Research starts with PhD students

Chapter 93 Zhang Shuo: I solved the Jebov conjecture, what do you think?
Computer room.

Zhang Shuo went to make two cups of coffee and also made one for Sun Xingli. He asked, "Brother Sun, what is the name of your research?"

"A method for testing the distribution of prime numbers starting from square numbers."

After Sun Xingli said the name, he added, "This is the name of my paper, but I actually want to change it to something that looks more professional and has more content, but I can't think of one."

"Just a name will do."

Zhang Shuo said nonchalantly, and quickly created a system task -

【Task 1】

[Research project name: Prime number distribution test method starting from square numbers (difficulty assessment: B). ]

【Progress: 0.001%.】

(The task can be canceled. Currently, the number of scientific research coins required to cancel the task is 0.)
(The remaining progress requires 500 scientific research coins.)
"500?"

Zhang Shuo looked carefully at the number of scientific research coins needed and couldn't help but grin. He looked at Sun Xingli with respect.

This difficulty is the same as the 'Further Proof of the Smoothness of the Solutions of the Monge-Ampere Equation', and the 'Proof of the Monge-Ampere Equation' belongs to the research field of partial differential equations.

The field of partial differential equations has the most papers in the branch of mathematics.

Even if you can't think of how to prove it, you can read other papers to find inspiration, or you can attend many academic seminars in the field of equations.

While doing his research, Luo Yongjun kept reading papers, including previous research on the Monge-Ampere equation and research on other similar types of equations.

These are all helpful for research.

Research in number theory is different. You can find some related papers, but there are very few with substantial content.

Number theory methodology, including the completed number theory results, are all scattered contents. It is normal that two papers that are both studies on prime number problems have no correlation.

In addition, some proofs in the field of number theory are often obscure and difficult to understand, and it is not easy to comprehend the logic behind them.

The most typical example is Andrew Wiles' proof of Fermat's conjecture. During Wiles' report, the reviewers of the Newton Institute had to divide it into several parts and understand them separately.

Until now, no scholar has clearly stated that he has fully understood the proof process.

Of course, it is also because most scholars are unwilling to spend so much time to understand a proof process.

Anyway, as long as it’s proven, that’s enough.

In short, the difficulty of a research depends not only on the number of scientific research coins required for the task, but also on the field to which it belongs.

With the same demand for scientific research coins, the field of number theory is definitely more difficult than the study of partial differential equations.

Zhang Shuo handed the coffee to Sun Xingli, then pulled a chair over and sat aside.

Sun Xingli did not take the printed paper, but a blank draft book, and said, "I discovered this method while studying the Jebov conjecture."

"If the method is OK, my next step is to apply for a project on the Gerbov conjecture. I feel that this method can be used in the study of the Gerbov conjecture, but I don't know if it can be completed."

He said, shaking his head.

Zhang Shuo had an idea after hearing this, and opened the system again to create a task -

【Task 2】

[Research project name: Proof of the Jebov conjecture (difficulty assessment: B). ]

【Progress: 0.001%.】

(The task can be canceled. Currently, the number of scientific research coins required to cancel the task is 0.)
(The remaining progress requires 600 scientific research coins.)
"600?"

Zhang Shuo frowned, then listened carefully to Sun Xingli's explanation.

Sun Xingli's research started with the coprime theorem of the basis of solutions of Diophantine equations and ternary equations.

Diophantine equations are an important branch of mathematics, also known as indeterminate equations or polynomial equations with integer coefficients.

The characteristics of this type of equation are that the values ​​of the variables are limited to integers and the coefficients of the equation are also integers.

The basis coprime theorem of solutions of ternary equations is a mathematical theory that, through the concept of cumulative coprime, demonstrates in detail how to solve a series of difficult mathematical problems, including the Goldbach conjecture, the twin prime conjecture, the abc conjecture, the Beer conjecture, the Riemann hypothesis, the Collatz conjecture, the NP problem and the four color conjecture, etc.

This theory proposes new mathematical tools - the theory of adjacency and the method of overlap. By seeking similarities and differences, it continuously expands the domain to achieve mutual transcendence, completes deep abstraction and underlying calculations, and thus solves these seemingly isolated problems.

Sun Xingli's research is centered around the coprime theorem of the solution base of ternary equations. He studies several Diophantine equations, analyzes them one by one, and completes the primality test starting from square numbers. Starting from square numbers, that is, the primality proof starting from a certain square number.

The method he studied had very demanding requirements and could only be proven complete under certain conditions. In most cases, it was impossible to form rigorous logic.

Sun Xingli explained slowly.

He actually didn't say much, and the entire process was written down in a draft book, which only had a few pages.

But the lecture lasted two hours.

Each step needs to be explained in detail, and many of them involve some very obscure mathematical knowledge.

During the continuous explanation, Sun Xingli's mentality improved. On the one hand, his explanation was equivalent to sorting out his research, and he did not find any problems in the process.

On the other hand, he found that Zhang Shuo was not that "divine" after all.

When some difficult points were explained, Zhang Shuo didn't understand and kept asking how the transformation was completed, what the principles were, etc.

Of course that's normal.

In the field of mathematics, Zhang Shuo's main direction is partial differential equations, which is completely different from number theory.

"Do you understand this part?"

"What I just said, the coprime relationship between solution sets, will become clear if you think about it in reverse."

"For example..."

Sun Xingli spoke more and more fluently.

Zhang Shuo listened patiently and nodded continuously. He would immediately ask questions to get to the bottom of things he didn't understand.

After three hours, he finally understood it all.

Sun Xingli felt more tired than giving a report. He said tiredly, "I have explained it to you once and it is very rewarding. There is indeed no problem with my research."

"I just don't know if this level is good enough to be ranked in the first district?"

The methodology of number theory is difficult to say.

This is not like the Monge-Ampere equation, you can tell how important it is just by stating the research content.

Sun Xingli has completed a method to study prime numbers, and the conditions for using the method are strictly restricted. Different people may have different judgments on the value of the research.

Zhang Shuo said seriously, "In terms of difficulty, it would be enough to publish in one of the four major mathematics journals."

“I don’t dare to think about that!”

Sun Xingli immediately smiled and shook his head.

"I mean it."

Zhang Shuo emphasized, then leaned in and asked, "Brother Sun, if I continue my research based on your method and solve the Jebov conjecture, what do you think?"

"What did you say?" Sun Xingli thought he had misheard.

Zhang Shuo repeated it again.

Sun Xingli laughed out loud, "If you can solve it, you're awesome! What else can I do?"

"If you prove the Gerbov conjecture, I think you should have a chance of winning the Fields Prize, but maybe it will be awarded to you, or maybe it will be awarded to me. It depends on how much my method helps in your proof."

"Eighty percent?"

"That's hard to say."

Sun Xingli laughed as he spoke, "Stop daydreaming. I feel this method is useful for studying the Jebov conjecture, but I don't dare to think that I can prove it..."

"I mean it."

"Really?" Sun Xingli looked over in confusion.

"real."

Zhang Shuo said, "I never joke about research. I think your method will have a direct effect on proving the Jebov conjecture."

(End of this chapter)