Chapter 158 New research direction: Goldbach’s conjecture!
Yang Yuan said that he had made two sets of data plans, and the wind pressure test evaluation values were both lower than 20, which really surprised Li Jianhua and his team.
Li Jianhua has been engaged in fighter aircraft design for a long time and is one of the most famous fighter aircraft design experts in China.
The team he leads has a dedicated power group, and the people in the power group are also top aerodynamics experts who have long been engaged in aerodynamic research on aircraft flight.
The study of low-altitude flight dynamics of fighter aircraft is the top priority of fighter flight dynamics research.
They are just a power group, and their research content is relatively complex. Their purpose is to provide support for aircraft design, rather than to study theoretical content.
But they are also very professional and know very well what the wind pressure test evaluation value below 20 means.
That is the most advanced level in the world. Even the most advanced fighter jets in the world cannot be lower than 20 even when conducting low-altitude flight wind pressure test evaluations.
The development speed of domestic military science and technology is very fast, and some aspects have caught up with the international level. But to say that it has surpassed the international level in research is indeed an exaggeration.
The research goals of Yang Yuan's team are also very high. To put it bluntly, the wind pressure assessment value is less than 20. However, when doing project research, the goals are just goals, and the goals are generally not reached.
If the wind pressure evaluation value is lower than 20, it is only the most ideal result.
Now that they heard Yang Yuan's affirmative words, the two aerodynamic experts present directly questioned and refuted it because they were so surprised.
Yang Yuan didn't care about being questioned. Of course he knew why the other party was losing his temper. He just said proudly, "We have experts to help us!"
"Do you know Professor Wang Hao from Xihai University? He is a super genius." He said with a thumbs up, "In the field of partial differential equations and in the research of NS equations, who can surpass him?"
“It’s hard to find it internationally, let alone domestically!”
This sentence sounded like big talk, but with the addition of the name "Wang Hao of Xihai University", Li Jianhua and his party stopped refuting it.
Wang Hao is really famous.
In the past year, he has been the mathematician who has appeared the most in public opinion, and his frequency of appearance is even higher than that of some 'hot mathematicians' and 'Internet celebrity scholars'.
Some mathematicians will become public opinion due to certain incidents and will be discussed for a long time.
Wang Hao, on the other hand, has been in the public opinion for certain incidents one after another, and most of his reports are due to his amazing results.
For example, Mersenne primes.
He found several Mersenne primes in a row, which directly shocked the international mathematics community. With his personal research results, he almost "defeated" GIMPS, which was searching for Mersenne primes. Therefore, GIMPS cooperated with Wang Hao and was able to continue to operate openly and support users. The search for Mersenne primes.
Another example is the proof of Kakutani’s conjecture.
Domestically, the Kakutani conjecture is a very famous mathematical conjecture, and its popularity can be said to be second only to Goldbach's conjecture.
Wang Hao completed the proof of Kakutani's conjecture and was suddenly considered one of the world's top mathematicians.
etc.
Some time ago, Wang Hao's results also appeared in the media and public opinion, and they were related to the research on "Approximate Solutions to NS Equations".
People in the academic circle find it very strange, because ordinary people cannot understand this result, and even if they can understand it, they probably won't be interested.
As a result, some time before the results were released, many people were discussing the importance of finding approximate solutions to NS equations, and then there was news that Wang Hao's paper was published in "New Advances in Mathematics", one of the four top magazines.
It feels like the front is trying to build momentum for Wang Hao.
However, well-informed people can still know that someone is deliberately leading public opinion, probably Fu Chunjie of Soochow University, but no one has evidence. As a result, Fu Chunjie seems to be stealing the chicken but not losing the rice. He is completely giving the king
Hao builds momentum.
Hearing Wang Hao's name from Yang Yuan's mouth, Li Jianhua and his group had a sudden feeling of "that's it."
However, they were still very surprised because they knew how difficult it was.
The most important thing to study on low-altitude flight dynamic wind pressure is to solve the numerical balance problem, which will definitely involve a very complex system of partial differential equations.
This system of equations is more difficult than a single NS equation, and the approximate solution can almost only be obtained by substituting numerical values.
There is no fixed solution to the system of equations, it can be said that there are countless solution systems.
Finding a suitable solution is unimaginably difficult. They usually can only demonstrate the data and then conduct experimental verification.
This will consume a lot of time and money, and it may not be possible to find a good data solution.
The people in the conference room thought carefully for a long time, and Li Jianhua suddenly asked, "Professor Wang Hao, haven't you already completed the analysis of the ns equation?"
"This is impossible!" came the immediate denial.
Yang Yuan also shook his head, "I have carefully paid attention to the data. He should have his own method to obtain approximate solution, and can make the solution more approximate to the exact solution, or find a balance."
"I don't quite understand it. You can only know this kind of thing by asking him himself."
"Anyway, Professor Wang Hao has provided us with two sets of solutions, which are worth thousands of dollars!" Yang Yuan shook his head with emotion.
Li Jianhua also nodded and said, "This kind of research is indeed worth a lot of money. Professor Wang Hao must have spent a lot of energy on it."
When Yang Yuan heard this, he remained silent for a while. The main reason was that Wang Hao's research speed was too fast. Even if the previous half month was included, it would definitely not exceed twenty days.
Twenty days, can you spend a lot of energy?
At this time, Cui Xunnian suddenly came over, leaned into Yang Yuan's ear and was about to whisper a report when he heard Yang Yuan say openly, "Xunnian, if you have anything to say, just say it directly, we are all our own people."
Li Jianhua and others also looked over.
Cui Xunnian simply said, "That's it. I just received another four sets of approximate solutions from Professor Wang Hao. He also said that if you need more solutions, you can send a message and he will help study it when he has time.
.”
"..."
"..."
The conference room suddenly became quiet.
After a long time, Li Jianhua broke the silence and corrected his previous statement, "Professor Wang Hao is really a genius."
…
Wang Hao had no idea that the several approximate solutions he had studied would bring such a great impetus to the research of Yang Yuan's team.
In fact, he only knew what Cui Xunnian was doing, and he had no idea about the rest. He had never participated in demonstrations related to aerodynamic research, nor had he participated in aircraft design projects. Even the researched decomposition represented nothing.
Not sure.
He was doing theoretical work, just finding approximate solutions to equations.
Cui Xunnian’s feedback seemed to be that he was satisfied with the results.
That's it.
Now Wang Hao feels lack of inspiration, and he finds that his research on the NS equation is completely stuck.
【Task 1】
[Inspiration value: 40].
This task has been going on for nearly a week, and the inspiration value has not increased at all. It is obviously a lack of inspiration and research direction.
"It seems that it will take a while." Wang Hao didn't think of a good way. For an S+ level difficulty task, every progress can be said to be a great achievement.
He hopes to make progress, but only if a direction is found.
"Just take it as it comes, just take a rest for a while!" Wang Hao didn't really care. He had been busy some time ago and just needed a break.
He regarded it as giving himself a holiday.
So for several days in a row, he stayed in the office in the complex building, watching movies, watching videos, reading the news, drinking coffee and tea. Life was about cultivating sentiments.
Zhang Zhiqiang noticed Wang Hao's leisurely attitude and said a little strangely, "Weren't you very busy a while ago? You were always in the laboratory. I saw that you even put up a 'Do Not Disturb' sign."
Wang Hao took a sip of coffee and said, "I haven't had much inspiration lately and I want to relax for a while."
"Yeah?"
Zhang Zhiqiang nodded and said, "That's fine. I'm too tired from being busy all the time. I also plan to take a break. The laboratory has been built, so it would be good for students to study there."
As he was talking, he suddenly remembered something, and he immediately came over and whispered, "I discovered a very strange thing recently, didn't you notice?"
"It seems that there is something wrong with Luo Dayong and Zhu Ping?"
"What's wrong?" Wang Hao asked.
"Didn't you notice? Luo Dayong has stopped talking about Zhu Ping recently, and Zhu Ping can't be seen scolding Luo Dayong."
"Isn't it nice to live in peace?"
"There must be something wrong." Zhang Zhiqiang said, "You may not have noticed that Luo Dayong's temper has not changed. This guy seems to only be targeting me."
"In the past, he always talked about Zhu Ping and occasionally talked about me, but when I think about Zhu Ping, I think it's normal."
"Now...it seems like I'm the only one left. You don't understand that feeling. Really, sometimes, I want to beat him." Zhang Zhiqiang shook his head as he spoke.
Wang Hao looked Zhang Zhiqiang up and down, and said after thinking, "You'd better not take action. Your body is no match for Luo Dayong."
Zhang Zhiqiang's face turned dark when he heard this.
Does it matter?
Wang Hao said, "Maybe the two have reconciled, or maybe Luo Dayong is too afraid of Zhu Ping, I don't know for sure."
He shook his head as he spoke and continued to watch his movie.
Of course he knew what happened between Luo Dayong and Zhu Ping. It seemed that since Helen said those words before school started, Luo Dayong rarely messed with Zhu Ping anymore.
Luo Dayong did not take the initiative to 'provoke', so Zhu Ping naturally had no reason to take action.
It probably involves the psychological problems of some men and women.
Wang Hao didn't care about this.
He still enjoys life with peace of mind. The only thing he does is to engage in teaching. As a university teacher, of course he hopes to teach a lot of geniuses.
In his spare time, Wang Hao also found Professor Wang Huanxin. He wanted Wang Huanxin to help him organize papers on solving partial differential equations, so as to compile a professional book on solving partial differential equations.
This is Qiu Chengwen’s suggestion.
Wang Hao also noticed that in the foreign paper index, his paper "Solution of Thirteen Types of Partial Differential Equations" had more than 3,000 citations and nearly 10,000 downloads.
This is simply incredible data for a mathematics paper.
Therefore, Wang Hao thought about Qiu Chengwen's suggestion and felt that a Chinese book should be published. Relevant domestic scholars can purchase the book directly instead of downloading English papers and studying it themselves.
After Wang Huanxin heard Wang Hao's intention, he was very excited, "Well, you can just ask me. I have a lot of free time!"
"And I have also studied several of your papers on solving partial differential equations, and I have mastered the methods in them."
"I also think it would be best to publish a book. This is a great idea and will definitely help many people."
Professor Wang Huanxin does have reason to be happy.
When he was young, he realized that he had no talent in basic mathematical research, so he concentrated on teaching. However, anyone who serves as a university professor hopes to achieve certain results, not just in teaching.
Now, instead of studying the results myself, I want to publish a professional book on partial differential equations.
Although I am just a ghostwriter, the book will definitely have an author's name, and it can be said to be his book when the time comes.
This is equivalent to the honor and achievement delivered to you.
Of course.
It is definitely not easy to come up with a professional book. Even if there is a thesis as the basis, it will take at least several months to research, organize, write some notes, other explanations, etc.
However, Wang Huanxin was still very happy.
Wang Hao asked Wang Huanxin to help because Wang Huanxin's level was not bad, but he didn't have much research mind, but his foundation and understanding were definitely no problem.
He had already contacted the publisher in advance.
Because he has a certain reputation, the publishing house also gave him a large profit margin. Whether he makes money is secondary, but he will definitely not lose money.
There is no fear of piracy for similar books, and no pirates will print such professional books.
Ordinary people will not spend money to buy such professional books, and professional scholars are unlikely to buy pirated copies.
By then, there will definitely be some universities and libraries ordering it, and there will also be some mathematics scholars who will specifically purchase it.
After talking about publishing a book, Wang Hao let go of his worries and continued to enjoy his life.
Teaching students is a very interesting thing.
He would take some time every day to go to the Mason Mathematical Science Laboratory, and students would come and ask questions.
Among the graduate students in mathematics, Xu Jie is the one who asks more questions. He always has some questions about basic mathematical knowledge.
Of course, it is said to be basic, but it is relative to the graduate and doctoral level, and the questions asked by Xu Jie cannot be answered directly.
Sometimes, Wang Hao will be asked to think for a while before he can give an answer.
Among the other three, Helen asked fewer questions, but the content was a bit troublesome and she couldn't ask some basic questions.
For example, she would not ask questions in some courses, even those that were difficult to solve, but would think and solve them herself.
She asked strange questions, such as, "Is Einstein's theory of relativity correct? What would happen if a particle exceeded the speed of light?"
She likes to discuss such issues.
If ordinary people ask these questions, they may be considered "ignorant", but obviously they cannot convince Helen with such words, because Helen can use mathematical language to explain some problems and even make Wang Hao think.
The follow-up discussions between the two fell into a strange philosophical circle every time.
After discussing many issues with Helen, Wang Hao even felt that he should study philosophy, which might bring more inspiration to his research.
Chen Mengmeng is the most lovable. She occasionally does not understand something, but she is the kind of very smart student who can understand problems with just a click.
This gave Wang Hao a sense of accomplishment in teaching students.
The only inactive person was Qiu Hui'an. He had almost no problems. He came to the laboratory workshop and stayed in his position. Most of the time, he studied and thought silently without knowing what he was doing.
On this day, Wang Hao found out.
While he was reading the news in his office, Qiu Hui'an walked in with a stack of information.
"Teacher Wang, I have a question that I have never been able to figure out. I want you to give me some direction." Qiu Hui'an put the information on the table and said.
"Tell me."
"I'm studying the Legendre conjecture." Qiu Hui'an's words shocked Wang Hao.
Of course he knows the Legendre Conjecture.
Legendre's conjecture is a famous conjecture related to number theory. The content is also very simple. It states that for any natural number n, there is at least one prime number p between the square of n and the square of (n+1).
This conjecture sounds simple, but it is too difficult to prove. Most people can't even find the direction.
"Tell me what you think." Wang Hao suddenly became interested.
Qiu Hui'an seemed a little embarrassed. He said, "I have studied your Mersenne prime number paper and Artin's conjecture paper. I still don't understand a small part of it, but I understand most of it."
Wang Hao nodded as he listened, and his evaluation of Qiu Hui'an immediately reached a new level. He did not expect that the 'mediocre' Qiu Hui'an could actually reach this point, studying his own papers and being able to read them.
Understanding most of the content is really impressive for a graduate level student.
Qiu Hui'an continued, "I am very interested in number theory, especially the study of prime numbers."
"I used your demonstration method for Mersenne primes to study Bertrand-Chebyshev's theorem, and then I hope to further prove Legendre's conjecture."
"But I encountered a problem. Your argument and analysis method for Mersenne primes can indeed cover the Legendre conjecture, but it can only cover it, rather than provide a detailed proof."
"So I want to find a new direction and method to do research combined with analysis and demonstration."
After Qiu Hui'an finished speaking, he looked at Wang Hao expectantly.
Wang Hao thought carefully about Qiu Hui'an's words. Using the Mersenne prime argument method to study the Legendre conjecture can indeed cover it, but at the same time it is indeed impossible to achieve a precise proof.
Because his argument method for Mersenne primes did not fully cover even Mersenne primes.
But it's different when combined with other means.
Wang Hao thought deeply and said, "I don't have a definite answer in this regard. I can only give you a few ideas and suggestions."
"The first is that as long as you use the method of functional analysis or other similar analysis methods, you can only achieve coverage research, but not detailed demonstration."
"The second is that you can consider other directions. There are many methods for the study of number theory, such as the study of prime numbers and the most basic sieve method. You can look at Mr. Chen Jingrun's proof of Goldbach's conjecture."
"In addition, on the assembly..."
When Wang Hao said this, an idea suddenly flashed in his mind.
Qiu Hui'an also said, "Yes, group theory! This direction may be helpful?"
In fact, what Wang Hao just wanted to say was sets, but he immediately thought of 'group theory'. He immediately realized that it was the effect of "The Gift of Scientific Research" and the inspiration provided by Qiu Hui'an.
Qiu Hui'an's reaction also illustrates the situation.
Wang Hao nodded with a smile, "I think the group theory method may be helpful to your research."
Qiu Hui'an was obviously very happy, "Thank you, Teacher Wang, I will go and study it right away."
He walked out thinking.
Wang Hao also fell into thinking. The effect of "Gift of Scientific Research" just now brought a fourfold inspiration bonus, but it also showed that Qiu Hui'an did have great ideas.
Group theory?
Study the prime number problem...
Wang Hao thought about it and felt that this was a very good idea.
Group theory is a mathematical method for studying groups, and its importance is mainly reflected in abstract algebra.
In the field of abstract algebra, algebraic structures such as rings, fields, modules, etc. can be seen to be formed by adding operations and axioms on the basis of groups.
Using group theory to study number theory and prime numbers is very novel when you think about it.
The most important thing is that the activation of inspiration just now proves that this is a feasible method. Since it is feasible to study Legendre's conjecture, it can naturally also be used to study other mathematical problems related to prime numbers.
Wang Hao immediately thought of a famous number theory conjecture - Goldbach's conjecture.
Most mathematicians have considered Goldbach's conjecture, because this conjecture is very simple to understand and sounds like it is solving a simple problem.
But when I think deeply, I find that most of the thinking is useless.
"If we use the method of group theory to study prime numbers and study the conceptual properties of prime numbers, can it be understood that we have solved the mystery of prime numbers?"
"So how do you combine group theory and prime numbers?"
"The Riemann Hypothesis or Zhou's Hypothesis may be studied using group theory methods, but this kind of research has an end point and is unlikely to be proved."
"Like Goldbach's conjecture, it's very difficult to connect..."
"this……"
Wang Hao thought and hesitated. He felt that he had found a direction to study number theory.
But the problem is...
The number of tasks is not enough.
‘Task One’ is the study of NS equations, ‘Task Three’ is the study of annihilation force, and there is only one ‘Task Two’ left, which is reserved for daily research.
The study of prime numbers is no small undertaking, and he is determined to study famous number theory conjectures.
Wang Hao hesitated for a long time, and finally made up his mind, "In the worst case, if you give up the mission, you will lose some teaching coins!"
Create a task——
【Task 2】
[R&D project name: Proof of Goldbach’s conjecture (Difficulty: S.)]
[Consuming teaching coins can increase the probability of obtaining related inspiration values within a certain period of time. 】
[Inspiration value: 0.]
[When the inspiration value reaches 100 points, it can be consumed once to assist in obtaining original relevant inspiration and knowledge correlation. 】
[Complete the S-level difficulty research, and you will get an additional number of teaching coins for each item: 3000.]
[After completing the task, you will receive a teaching coin reward.]