"Okay...if it's a new axiom system..."

After being silent for a long time, Zhang Yuantang shook his head and said seriously: "Since you have this idea, you must have studied it. This will be a huge project. And if you really do it, I even think that you can do it." Compared with this new system, the twin prime conjecture is not so important."

Qiao Yu nodded seriously and said seriously: "Yes, solving the twin prime conjecture is just the beginning. Because everyone said that I have hope of solving the Riemann Hypothesis.

So if I can construct such an axiom system, I definitely hope that it can help me prove that all non-trivial zero points of the ζ function are distributed on the critical line of the complex plane in the future."

Zhang Yuantang glanced at Tian Yanzhen, who was also looking at him seriously. At this time, he seemed to feel the ambition hidden in this room and couldn't help but laugh.

"Godel said that before proving the Riemann Hypothesis, it is necessary to find a new cornerstone for mathematics. Before, I always thought that Grothendieck was the person closest to solving the cornerstone. If he had not gone crazy before.

How should I put it, Qiao Yu, I am also very optimistic about your ability and admire your courage. But I hope you can have a more peaceful mind. The Riemann Hypothesis has caused many mathematicians who studied it to go crazy.

I hope this situation will not happen to you. Of course, I can also share some of my research experience with you, although I don’t know if it will be useful to you.”

Qiao Yu said seriously: "Don't worry, Professor Zhang. I understand everything you said. And to be honest with you, I am very interested in your research.

Because to be honest, I have thought of many ways during this period. But I haven’t thought of a specific entry point yet.”

Zhang Yuantang nodded, sensing Qiao Yu's seriousness, he simply let go.

"If you want to listen to my advice, it is that when you can't find an entry point, you might as well put the question about prime numbers aside first. Don't worry about prime numbers, but study the number structure itself first.

For example, the distribution rules and mutual relationships of integers in larger structures. After all, your focus is on an axiomatic system, which means finding a relatively general structural principle, not just limited to the specific properties of prime numbers.

Prime numbers are just a phenomenon in number structures, and what you first need is to understand the more general behavior of numbers, their distribution patterns, and their interrelationships in different structures.

When you finish this step and return to the problem of prime numbers, you may be able to find a natural path to explain their distribution and properties in this axiomatic framework..."

What Tian Yanzhen didn't expect was that the conversation lasted for more than three hours.

This made him very happy.

For a mathematician like Zhang Yuantang, when discussing mathematical problems with a junior, he is not willing to answer them carefully just to look at his face or to listen to the junior's bragging.

The key is that the questions raised by Qiao Yu can make him feel that the answers are meaningful.

This is actually the same as teachers teaching students.

If a student always asks the teacher some simple and obvious questions, the teacher will not think that the student is easy to learn.

I will only wonder in my heart whether the student is serious about class or whether he is listening carefully. Naturally, there is no enthusiasm in answering, and he may even be perfunctory.

But if the questions asked by the students are of great value and thought, the teacher can be motivated and even willing to spend some time discussing with such students.

If the questions asked by students can even make the teacher forget to eat or other important things...

This shows that the student's question not only mobilized the teacher's enthusiasm, but also made the teacher feel that the discussion with the student could inspire his research.

There is no doubt that the situation at this time belongs to the third type.

As the discussion between the two on twin prime numbers continued, many of Qiao Yu's questions directly scratched Zhang Yuantang's itch. Even Tian Yanzhen listened with interest and even occasionally couldn't help but chime in.

For example, Qiao Yu asked whether it was possible to define a basic set. The elements in the set are neither individual integers nor prime numbers. Instead, they are embedded in a space with topological and algebraic structures.

Each number among them will be regarded as a point in this framework, and the relationship between points is defined by a specific mapping.

Another example is by constructing a new modulus space in which the points are different pairs of prime numbers, trying to transform the existence of twin prime numbers into a geometric closed-circuit problem...

It can only be said that Qiao Yu's idea is indeed unreasonable. But after thinking about it carefully, it seems that it is indeed a good entry direction.

That's it, until Tian Yan really felt that Zhang Yuantang couldn't handle it anymore...

Well, Lao Tian even felt that he had become sluggish, he must have felt it a long time ago.

Because Zhang Yuantang's answers were getting slower and slower, and his thinking time was getting longer and longer. It was not until he finally looked at him from time to time that Tian Yanzhen reacted.

I glanced at the time subconsciously, and it was already half past six in the afternoon.

So he immediately said: "Okay, Qiao Yu, it's almost time. Professor Zhang and I are going to have dinner. Professor Zhang's lecture is tomorrow. If you have any questions, please leave them to discuss tomorrow."

Qiao Yu, who felt that he had just entered the state, was stunned for a moment, and then he took out his mobile phone and looked at the time.

Then he looked at the instructor innocently, blinked and said, "Well, Director Tian, ​​I haven't eaten yet. You can take me with you when you go to eat, so that I can ask Professor Zhang some questions while we eat. "

Tian Yanzhen glared at Qiao Yu and said, "Who did you hear that instructors are also responsible for students' eating problems? You won't go to the cafeteria without eating? I told you that Professor Zhang is tired today. If you have any questions, we will talk about it tomorrow! "

After saying that, Tian Yanzhen raised his hand and pointed at the door of the office: "Hurry up and do your thing."

"Oh, thank you, Professor Zhang." Qiao Yu stood up and politely thanked Zhang Yuantang.

"You're welcome, your question is actually very insightful." Zhang Yuantang complimented.

Qiao Yu smiled politely, and then walked out, turning his head three times.

He also hoped that Professor Zhang would be polite, so that he would be shameless enough to join the two professors.

What disappointed him was that neither Tian Yanzhen nor Zhang Yuantang had any intention of keeping him.

Very embarrassing...

…

After seeing Qiao Yu leave, Tian Yanzhen smiled and said, "I'm not a bad student."

Zhang Yuantang smiled bitterly: "It's more than good. I really couldn't handle his questions. At first, I thought he was a little whimsical.

However, some of his ideas and questions are indeed worth pondering, especially the idea about modal space and modal numbers he just proposed, which I find very interesting.

But I’m really not sure if this idea is feasible. But if he can really follow this idea..."

As he spoke, Zhang Yuantang frowned, feeling that his brain was lacking oxygen.

"Haha, don't think about it. Let's go eat first. You have just recovered from the jet lag and still need to rest. That kid has a lot of fantastic ideas, and he might have a lot more ideas tomorrow."

Tian Yanzhen said with a smile.

This is actually the reason why he canceled half-day tutoring with Qiao Yu every week.

This guy's questions are getting more and more tricky.

Many times he has to think for a long time before he can give some insights.

Yes, it can only provide some insights. In fact, it cannot fully answer Qiao Yu's question.

If he had to experience this kind of afternoon every week, Tian Yan really felt that his mentor would soon lose his sense of mystery...

Some students cannot be stared at all the time.

Zhang Yuantang shook his head, then stood up and joked: "Really, if I had known that you, a student, were so difficult to deal with, I really wouldn't have come."

…

On the other side, Qiao Yu walked out of Tian Yanzhen's office depressedly, took out his cell phone and called Qiao Xi.

The mentor who always loved him didn't even take him to dinner... He planned to file a complaint with Qiao Xi.

In terms of seniority, Qiao Xi is now Tian Yanzhen's junior sister. After Qiao Xi goes to Huaqing, she can mention this matter in front of Mr. Yuan...

It would be best to ask his master's grandfather to tell his tutor that this kind of behavior of driving students away when it's dinner time is very inappropriate.

Qiao Xi soon answered the phone, and to Qiao Yu's surprise, the other end of the phone seemed quite lively.

"Mom, are you outside?"

"Well, I'm treating your Uncle Xia and Aunt Liu's family to dinner."

As soon as he finished speaking, Qiao Yu heard Xia Keke's voice: "Qiao Yu, have you eaten?"

Qiao Yu, who was in a bad mood, said directly: "Call me brother! Let's see what you can do...I haven't eaten yet! Eat more and try to become fatter..."

"Aunt Qiao, Qiao Yu bullied me again..."

"Okay, please stop making trouble and let your Aunt Qiao answer the phone."

After Aunt Liu's voice passed by, Qiao Xi's voice came again.

"Did Mr. Yuan tell you that I will go to Huaqing tomorrow?"

"Ah? You're coming tomorrow?" After hearing this, Qiao Yu was a little surprised.

Because Mr. Yuan said last time that he planned to ask Qiao Xi to wait until mid-September.

"You don't know? Then why are you calling?"

"Why are you coming here tomorrow?"

"I really can't stay at home anymore." Qiao Xi explained simply, but Qiao Yu understood it instantly.

Some people are born to adapt to living in the spotlight. In fact, Qiao Xi should have been able to adapt before.

But anyone who has been criticized behind someone’s back for a few years will probably instinctively resist receiving too much attention.

Especially when her attention now overlaps with those of those who once pointed fingers at her.

This not only takes time to heal, but also requires a process of rebuilding confidence.

"That's great! But I don't know if I can make time to pick you up tomorrow. Director Tian has specially invited a professor to give a lecture, which will also be tomorrow."

"You don't need to pick me up. Mr. Yuan said that everything has been arranged for me. Tell me quickly why you called?"

"Hey, Director Tian kept chatting with Professor Zhang who will give a lecture tomorrow, and then he took Professor Zhang to dinner and refused to let me go. When you come tomorrow, help me talk to Mr. Yuan and find an opportunity. Criticize Director Tian."

"Well, I got it, you're itchy, right? When I go to the capital tomorrow, I'll beat you up tonight. Is there anything else? I'm hanging up."
To be continued...