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Chapter 158 New research direction: Goldbach’s conjecture!(2/3)

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..."
To be continued...
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