Chapter 150 Research on NS Equations and the Chern Mathematics Prize
Faculty cafeteria, small round table.
Zhu Ping said in surprise, "That blond-haired foreign girl just now was your graduate student? She is so exquisite. How old is she?"
"16 years old."
Wang Hao added, "This is what the information says."
Zhu Ping immediately covered her mouth in surprise and exaggerated, "Only 16 years old, a graduate student?"
Wang Hao simply gave a brief introduction, "Graduated from Stanford University, double major in mathematics and biological sciences. But that's normal. If you know, her whole family are professors, and one of them won the Turing Award and served as the vice president of Google." Grandpa, I think it’s nothing special.”
His tone was very calm, but what he said was really shocking.
Zhu Ping covered her mouth for a long time, not knowing what to say or how to jump in her mind. She suddenly asked, "By the way, what did she just say? I didn't understand."
Luo Dayong showed an expression of "Sure enough," and it could be seen that he still breathed a sigh of relief.
Zhu Ping really didn't understand.
She just heard the first sentence of "you-like-her". Putting it in the scene on the road just now, she suddenly felt a little weird and a little embarrassed.
I didn't understand the last sentence at all.
Wang Hao was a little surprised. He really didn't expect that his English level was not bad and he could generally understand it. Luo Dayong was a little worse, but his English pronunciation was also understandable.
Zhu Ping...
Considering that he has no experience studying abroad, and has only passed CET-6 in English, he can barely write a paper, and it is normal for him to have difficulty understanding spoken English.
At this time, Luo Dayong also commented, "That girl... has a lot of character, but she doesn't seem to know how to speak. She has some issues with her emotional intelligence, and her judgment is wrong."
Zhu Ping looked at Luo Dayong in surprise and said in disbelief, "You actually think that others can't speak?"
"..."
"What judgment? What did she say?"
"..."
Wang Hao sat on the side of the small cone, listening to the expressions and conversations of the two people, and felt that sitting here seemed a bit redundant.
He was wrong.
His mistake was that he shouldn't have come to dinner with the two of them. He should have found an excuse and walked away quickly.
So he immediately speeded up his eating and filled his stomach with food in only three minutes.
Take a drink of water, get it done, call it a day!
He immediately stood up, took two steps away and waved his hand behind him, "You guys eat first, I'm still busy, so I'm leaving now, bye!"
…
The new semester is about to begin.
After Helen came to Xihai University, she took the initiative to contact Wang Hao and even went to the office to find Wang Hao.
Wang Hao still attaches great importance to Helen. Helen's emotional intelligence seems to be relatively low, and her thinking is different from that of normal people, but it must be said that Helen is indeed a genius.
Wang Hao issued a test paper and asked Helen to answer the questions to check her progress in mathematics learning, and then found that Helen's foundation was very solid.
The questions in many subjects are simply not difficult.
However, there are still some subjects that are not covered. For example, "Discrete Mathematics" involves difficult content, and Helen can't answer it at all.
Regarding the content of "Differential Equations", I only understand the basics and have no exposure to advanced knowledge.
She has also never been exposed to cross-disciplinary operations, such as using functional analysis methods to solve partial differential equations.
When he discovered that Helen had not completed many questions, Wang Hao breathed a sigh of relief.
This shows that Helen falls within the range of "normal genius". She only completed her undergraduate degree at Stanford University, rather than mastering more difficult mathematics knowledge in advance.
"fine!"
“This way you won’t learn nothing!”
If a lot of knowledge is mastered in advance, postgraduate subjects will lose their meaning to her.
Now she still has a lot to learn.
Wang Hao can also guide her in the same way as other students, without having to spend time alone to guide her.
Of course, another thing is more important, "You must learn Chinese well. You are not required to be as fluent as others, but you must be able to understand the lessons."
"In the university, except for English classes, there will be no other teachers teaching in English."
Helen blinked her big eyes and said seriously, "I'm studying."
Wang Hao stared at Helen's face and found that Zhu Ping's description was indeed correct. She was indeed very delicate.
And think about Jeffrey Hinton's face...
"What I judged before was indeed correct. Helen's appearance is due to her breast-brain inheritance. It seems to be from the Hinton family..."
"I'm so lucky to have inherited all my good genes!"
Wang Hao looked in the mirror, smoothed his hair in the front with his hands, looked at it carefully and said, "Old Wang's genes are good, he is handsome, and his mind is very good. There is no need to improve..."
"Mainly, you want to steal my genes?"
"Don't even think about it!"
…
School season.
The students all returned to school to prepare for the new semester. Many people began to look at the class schedule and paid attention to Wang Hao's courses. It turned out that Wang Hao had left the undergraduate courses and the two main courses he offered were graduate courses.
"Lie Group Lie Algebra".
"Modern Partial Differential Equations".
These two courses appear to be very difficult at first glance and are not accessible to undergraduates at all.
Fortunately, Wang Hao also opened an elective course called "Basics of Theoretical Physics", which is a mathematical physics course. The mathematics department and the physics department give priority to the course.
Many students are paying close attention to this course.
Ding Zhiqiang had no interest in studying the courses at all. He spent the whole summer reading the two mathematics textbooks given by Wang Hao, reading all the knowledge points, and doing after-class exercises accordingly.
One summer, two very difficult mathematics subjects...
Ding Zhiqiang felt that his mind was filled with all kinds of mathematical symbols. What he wanted most was to relax and play two games. But when he turned on his phone, he found that the game had been uninstalled at some point.
When he was preparing to download, he suddenly felt very boring again and found that his preferences seemed to have completely changed.
That kind of simple happiness has left you?
Ding Zhiqiang was very frightened by this discovery. At this moment, a voice came from outside, "Ding Zhiqiang, Teacher Wang is calling you to go to the Teaching and Research Office of the School of Science."
"Ah? Which Teacher Wang?"
"Teacher Wang Hao!"
Ding Zhiqiang turned on his phone and found that Wang Hao had sent a message half an hour ago.
Since he never responded, I asked someone to come over and shout.
"I'll go right away..." Ding Zhiqiang responded.
As soon as he thought about it, he knew what Wang Hao wanted to do with him. It must be to check his study progress during the summer vacation.
While on the road, Ding Zhiqiang recalled the "cruel" holiday. The more he thought about it, the more unwilling he became. He didn't want to go on like this forever and hoped to find the happiness he once had.
He thought of a way, "Many people have high expectations for me now. If my results disappoint..."
"When Teacher Wang Hao inspected me, I deliberately did something wrong. In this way, he might be disappointed? Then give up on me?"
Ding Zhiqiang thought carefully, and his eyes suddenly lit up.
Teaching and Research Section.
Wang Hao was waiting with several teachers.
They had just attended the internal meeting for the opening of the Faculty of Science, which was about course allocation and teaching matters.
After the meeting ended, Wang Hao thought of Ding Zhiqiang and decided to wait in the teaching and research office to conduct a small inspection of Ding Zhiqiang.
Several other people were very interested after hearing it, and helped come up with several questions corresponding to the content, including professors such as Zhou Qingyuan and Huang Pei from the School of Science.
They wanted to see what Wang Hao's 'excellent students' looked like.
Ding Zhiqiang is here.
He didn't expect to see so many people, including several professors, and he suddenly felt very nervous.
"Teacher Wang..." Ding Zhiqiang shouted.
Wang Hao asked Ding Zhiqiang to sit down and took out the questions that the teachers had just asked, "Just try these questions and see how many points you can get."
Ding Zhiqiang was mentally prepared, so he picked up the pen and started working.
Wang Hao and other teachers consciously did not disturb him, so they simply stood at the door and started talking, "At the end of last semester, I gave him two textbooks, one was "Functional Analysis" and the other was "Modern Partial Differential Equations"."
""Functional Analysis" is better and not that difficult to understand. "Modern Partial Differential Equations" is more difficult. If you can get half the score in self-study, it will be fine."
This is Wang Hao's judgment.
The other teachers nodded after hearing this. In courses like "Modern Partial Differential Equations", some of the questions are a bit convoluted, and even they feel a headache. It is really impressive to be able to understand the content of the textbook through self-study.
Ding Zhiqiang doesn't know what the teachers outside are talking about. In his understanding, one must do all the math questions correctly to be excellent.
He studied hard for two months and passed most of the knowledge points. The questions on the test paper were very familiar. If he thought about it carefully, he could solve many of the questions and he would probably get a score of more than seventy points.
However, Ding Zhiqiang didn't want to answer the question properly.
Therefore, I only did a little bit of several difficult questions, and deliberately did not continue to answer them later. I completed the first two questions completely.
He estimated that he would definitely fail the exam.
Then he handed in the paper.
"Teacher Wang, I'm done." Ding Zhiqiang handed the test paper to Wang Hao and lowered his head with a "lost" look.
Wang Hao picked up the test paper, looked at it carefully, and scored each question. He calculated that the total was 51 points.
"51 points!" Wang Hao was very satisfied because he had reached his expectations.
Other teachers also thought it was very good.
But of course Wang Hao would not say that. Sometimes students need encouragement, but sometimes they also need to use denial to achieve their goals, so that students can have more opportunities to grow.
Wang Hao looked at Ding Zhiqiang and said seriously, "51 points, failed!"
Ding Zhiqiang continued to lower his head and murmured, "Teacher Wang, I try my best, but I feel that I am not suitable for learning mathematics. For me, mathematics is too difficult."
"Right."
Ding Zhiqiang was immediately happy after hearing this.
Wang Haodao, "You are just self-study, and it is not easy to get half the score in the exam. Let's do this. This semester, you will take the "Functional Analysis" course for the mathematics major, and the "Modern Partial Differential Equations" course for the graduate students.
That's my class."
After he finished speaking, he added, "I saw your senior physics course schedule, and it doesn't conflict."
"..."
Ding Zhiqiang finally raised his head and looked at Wang Hao with wide eyes. He did not expect this result at all.
What?
Because I don't do well in answering questions, I have to follow the class?
A young teacher next to him shouted, "Functional Analysis in the Department of Physics is my class. Professor Wang, don't worry, I will take care of him."
"Okay, thank you."
Wang Hao heard the voice and looked over. He felt that the other person seemed familiar, but he couldn't name him for a while.
The two agreed.
Ding Zhiqiang had no right to speak at all. He walked out of the teaching and research room with dull eyes. He thought about it carefully and gave himself a hard slap in the face.
"Snapped!"
"Why didn't you answer the questions well? If I could get seventy points, I wouldn't have to follow the class!"
He scratched his head with regret.
…
The next morning, Wang Hao went to the office in the complex building.
When we got to the corridor, we happened to meet Zhang Zhiqiang who was about to go in.
Zhang Zhiqiang grabbed Wang Hao, pointed to the door and said, "There is a new person here. It is said that he is a stay-at-home student from the School of Science, a student taught by Professor Huang Pei."
Wang Hao looked over and found that it was the teacher who taught "Functional Analysis" yesterday.
Zhang Zhiqiang complained, "You look dumbfounded and don't say anything. You're already here, why should you be more enthusiastic?"
"What's his name?" Wang Hao asked again, thinking, "It seems his surname is Sun..."
"You know? Sun Jian!"
"oh!"
As soon as Zhang Zhiqiang said his name, Wang Hao suddenly remembered it.
They entered the door together.
Sun Jian was tidying up his desk. He looked up and saw Wang Hao walking in. He immediately said hello and said, "Teacher Wang, you are here. I will be in the same office with you from now on. Please give me your advice."
"welcome!"
Wang Hao also said hello, and then looked at Zhang Zhiqiang, his eyes saying, 'Isn't this very enthusiastic?'
Zhang Zhiqiang grinned.
Sun Jian was indeed very enthusiastic. After cleaning up his desk, he came over and said a few words to Wang Hao. When he saw that the coffee cup on Wang Hao's desk was empty, he immediately went to his bag to find a bag of instant coffee.
He helped Wang Hao make coffee, and when he brought it over, he said, "Professor Wang, my classmate bought this coffee for me. It's from South America. A small pack costs more than 20 yuan. You can't buy it in China. You can try it."
Wang Hao felt a little uncomfortable, but he still took a sip and nodded with satisfaction, "The taste is very rich."
"As long as you like it!"
Sun Jian also took the opportunity to talk, "I just stayed in school this semester. If I have any questions, please give me your advice."
"I recently studied your study of Monge's Ampere equation. The analytical method is really superb. After reading it, I feel that there are many things that I can understand..."
Sun Jian kept talking with an admiring tone.
beside.
Zhang Zhiqiang looked at the coffee on Wang Hao's table and thought about words such as 'More than twenty yuan, which can't be bought in China'. Then he saw the enthusiastic Sun Jian, compared with his attitude towards him just now, he muttered in a depressed tone, "I
He’s also a professor... My coffee cup is also empty, and I also want to drink it without making coffee..."
Luo Dayong turned his head, operated on the phone, and then handed the screen to Zhang Zhiqiang.
Zhang Zhiqiang was suddenly surprised, "You found it? What kind of coffee is that?"
Luo Dayong said, "Didn't you just say that you want to drink coffee without brewing it? Look, a whole box of coffee, twenty-four bottles per box, one hundred and twenty, costs an average of five yuan per bottle, which is not expensive.
The courier can also deliver it upstairs."
After he finished speaking, he added, "After you buy it, just put it here with me and we can drink it together."
Zhang Zhiqiang's expression was fixed on his face, and he felt Zhu Ping's feeling again.
This guy really deserves a beating!
…
Life in the office has not changed because of the arrival of new people. Everyone still spends most of their time studying and researching.
The same goes for Wang Hao.
He formally invested in the study of NS equations, not to directly solve the problem of NS equations, but to research in this direction.
The NS equation is a general direction and is directly related to fluid mechanics.
Fluid mechanics can be simply understood as the study of fluids based on Newtonian mechanics, and the NS equation is the formulation of Newton's second law for fluids.
The application of fluid mechanics can be said to be in all aspects, including mechanical, civil, chemical and biomedical engineering, geophysics, oceanography, meteorology, astrophysics... etc. Fluid mechanics is used in many disciplines, and it is very important.
The NS equation is also widely used.
Wang Hao has not yet found his first research direction.
Of course he hopes to directly solve the biggest problem, but in fact, it is impossible to directly solve the biggest problem without laying a good foundation.
The research method Wang Hao chose was to read some mathematical content related to fluid mechanics, as well as some papers on NS equations.
There are also several papers on "Proving the regularity of NS equations".
Of course, those are not recognized. Some of them have been published in foreign magazines, and they are also small mathematics magazines. It can even be said that they can be published by paying money.
Some papers can also be retrieved in SCI.
Wang Hao looked at it carefully and could only say that the idea was of great reference value, but the proof was not perfect.
One of the most meaningful papers is about finding approximate solutions to ns equations.
This paper is very influential because it has a wide range of applications.
Finding approximate solutions to NS equations using numerical methods is a very important research direction because it is very practical and can be used in many aspects.
It is very simple to understand that when an exact solution to a very important equation cannot be obtained, it is naturally very important to be able to obtain an approximate solution.
For example, calculate the mechanical problems of a submarine in the water, and use this as a reference to design the shape of the submarine.
If it is not possible to obtain the most accurate and minimum force situation, it is also valuable to find an approximate situation.
Wang Hao briefly browsed the content and glanced at the author of the paper - Fu Chunjie of Soochow University.
He looked at it carefully.
…
Mathematics Center of Soochow University.
Fu Chunjie is the director of the Mathematics Center. He is fifty-two years old, barely old enough to be considered an "old professor," but he still considers himself to be a member of the young and middle-aged group.
Because he wanted to win the ‘Chan Shengshen Mathematics Prize’.
The "Chern Shengshen Mathematics Award" is very popular. It is recognized by the domestic mathematics community as a "reserve for academicians".
As long as you can be awarded the Chen Shengshen Mathematics Award, you will be able to be added to the list of academicians the next year.
Otherwise, there are no international mathematics awards, nor domestic heavyweight awards. If you want to be nominated as an academician, not many mathematics academicians are willing to recommend it.
At this time, Fu Chunjie was complaining to an old academician, "Academician Liu, tell me, this year, I was guaranteed to win the award, but then Wang Hao came out, how old is he?"
"I'm in my twenties, when can I win an award? Does it have to be this year?"
"I really don't know what those people in the Mathematical Society are thinking."
Liu Yuqun shook his head and said, "Isn't it confirmed yet? I don't know who it is, but it might be you."
"Besides, Wang Hao's achievements are so high. How can he compare if a proof of Kakutani's conjecture is released?"
Of course Fu Chunjie knows that he cannot compare with him in terms of big results, but he has studied mathematics for decades, published hundreds of papers, and has some top results.
For example, the study of approximate solutions to NS equations.
After this research came out, he was invited to give a report at the International Congress of Mathematicians.
Fu Chunjie was still dissatisfied and said, "Kakutani's conjecture is indeed famous, but it is not practical."
Liu Yuqun said, "Even if we don't talk about Kakutani's conjecture, we also have research on Mersenne prime numbers and Artin's conjecture. Some time ago, his mathematical analysis was even published in Nature magazine. In terms of big results, you definitely can't compare with them.
.”
"Of course, we will definitely recommend you, but if you really don't win the award, there is nothing we can do."
"One of your current advantages is your high qualifications, and the other is that your research on the NS equation is relatively strong and applicable."
"To put it bluntly, qualifications are of little use nowadays. I dare not mention them even if I take them out."
Liu Yuqun is old, but he still understands the current situation.
A few decades ago, qualifications would still be very useful. If you have been engaged in mathematics research for decades, it is definitely not comparable to that of a young person.
Now is not the time to fight for qualifications. If you say that a person wins an award because of his high qualifications, he will probably be scolded as "untalented" or "idiot". What's more, what he says is very reasonable, "You have such high qualifications, why are your results not as good as others?"
?”
By then, the reputation of the person who said it will be bad.
Therefore, at least on the surface, awards still depend on personal achievements. Fu Chunjie's only advantage is that the application value of his achievements is relatively high.
Many current studies on fluid mechanics will use the approximate solution method he developed.
However, considering the development and contribution of mathematics, the application value is actually a draw.
According to the ideas of top mathematicians, what is the application value?
Application, isn’t it engineering?
Research on mathematical theory is the most important, and application is simply the domain of "engineering talents" and has nothing to do with mathematical research.
Therefore, it is difficult for Fu Chunjie to win the award.
Chen Shengshen Mathematics Prize is awarded once every two years, and two people are selected at a time.
Now there are three people who have the best chance to win the award, one is Wang Hao, one is Fu Chunjie, and the other is Zhong Mingchu, director of the Department of Mathematics at Donggang University.
Fu Chunjie was able to compete with Wang Hao who "suddenly appeared", but when faced with Zhong Mingchu, he was crushed in all aspects.
Achievements, contributions, fame, status, qualifications, even connections, backstage... The only advantage he has is age. He is four years older than Zhong Mingchu, but age is obviously only a draw.
It was even said that even Zhong Mingchu did not expect Fu Chunjie to win the award.
The human heart is very complex.
If Fu Chunjie wins the award and there are rumors that Wang Hao does not win, then Zhong Mingchu, like Fu Chunjie, may become the target of public opinion attack.
Wang Hao didn’t comment?
For solving Kakutani's conjecture, no one who is about to win an international mathematics award will be awarded a domestic mathematics award?
So what are the levels of the two winners?
What are the results?
By then, Zhong Mingchu and Fu Chunjie will definitely be questioned together. Even if they have some good results, they will be compared with Wang Hao's results.
Naturally, the difference is obvious.
Under this situation, might Zhong Mingchu hope that Fu Chunjie can win the award?
Therefore, Fu Chunjie’s hope of being awarded the award is slim...