried out in continuation of the conventional value argument. So it can be merged with the previous paper..."

Later, Zhu Jianrong didn't listen at all, his mind was always 'proving the NS equation', he took a deep breath and said, "Professor Wang, are you sure? This news is too important!"

"Yes!" Wang Hao nodded seriously.

Zhu Jianrong took another deep breath and asked, "Professor Wang, how do you need the school to cooperate?"

"Publish the announcement directly." Wang Hao said his thoughts, "Generally, the papers are published in the public information, but I want to make the information public in advance, because the follow-up proof is very complicated, and it is difficult to review the manuscript when it is submitted to an official journal. I thought about finalizing it first, then posting the thesis online and then making a report.”

"no problem."

Zhu Jianrong nodded vigorously, "As long as you say, I will cooperate."

Although the thesis has not been published, it does not conform to the school's announcement process, but considering that the content is ns equation, which is one of the most important mathematical problems in the world, it doesn't matter if the process is not the process.

What's more, the research completed by Wang Hao is still very reliable. Just to support Wang Hao, the school must cooperate with the announcement.

...

After Wang Hao and Zhu Jianrong had a good talk, they returned to the office of the laboratory and posted the content of the follow-up demonstration on the Internet.

He posted them on two websites.

In China, it is posted on personal blogs, and in foreign countries, it is posted on the pre-recorded Arxiv website.

The Arxiv website is a pre-collected website, and there are many free papers on it. In order to prevent your own research from being plagiarized before publication, you can publish your papers on Arxiv, and the time of publication will prove the ownership of the paper.

Because of the nature of the Arxiv website, there will be various papers on it, most of which can be classified as "garbage". Some scholars have not completed their research, and feel that it is a pity not to publish the completed part, so they simply posted it on Arxiv .

Of course, there will be very few very outstanding ones, which need to be carefully studied and checked.

The impression of many scholars on Arxiv is that on this website, you can read papers for free, and you can also see a lot of novel research and ideas.

After posting the paper on the blog and Arxiv, Wang Hao also breathed a sigh of relief.

The research is considered complete, and the rest is just to make a report.

I haven't decided where to give the report, and Wang Hao doesn't need to choose a place. He will definitely receive various invitations in the future.

at the same time.

The official website of Xihai University also updated a message, which was still in bold red font, and even hung a picture on the home page news.

There are two key words on the picture - Wang Hao and NS equation.

The explanation of the following line of text is, "Congratulations to Professor Wang Hao of our school for completing the international major mathematical problem-the demonstration of the smoothness of the solution set of NS equations!"