Chapter 157: A New Research Direction: Goldbach's Conjecture!
Yang Yuan said that he had made two sets of data schemes, and the wind pressure test evaluation values were lower than 20, which really surprised Li Jianhua and his party.
Li Jianhua has been engaged in fighter design for a long time and is one of the most famous fighter design experts in China.
The team he led has a special power group, and the people in the power group are also top aerodynamics experts, who have been engaged in aerodynamic research on aircraft flight for a long time.
The study of low-altitude flight dynamics of fighters is the top priority of the study of fighter flight dynamics.
They are just a power group, and the content of the research is relatively mixed, and the purpose is also to support the aircraft design, not the content of the research theory.
But they are also very professional and understand what it means for a wind pressure test evaluation value below 20.
That is, the most advanced level in the world, the most advanced fighter in the world, and the wind pressure test evaluation of low-altitude flight cannot be lower than 20.
The development of domestic military science and technology is very fast, and in some respects it has caught up with the international level, but to say that it has surpassed the international level in research is indeed a big talk.
The research goal of Yang Yuan's team is also very high, saying that the wind pressure assessment value is less than 20, but when doing project research, the goal is only the goal, and the goal is generally not reached.
A wind pressure assessment of less than 20 is just the best result.
Now that they heard Yang Yuan's affirmative words, the two aerodynamics experts present directly questioned and refuted them, because they were so surprised.
Yang Yuan didn't care about being questioned, of course he knew why the other party was out of shape, but said proudly, "We have a master to help us!" ”
"Do you know Professor Wang Hao of Xihai University? That's super genius. He gave him a thumbs up, "In the field of partial differential equations, in the study of NS equations, who can surpass him?" ”
"Don't say it's domestic, it's hard to find internationally!"
This sentence makes people feel like they are talking big, but with the addition of the name 'Wang Hao of Xihai University', Li Jianhua and his party did not refute it anymore.
Wang Hao is so famous.
In the past year, he has appeared the mathematician the most in public opinion, and the frequency of his appearance is even higher than that of some 'hot mathematicians' and 'Internet celebrity scholars'.
Some mathematicians will be discussed for a long time because of certain events.
Wang Hao has been on the public opinion because of certain incidents, and most of his reports are because of amazing results.
For example, the Mersenne prime.
He found several Mersenne primes in a row, which directly shook the international mathematical community, and with his personal research results, he almost 'crushed' GIMPS looking for Mersenne primes, and GIMPS also cooperated with Wang Hao to continue to open up and support users to search for Mersenne primes.
Another example is the proof of Kadotani'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 immediately considered one of the world's top mathematicians.
Wait a minute.
Some time ago, Wang Hao's work also appeared in the media, which was about the study of 'finding an approximate solution to the NS equation'.
People in the academic circle feel very strange, because ordinary people can't understand this achievement, and even if they can understand it, they probably won't be interested.
As a result, some time before the release of the results, many people were discussing the importance of finding approximate solutions to the NS equation, and then it was reported that Wang Hao's paper was published in New Advances in Mathematics, one of the four top journals.
This feels like building momentum for Wang Hao in front.
However, well-informed people can still know that someone deliberately guided public opinion in front of him, and it is likely to be Fu Chunjie of Sudong University, but no one has evidence, and as a result, Fu Chunjie seems to be stealing chickens and rice, and he is completely building momentum for Wang Hao.
Hearing Wang Hao's name from Yang Yuan's mouth, Li Jianhua and his party had a sense of 'so it was'.
However, they were still very surprised, because they knew how difficult it was.
The main study of dynamic wind pressure in low-altitude flight is to solve the problem of numerical balance, which will definitely involve a very complex system of partial differential equations.
This system of equations is even more difficult than a single NS equation, and can almost only be approximated by substituting numerical values.
There is no fixed solution to a system of equations, and it can be said that there are countless groups of solutions.
It is unimaginably difficult to find a suitable solution from it, and they can only demonstrate the data and then verify it experimentally.
This consumes a lot of time and money, and it is not always possible to find a good data solution.
The people in the conference room pondered carefully for a long time, and Li Jianhua suddenly asked, "Professor Wang Hao, can't it be that the analysis of the ns equation has been completed?" ”
"It can't be!" There was a negative right away.
Yang Yuan also shook his head, "I have paid close attention to the data, he should have his own method to find an approximate solution, and he can make the solution more approximate to the exact solution, or find a balance." ”
"I don't quite understand either. This kind of thing can only be known by asking him himself. ”
"Anyway, Professor Wang Hao provided us with two sets of solutions, which are worth a thousand gold!" Yang Yuan shook his head with emotion.
Li Jianhua also nodded, "This kind of research is indeed worth a thousand dollars, and Professor Wang Hao must have spent a lot of energy." ”
When Yang Yuan heard this, he was silent for a while and didn't speak, mainly because Wang Hao's research speed was too fast, even if he added the previous half a month, it would definitely not exceed twenty days.
Twenty days, can you spend a lot of energy?
At this time, Cui Xunnian suddenly walked over, leaned into Yang Yuan's ear and was about to whisper a report, when he heard Yang Yuan say very brightly, "Xunnian, if you have anything to say, just say it directly, it's all your own people." ”
Li Jianhua and others also looked at it.
Cui Xunnian said simply, "That's right, just now I received four other sets of approximate solutions from Professor Wang Hao, and he also said that if you need more solutions, you can send a message over, and he will help study it when he is free." ”
“……”
“……”
The conference room fell silent.
After a long time, Li Jianhua broke his silence and corrected what he had just said, "Professor Wang Hao, he is really a genius." ”
……
Wang Hao didn't know that the several approximate decompositions he had studied would bring such a big boost to the research of Yang Yuan's team.
In fact, he only knew what Cui Xunnian was doing research, and the rest was completely unclear, he had not participated in the arguments related to aerodynamics research, let alone the aircraft design project, and he did not even know what the research dissolution represented.
He did theoretical work, and he just found the approximate solution of the equation.
Choi Hoon-nian's feedback seemed to be very happy with the results.
That's it.
Now Wang Hao feels that he is lacking inspiration, and he finds that the research on the NS equation is completely stuck.
[Task 1]
[Inspiration value: 40].
This task lasted for nearly a week, and the inspiration value did not increase at all, obviously lacking inspiration and research direction.
"It looks like it's going to be deposited for a while." Wang Hao didn't think of a good way, S+-level difficulty tasks, every progress can be said to be a great achievement.
He hopes that progress can be made, but only if he finds direction.
"Just go with the flow, and rest for a while!" Wang Haozhi didn't care very much, he had been busy for a while ago, and he just needed to rest for a while.
He thought of it as a vacation for himself.
So for several days in a row, he stayed in the office of the complex building, watching movies, watching videos, watching news, drinking coffee and tea, and life was to cultivate his sentiments.
Zhang Zhiqiang noticed Wang Hao's leisure, and he said a little strangely, "Weren't you very busy a while ago?" It's been at the lab all the time, and I see you've got a 'Do Not Disturb' sign. ”
Wang Hao took a sip of coffee and said, "I haven't had any inspiration lately, and I want to relax for a while." ”
"Really?"
Zhang Zhiqiang nodded and said, "That's fine, it's too tiring to be busy all the time, I also plan to take a break, the laboratory has been built over there, so it's good to let students study there." ”
As he spoke, he suddenly remembered something, and suddenly leaned over and whispered, "I recently discovered a very strange thing, didn't you notice it?" ”
"It seems that Luo Dayong and Zhu Ping are wrong?"
"What's wrong?" Wang Hao asked.
"Didn't you notice? Luo Dayong didn't talk about Zhu Ping recently, and he couldn't see Zhu Ping scolding Luo Dayong. ”
"Wouldn't it be nice to live in peace?"
"Something must be wrong." Zhang Zhiqiang said, "You may not have noticed that Luo Dayong's temperament has not changed, this guy seems to be only targeting me." ”
"In the past, he always said Zhu Ping, and occasionally me, but thinking about Zhu Ping, I think it's normal."
"Now...... It seems like it's just me. You don't understand that feeling, it's really, sometimes, I want to beat him up. Zhang Zhiqiang shook his head as he spoke.
Wang Hao looked Zhang Zhiqiang up and down, thought about it and said, "You'd better not do it, your body is not Luo Dayong's opponent." ”
Zhang Zhiqiang's face darkened when he heard this.
Does it matter?
Wang Hao said, "Maybe the two of them are reconciled, or Luo Dayong is too afraid of Zhu Ping, and it is not necessarily." ”
He shook his head as he spoke, and continued watching his movie.
Of course he knew what was going on between Luo Dayong and Zhu Ping, it seemed that since Helen said those words before the start of school, Luo Dayong rarely provoked Zhu Ping again.
Luo Dayong did not take the initiative to 'provoke', so Zhu Ping naturally had no reason to do it.
It probably involves some problems in the hearts of men and women.
Wang Hao doesn't care about this.
He still enjoys life with peace of mind, and the only thing he does is to engage in teaching, and as a university teacher, he certainly hopes to teach a bunch of geniuses.
In his spare time, Wang Hao also found Professor Wang Huanxin, and he wanted Wang Changxin to help him sort out the paper on solving partial differential equations, so as to organize a professional book on solving partial differential equations.
This is Qiu Chengwen's suggestion.
Wang Hao also noticed that in the index of foreign papers, his paper "Solving Thirteen Types of Partial Differential Equations" has a citation rate of more than 3,000 and a download of nearly 10,000.
That's incredible data for a math paper.
Therefore, Wang Hao thought about Qiu Chengwen's suggestion and felt that a book in Chinese should indeed be published, and relevant domestic scholars could directly buy the book, rather than download English papers to study by themselves.
After Wang Huanxin heard Wang Hao's intention, he was immediately very excited, "This, you are right to find me, I have a lot of free time!" ”
"And I've also studied several of your papers on solving partial differential equations, and I've mastered the methods in them."
"I also think it's best to publish a book, it's a great idea, and it's sure to help a lot of people."
Professor Wang Huanxin does have reason to be happy.
At a young age, he realized that he had no talent for basic mathematical research, so he concentrated on teaching, but anyone who became a university professor wanted to achieve certain results, not just in teaching.
Now I am not going to research on my own, but to publish a professional book on partial differential equations.
Although he is only a ghostwriter, the book must have an author's name, and it can also be said to be his book when the time comes.
This is equivalent to the honor and achievement delivered to the hand.
Of course.
It must be very difficult to come up with a professional book, and even if there is a thesis as the basis, it will take at least a few months to research, organize, and write some notes, and other explanations, and so on.
However, Wang Huanxin was still very happy.
Wang Hao asked Wang Huanxin to help, also because Wang Huanxin's level is not bad, but he doesn't have much research mind, but there is definitely no problem with foundation and understanding.
He had already contacted the publisher in advance.
Because he has a certain reputation, and the publishing house has also given a lot of concessions, whether he makes money or not is secondary, but he will definitely not lose money.
Similar books are not afraid of piracy at all, and there will be no pirates who will print such professional books.
Ordinary people don't spend money on such specialized books, and professional academics are less likely to buy pirated copies.
When the time comes, there will definitely be some universities, libraries to order, and there will also be some mathematicians who will buy it specifically.
After talking about the publication of the book, Wang Hao also let go of his worries, and he continued to enjoy his life.
Teaching students is a very interesting thing.
He would take some time out every day to go to the Mason Math Science Lab, and students would come over and ask questions.
Among the graduate students in several mathematics directions, Xu Jie asks more questions, and he always has some questions in terms of basic mathematical knowledge.
Of course, it is said that it is the foundation, and it is also relative to the graduate student, doctoral level, and the questions asked by Xu Jie are not directly answerable.
Sometimes, it will make Wang Hao think for a while before giving an answer.
Of the other three, Helen asks fewer questions, but the content is a bit of a headache, and she doesn't ask basic questions.
For example, some of the problems in the course, even if they are difficult to solve, she will not ask, but think and solve them by herself.
She asks strange questions, such as, "Was Einstein's theory of relativity correct?" What happens if a particle exceeds the speed of light? ”
She enjoys discussing these kinds of issues.
Ordinary people may be considered 'ignorant' when they ask these questions, but obviously they can't convince Helen with such words, because Helen can use mathematical language to explain some problems, and even cause Wang Hao to think.
The follow-up of the discussion between the two fell into a strange circle of philosophy every time.
After discussing problems with Helen more times, Wang Hao even felt that he should study philosophy, which might bring more inspiration to his research.
Chen Mengmeng is the most likable, and she occasionally has something she doesn't understand, but she is the kind of student who is very smart and can understand when she has a problem.
This gives Wang Hao a sense of accomplishment in teaching students.
The only one who is not active is Qiu Hui'an, he has almost no problems, he comes to the laboratory workshop, he stays in his position, most of the time is silently studying, thinking, and I don't know what he is doing.
On this day, Wang Hao knew.
When he was scrolling through the news in the office, Qiu Huian walked in with a stack of materials.
"Mr. Wang, I have a question that I have never figured out, and I want you to point me in a direction." Qiu Huian put the information on the table and said.
"Tell me."
"I'm working on the Legent conjecture." Qiu Hui'an's words shocked Wang Hao.
Of course, he knew about the Legent conjecture.
The Legendre conjecture is a well-known conjecture related to number theory, and the content is also very simple, saying that for any natural number n, between the square of n and the square of (n+1), there is at least one prime number p.
This conjecture sounds simple, but it is so difficult to prove that 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, and he said, "I have studied your Mason prime number paper, as well as the Atin conjecture paper, and a small part of it is still incomprehensible, but most of it is understood. ”
Wang Hao listened and nodded, and his evaluation of Qiu Hui'an suddenly went up a notch, he didn't expect that the 'mediocre' Qiu Hui'an had reached such a point, studying his own papers, and being able to understand most of the content, for the graduate level, it was indeed very remarkable.
Qiu continued, "I am very interested in number theory, especially the study of prime numbers. ”
"I used your method of argumentation for Mersenne primes to study the Bertrand-Chebyshev theorem, and then I wanted to further prove the Legendre conjecture."
"But I have a problem, your argumentation and analysis of the Mersenne prime can indeed cover the Legendre conjecture, but only to override, not to prove in detail."
"So I want to find a new direction and method, and do research in combination with analysis and argumentation."
After Qiu Hui'an finished speaking, he looked at Wang Hao expectantly.
Wang Hao pondered Qiu Hui'an's words carefully. Using the method of argumentation of Mersenne primes to study the Lejende conjecture can indeed be covered, but at the same time, it is indeed impossible to achieve fine proofs.
Because of his method of argumentation for Mersenne primes, even Mersenne primes are not completely covered.
But when combined with other means, it's different.
Wang Hao thought about it and said, "In this regard, I don't have a definite answer, I can only give you a few thoughts and suggestions." ”
"The first is that as long as you use the method of functional analysis, or other similar analysis methods, you can only cover the research, but not the detailed argument."
"The second is that you can consider other directions, the study of number theory, there are many methods, such as the study of prime numbers, the most basic sieve method, you can look at Mr. Chen Jingrun's proof of Goldbach's conjecture."
"In addition, the assembly is ......"
When Wang Hao said this, a flash of inspiration suddenly flashed in his mind.
Qiu Hui'an also said at the same time, "That's right, group theory! This direction might help? ”
In fact, what Wang Hao wanted to talk about just now was a collection, but he directly thought of 'group theory', and he immediately reacted that it was the effect of "The Gift of Scientific Research" and the inspiration provided by Qiu Hui'an.
Qiu Hoi An's reaction also illustrates the situation.
Wang Hao nodded with a smile, "I think the method of group theory may be helpful for your research." ”
Qiu Hui'an was obviously very happy, "Thank you, Teacher Wang, I'll go study it right away." ”
He walked out with thoughts.
Wang Hao also fell into thinking, just now it was the effect of "The Gift of Scientific Research", which brought a fourfold inspiration bonus, but it also showed that Qiu Hui'an was indeed very thoughtful.
Group theory?
Studying Prime Number Problems......
Wang Hao thought about it and felt that this was a very good idea.
Group theory is a mathematical method for the study of groups, and its importance is mainly reflected in abstract algebra.
In the field of abstract algebra, algebraic structures such as rings, fields, and modulos 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 inspiration just now proved that this is a feasible method, and since it is feasible to study the Legendre conjecture, it can 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 the Goldbach conjecture because it is so simple to understand that it sounds like solving a simple problem.
But when I think about it deeply, I find that most of my thinking is useless.
"If we use the method of group theory to study prime numbers and study the conceptual properties of prime numbers, can we understand that we have solved the mystery of prime numbers?"
"So how do you combine group theory with prime numbers?"
"The Riemann conjecture or the Zhou conjecture may be able to be studied using the method of group theory, but this kind of research has an end point and is unlikely to achieve proof."
"It's like Goldbach's conjecture, but it's hard to ...... to connect"
"This ......"
Wang Hao thought about it and hesitated, he felt that he had found a direction to study number theory.
But here's the problem......
The number of tasks is not enough.
'Task 1' is the study of the NS equation, 'Task 3' is the study of annihilation, and only one 'Task 2' is left for daily research.
The study of prime numbers is not a small study, and he has the heart to study the famous number theory conjecture.
Wang Hao hesitated for a long time, and finally made up his mind, "It's a big deal to give up the task, and you will lose some teaching coins!" ”
Establish a task –
[Task 2]
[R&D Project Name: Proof of Goldbach's Conjecture (Difficulty: S. )】
[Consuming Teaching Coins can increase the chance of obtaining inspiration points related to it for a certain period of time.] 】
[Inspiration value: 0.] 】
[The accumulation of inspiration points reaches 100 points, which can be consumed at one time to assist in obtaining the interconnection of original related inspiration and knowledge.] 】
[Complete the S-level difficulty research, and each additional amount of teaching coins will be obtained: 3000.] 】
[Task settlement, get the reward of teaching coins.] 】
“……”
"Goldbach conjecture, only S-class?"