The research on NS equation has reached the final sprint stage.
This research lasted for nearly a year, and every progress made during the process was a result, some in theory and some in application.
When he reached the final stage, his mentality was actually very calm, because it felt natural.
The attack stage this time is also different from before.
At the end of some previous research, you will encounter some problems that you can't figure out, and it is not easy to sell it when you are close to the goal.
Now I feel that everything has been figured out, but there are some details of the argument in the middle that still need to be carefully considered.
"Probably because the accumulation has been enough and the preliminary proofs have been completed. What is left is just sorting out the complex calculation logic."
Wang Hao thought.
The preliminary proof of the research is "the smoothness of the solution set of NS equations under the conventional value range." When the inspiration value was sixty points, he had already completed the correlation theory i
, and published related papers in "New Advances in Mathematics".
Now it is time to connect the previous arguments and expand the value range to infinite, which requires a detailed combing of the value range and calculation logic.
There is not much work left.
Wang Hao did not just do research. He just spent 3 to 5 hours every day thinking and recording, hoping to slowly improve relevant arguments.
"According to this progress, it will probably take half a full moon."
Wang Hao thought, "There is no need to revise the completed argument again. When the argument is completed, it will be summarized again."
"By then, there should be no problem."
Research related to the NS equation has lasted for one year, and we are looking forward to completing it soon.
at the same time.
Japan: Kosaka City held an academic conference on the theory and application of nonlinear partial differential equations advocated by the International Mathematical Society.
Often, in similar conferences, only a small number of mathematicians from their own countries participate, while the number of scholars from other countries participating is relatively large.
That meeting was nothing of the same kind.
The organizer invited few well-known experts in the field of partial differential equations, including Princeton Elementary School, Stanford Elementary School, Oxford Elementary School, etc., but no relevant scholars participated.
Among the very unknown ones are the Italian mathematician Alessio Figali, the Austrian mathematician Martin Haier and the Japanese mathematician Mikio Tian.
The next two are Fields winners, and the first one is Wolfe winner.
Domestic scholars in related fields also participated, such as Zhou Qingyuan from the Institute of Mathematics of the Academy of Sciences, Shao Enqi from Capital: Primary School, and so on.
The study of nonlinear partial differential equations is a very important area in the field of mathematics: as a small direction, there are only a dozen related topics planned at the conference.
Research related to NS equations is also one of the topics.
Research in that direction is taken very seriously, and the number of interested scholars is also the smallest. One of the important reasons is that the roughness of the NS equation in conventional values has been revealed.
Top mathematicians pay more attention to theoretical research, and Wang Hao's proof of the roughness of NS equations was discussed during the meeting.
The relevant discussion is not my proof process, but an expansion of my proof to find ideas and ideas for solving NS equation problems.
Many people expressed their opinions.
A few scholars believe that Wang Hao's proof idea cannot cover all values, and it is not possible to complete all the proofs according to my ideas and methods.
Professor Masao Nakamura of Waseda Elementary School in Japan explained the reason in his report, "Including Chen Jingrun who conjectured Goldbach's conjecture, and Kazuki Brook who conjectured Taniyama Kazushimura.
Sen, etc., for a series of major and minor mathematical problems in the past, scholars who have completed enhanced proofs have been able to perfect the proofs. 「
"Wang Hao used a value analysis method to prove the roughness of the solution set of NS equations on conventional values."
"That method cannot be said to be tricky, and because of this, there is a way to continue to expand the simple argument to a finite one."
Masao Nakamura’s views are recognized by few scholars.
Yes, some people are unconvinced, such as the young Fields winner Alessio Figali. I think mathematics can be used to make relevant inferences based on past experience.
My research also involves the field of partial differential equations, but I think my level is higher than that of Wang Hao. I can't tell just by looking at the results.
When the level is not as good as that of others, it cannot be said to be a stupid approach to evaluate other people's proof based on past experience.
Mathematics is history.
Every research is independent, so there is no point in summarizing experience from the so-called "history"?
Zhou Qingyuan from the Institute of Mathematics of the Academy of Sciences also expressed his opinion. I think "no one can complete the proof of the ns equation within a few years. That person must be Wang Hao." "Wang Hao
My understanding of NS equations is not yet the best in the world. 「
Zhou Qingyuan admired Wang Hao very much.
Other scholars in our country just listened. We also have ways to refute Zhou Qingyuan. Bi Jinglingtian completed the proof of the set cause of the solution of NS equations in the conventional value range.
bright.
In this area of research, there is no say in whether there are internationally shocking results.
Wang Hao's discussion was just an interlude.
Many scholars have expressed their opinions and ideas on how to continue to demonstrate equations through the study of causal factors in the continuation of the topic.
Related issues lasted for two hours.
The meeting was postponed for eight days. Before the meeting was all concluded, the sponsor, the Japanese Shimada Kepu Company, announced an important news.
The roughness of the solution set of NS equations is very important to promote the development of mathematical theory. The company decided to spend 700 million yen to find mathematicians who can solve NS problems.
Xihai: primary school.
Wang Hao still lives an abnormal life, but he only takes a certain amount of time to do research every day. The withdrawal from the exhibition is still very smooth, and Yin Dao has completed 40%.
When I went to the restaurant to dine, I happened to bump into Zhu Jianrong and walked over with a dinner plate.
Zhu Jianrong shared the news with me, "Does he know? No company in Japan has announced that it will spend 700 million yen to punish mathematicians who solve NS equation problems."
I smiled and said, "That punishment, it feels like he has no chance."
Wang Hao was stunned when he heard this, "Did the Clay Institute give the prize for the Millennium Mathematics Conjecture?"
"That's the latest."
Zhu Jianrong shook his head and said with a smile, "The sponsor decided on the Japanese Partial Differential Equations Conference that just passed. It was probably a propaganda method, like that kind of important and small issues, because they were too many.
It will be difficult for no one to complete it in a few years or decades. 「
I said and suddenly asked, "Do you think his paper airplanes are very good at folding them? This should be a research project, it's really amazing. Hasn't he been continuing related research recently?"
"It just keeps going."
Wang Hao answered and then asked, "With the punishment just announced, you must have completed the research very slowly. Will we award a bonus?"
"Of course."
Ling Tianrong said, "We just need to say it publicly. If no one completes the proof, we will give a bonus. Seventy million yen sounds like a small amount, but in fact it is only 20 to 80 million yen."
, a small company is likely to damage its reputation for that money. 「
"Right."
Wang Hao suddenly lost his expectations.
"By the way, how is his research?" Zhu Jianrong asked.
"Isn't it very slow?"
Zhu Jianrong was stunned when he heard this, "Is it too slow?"
"kindness."
Seeing Ling Tian nodding his head in denial, I suddenly lost my excitement, "Come on! I can definitely complete that research, that's great."
"Thanks."
Ling Tian was also looking forward to it very much. When he heard that he would receive less than two million U.S. dollars in bonus, the feeling of expectation in his heart became even stronger.
I hurried back to the office before finishing my meal.
Zhu Jianrong sat dumbfounded under his seat. I have a lot of trust in Wang Hao. Since Wang Hao said he would complete the research very slowly, it would be very slow if it were not so.
How slow is it specifically?
"How many months should it take to complete it? Half a year? Seven months?"
I thought about it.
Wang Hao retreated into a "retreat" state.
I rushed out of the office of Mason Mathematics Laboratory and hung a "Please excuse me" sign under the door.
The others were not in a daze, and started discussing, "How long do they think Teacher Wang will stay outside that time?"
"Next time it will be a little less than a week, yes, less than half a month!"
"It seems that next time it will be Goldbach's conjecture. What was it studied that time?"
"I also asked you to bring me food tonight. If it's a minor research, do you think it's the NS equation?"
"Because it has nothing to do with NS equations, but I just know what the research is. I made a paper airplane for my next research. Was it a smaller one that time?"
",……no way?"
We all guessed wrong.
Wang Hao was indeed in "retreat", but I was in "retreat" for only one day. I mistakenly said that I left the office in the morning and came out early in the morning on the seventh day.
One o'clock.
The first person to arrive at the laboratory was Qiu Hui'an. As soon as I got out of the elevator, I saw Wang Hao. I was surprised and asked, "Teacher Wang, why are you out here?"
"You can still come out?" Wang Hao stretched and asked.
"Yes, that's what you mean." Qiu Hui'an waved his hand quickly, "Are you doing research?"
"Yes, the Word is finished."
Ling Tian nodded and said, "By the way, wait a minute, he will go to the academic building and help you find Director Yuan Peizhi Zhu, and let me come to the laboratory."
I simply shook my head and said, "Forget it, you'd better go there by yourself."
After that, he walked out.
The campus was not very busy in the early morning. I first went to the playground to run twice, and then went to the restaurant to have breakfast slowly or quickly.
At that time, it was not even four o'clock, so I went to the academic building.
When I called the Academic Affairs Building, I happened to see Yuan Peizhi walking over. Wang Hao stopped me and said, "Director Zhu, wait a minute."
"Professor Wang?" Yuan Peizhi waited for Wang Hao and asked, "He is looking for you?"
"Go back and say."
Wang Hao and Ling Tianrong went to the science and technology office of the school together. After leaving the office, he directly explained the reason for their visit, "You don't have any research results. Please tell the school and take a look."
Can the school cooperate with the announcement? 「
Yuan Peizhi was stunned for a moment, and then he was no longer moved.
After that, Wang Hao completed very few results, but many of them were not published in journals before the school learned about the news.
Is Jingran delaying his report now?
So touching!
I quickly asked, "What results? If there is a problem, as long as it is his research, the school will cooperate 100%."
Wang Hao nodded, "NS equation."
"What?" Yuan Peizhi thought he heard wrongly.
"NS equation." Ling Tian said it again and explained, "That time was a complete proof. It was a demonstration of the roughness of the NS solution set for all values, and it was part of the proof.
It is a continuation of the conventional value argument, so it will be merged with the next paper... "
Yuan Peizhi didn’t even listen to the words before. He kept thinking “Prove the NS equation” in his mind. I took a deep breath and said, “Professor Wang, is he sure? That news is too important.
Got it! 「
"Yes!" Ling Tian nodded seriously.
Yuan Peizhi took a deep breath again and asked, "Professor Wang, how does he need the school's cooperation?"
"Issuing an announcement directly." Wang Hao expressed his thoughts, "Because the paper is published in public information, but you want to delay the disclosure of information because of the previous evidence.
It's very simple. It is difficult to review manuscripts submitted to official journals. You just want to confirm it first, and then post the paper online before making a report. 「
"has a problem."
Yuan Peizhi nodded vigorously, "As long as he says, I will definitely cooperate."
Although the paper has not been published, it is in line with the school's announcement process, but considering that the content is the NS equation, which is one of the most important small mathematics problems in the world, the process is flow.
That's what's important.
What's more, the research was done by Wang Hao, and its credibility is still very low. Just to support Ling Tian, the school must also cooperate in issuing an announcement.
Before Wang Hao and Yuan Peizhi settled down, they returned to the laboratory office and posted the content of the previous demonstration online.
I posted them on two websites respectively.
In China, I post it on my personal blog, and in China, I post it on the pre-included Arxiv website.
The Arxiv website is a pre-included website, and there are not many free papers on it. In order to prevent your research from being plagiarized after it is published, you cannot publish your papers on Arxiv.
The time table proves the ownership of the paper.
Due to the nature of the Arxiv website, there will not be all kinds of papers on it, and a small number of them cannot be classified as "junk". Some scholars have not completed the research and have completed it.
I felt that it was a pity to publish the part, so I simply posted it on Arxiv.
Of course, there won’t be many that are outstanding, so careless research is needed.
Many scholars have the wrong impression of Arxiv. The website does not allow free access to papers, and very few novel research and ideas can be seen.
Before posting the paper to his blog and Arxiv, Wang Hao also breathed a sigh of relief.
The research is now complete, and all that's left is to make a report.
I haven't decided where to give the report yet. Wang Hao also chooses a place in general, as he will receive various invitations.
at the same time.
The official website of Xihai Primary School has also updated a message, which is still in red and bold, and even has a picture under the news on the home page.
There are two small words under the picture that highlight Wang Hao and NS equation.
The explanation of the above line of text is, "Congratulations to Professor Wang Hao from your school for completing the international major: small\mathematical problem-the demonstration of the roughness of the solution set of NS equations!"
