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Chapter 144 On the Axiom System of Generalized Modal Number Theory on Multiple Transcendental Spaces

After this meal, Qiao Yu took Qiao Xi to play in Beijing for three days. Then Qiao Yu was informed that he could not return to Xingcheng this summer vacation.

Because next Tian Yanzhen invited Professor Zhang Yuantang from the University of California, Santa Barbara to give a lecture.

For Qiao Yu, who is determined to solve the twin prime conjecture, this lecture is definitely not to be missed.

In addition, there is a Natural Science Foundation research review meeting in late August. Tian Yan really hopes that Qiao Yu can also participate to broaden his horizons.

Going home in this situation would be a waste of time. So when they go back, it's only Qiao Xi and Xia Keke.

Mr. Yuan asked Qiao Xi to report to Huaqing in mid-September.

Unlike Qiao Yu's situation, Qiao Xi may be admitted to Huaqing University in the 3+2+3 method.

So she needs to go back to Star City to prepare a series of information and corresponding certificates.

Then, when I came to Huaqing, I first followed the leading class to take the basic courses. This was because Qiao Xi's foundation in advanced mathematics was a little worse than Qiao Yu's.

However, in Yuan's opinion, these are not important. It is just a matter of asking substitute lecturers and professors to give more private lessons.

Mr. Yuan felt that the professors should be very happy.

There are not only few female students in science and engineering, but also few female professors. Qiao Xi is very beautiful and has an indescribable temperament. In Tan Luyuan's words, she is like a star.

Yuan Zhengxin was even afraid that after Qiao Xi came, those relatively young, single and not-so-single professors would become aroused.

Some people's excellence requires in-depth understanding to know. But some people's excellence can be seen from the outside. It's unfair, but there's nothing we can do. Since the day society was born, this world has never been truly fair.

At the age of 34, in the mathematics world, from a research perspective, you are no longer young, but if you just talk about age, you are actually not that old.

It is not an exception for a PhD to have not graduated at this age. Huaqing has ready-made ones.

Even though Qiao Xi had a child, and it was Qiao Yu, this even became a plus point.

Mr. Yuan even felt that he had to keep an eye on Qiao Xi. Those professors with more ulterior motives had to be kept away from Qiao Xi.

……

As for Qiao Yu, if Mr. Yuan had not asked Qiao Xi to study at Huaqing, he would probably have been a little resistant to Tian Yan's arrangement.

It was finally summer vacation, but not letting him go home was a bit too much. Even a donkey in a production team needs to have a proper rest, right?
However, considering that Qiao Xi will be coming to Beijing in September and he will be able to see her every day, the boy's restless heart was healed.

never mind.

If he couldn't go back, then he didn't have to. He wasn't the only one at the Mathematics Research Center who couldn't go back.

Qiao Yu felt that it was nothing, but Xia Keke was the most depressed.

On the last day of the summer camp, Qiao Yu took Xia Keke to visit Mr. Yuan again.

To be honest, Xia Keke's performance was pretty good, but with Qiao Xi's performance as good as hers, she seemed a little ordinary.

So Mr. Yuan just gave him a few words of encouragement.

The general meaning is that you still need to study hard and take the college entrance examination, but you don't need to focus on mathematics, or mathematical research.

This is also understandable.

After the tutor's appetite was spoiled, he began to look down on children with less talent. After all, ordinary intelligence and genius intelligence are two different kinds of intelligence.

If I must explain it, it's probably that the upper limit of the former can be roughly estimated, but the upper limit of the latter cannot be estimated at all.

Even before parting, Yuan Lao even grumbled that Qiao Xi had wasted more than ten years. If he had met him ten years earlier, his achievements would probably be limitless.

Qiao Yu liked to hear this sentence. But even if we push it back another ten years, Qiao Xi is only 44 years old. Qiao Yu thinks that he is still quite young.

As for Xia Keke, she was probably shocked.

Qiao Yu was admitted to Yanbei University in advance without taking the college entrance examination, which she could understand. Her aunt Qiao was also admitted to Huaqing University in advance, and was accepted as a student by Mr. Yuan...

There is a feeling that my three perspectives as a young person have been overturned.

She knew that Aunt Qiao was also very capable, but she never expected her to be this capable.

The only pity was that Qiao Xi repeatedly told her not to tell anyone about this for the time being.

Xia Keke could only keep it to herself, which made her very upset. Not only could she not come with Teacher Yang, Qiao Xi even asked her not to tell her parents for the time being...

Fortunately, Xia Keke didn't hold it in for too long.

After returning to Star City, it didn't take long for the news to spread inevitably.

There is no way that it is as easy for adults to obtain student registration as it is for students.

He needs to deal with the community and various administrative departments in the jurisdiction, such as the district education bureau, police station, etc. He also has to go to Qiao Xi's high school alma mater to handle some procedures.

Thanks to Qiao Yu, Qiao Xi happened to be a famous person in the area, and the head of the district education bureau happened to be Principal Zhang who had just been promoted from Xingtie No. 1 Middle School...

So even though Xia Keke kept her mouth shut during the summer vacation and felt uncomfortable holding it in, Old Xia and Liu Lu still learned the news from other people.

There is no way, there are too many sources of information.

……

"Keke, Qiao Yu's mother is going to study at Huaqing? Did you know about this?"

"Hey, how do you know?"

"I heard it from your Aunt Wang while I was on duty. She also said that he had spread the news in the parents' group of Tieyi Middle School."

"Ha, that's what I told you. Of course I knew. Not only did I know that Aunt Qiao was going to study at Huaqing, but I also knew that Academician Yuan was going to accept Aunt Qiao as a student."

"Academician Yuan? Another academician? I remember Qiao Yu's mentor was also an academician."

"Academician Yuan Zhengxin, why don't you search on Baidu? He is a great mathematician, the mentor of Professor Qiao Yu, and a winner of the Fields Medal? Um, you know the Fields Medal, right?"

"Is this... Qiao Yu's fault?"

"It's definitely not just because of Qiao Yu. Academician Yuan arranged an exam for Aunt Qiao. Aunt Qiao passed. Alas, Qiao Yu also helped me get a chance, but unfortunately I didn't pass.

But Academician Yuan also told me that as long as I maintain my current grades, it won’t be difficult to get into Yanbei or Huaqing in the college entrance examination..."

While eating, they listened to what Xia Keke said and were completely shocked.

Before this, they had always felt sorry for the mother and son downstairs. One went to Yanbei and the other was about to go to Huaqing. The future achievements of the two were probably beyond their reach.

If Qiao Yu was suddenly discovered, it would be understandable. After all, he was still a genius who was still studying, and such things were often seen in the news.

But Qiao Xi is in her thirties after all, and she is not a student anymore... Really, it seems that there is no such thing in the movie.

This makes people feel a little unreal.

The most important thing is that these two people are neighbors they have known since childhood and are people who live around them.

So much so that when they went to bed at night, they were still talking about it.

"Qiao Xi is also a math genius? I can't tell."

"Nonsense. Can we see it? Did you see that Qiao Yu was a genius before?"

"That's right, but this is a good thing, right? Qiao Xi likes Keke very much. When Keke passes the college entrance examination and goes to Beijing, she will have someone to take care of her."

"Yeah, at the parents' meeting, the teacher said that Keke really has a chance of getting into Yanbei or Huaqing, hehe..."

"Okay, stop grinning and go to sleep."

……

When the Xia family knew about this, it basically meant that the entire community knew about it.

The specific manifestation is probably that more and more people say hello to her when she goes out...

There is no doubt that the neighbors' reputation towards the Qiao family has reached a peak, but for Qiao Xi, this is undoubtedly a very troublesome thing.

In fact, it is not just the railway community that is affected.

Qiao Xi’s alma mater, Xingcheng No. 1 High School, was actually also very confused. It was very baffling. How could a student who had graduated for more than ten years suddenly be admitted to Huaqing?

And it is said that he is the student appointed by Mr. Yuan...

Of course, for Xingcheng No. 1 Middle School, the news is more than that.

After all, Qiao Yu has become a legend in the Xingcheng education system. Even the current leaders of the city’s No. 1 Middle School would never have thought that Qiao Yu’s mother actually attended their own school sixteen years ago.

Moreover, Qiao Xi's situation is quite special.

I didn't have a job after graduating from high school. After my academic record was sealed by the school for a period of time, it was transferred to the local talent management center.

So the situation that had troubled Qiao Xi also made things much simpler.

After all, if someone else encountered this situation, the school would probably let him go to the talent center to transfer his files.

But when Qiao Xi went to consult how to deal with this matter, the school specially sent two teachers in charge of academic records to contact the talent center to help find Qiao Xi's academic record.

In addition, with the cooperation of the education department and the special dispatch of teachers from Huaqing University to help handle various matters, the whole process went very smoothly.

Moreover, according to Zhang Tiejun, in order to facilitate this matter, Yuan made a rare direct phone call to the ministry, reportedly begging the leadership to make an exception for the development of Chinese mathematics.

In short, this August was an unprecedentedly fulfilling month for Qiao Xi, and it also made her realize that she really couldn't stay in Xingcheng anymore...

After all, she really couldn't adapt to a life where she would be watched every time she went out and someone would invite her out almost every day.

Even the principal of No. 1 Middle School tentatively asked if I was willing to be interviewed...

Qiao Xi thought Qiao Yu was interviewed and it was just interesting, but if she were to be interviewed... Qiao Xi felt that she would definitely mess everything up.

So, after completing all the necessary procedures in Xingcheng, Qiao Xi contacted Mr. Yuan once, and then chose to go directly to Huaqing before September.

After confirming the itinerary with Mr. Yuan, Qiao Xi invited the Xia family to have dinner at a better restaurant in Xingcheng, and boarded the high-speed train to Beijing the next day.

……

While Qiao Xi was busy dealing with student status, Qiao Yu was also busy in the capital.

In fact, Qiao Yu was also very excited during this period, and it could be said that he was always in a state of excitement.

Qiao Xi was actually able to come to Huaqing to study. This was undoubtedly the biggest surprise for Qiao Yu at this stage of his life.

So naturally I am full of energy.

The proposal report on solving the twin prime conjecture has already been submitted to Professor Tian.

However, during this period of time, Qiao Yu did not think about this problem, but instead studied the relevant number theory knowledge and the contents of the Langlands Program.

Although Qiao Yu did have a high opinion of himself, he was still somewhat in awe of this global problem.

Just as Tian Yanzhen said, if these problems were really that simple, mathematicians wouldn't have spent their entire lives on them and gained nothing.

For example, the Riemann hypothesis, although it is one of the seven conjectures listed in the millennium, was only proposed by Riemann in 1859.

A century and a half has passed since then, and God knows how many studies and papers have been based on its establishment over the years.

Although the twin prime conjecture is two independent problems from the perspective of number theory, their commonality is that they are both closely related to the distribution of prime numbers.

It can be said that if the twin prime conjecture can be proved, then the mathematical tools and techniques used will most likely also be able to help prove the Riemann hypothesis.

Qiao Yu really wanted to prove himself as soon as possible. If telling Tian Yan that he wanted to solve this problem directly was a bit of bragging, now he was really determined.

On August 17, after lunch, Qiao Yu was flipping through his papers in his small study room as usual.

Today Qiao Yu is studying "Langlands Fundamental Lemma and Its Applications".

This is an interesting paper by a Vietnamese mathematician named Ngo Bao Chau, who used geometric methods to prove the fundamental lemma of automorphic forms in the Langlands program.

This breakthrough was named one of the top ten scientific advances of 2009 by Time magazine, which still had some credibility at the time.

It was precisely because of his achievements in this area that this Vietnamese mathematician won the 2010 Fields Medal.

Of course, this mathematician also became the first and only Fields Medal winner in Southeast Asia.

Just when he was watching the exciting part, Qiao Yu received a call from Tian Yanzhen.

"Come to my office right now."

After saying that, Tian Yanzhen hung up the phone without even waiting for Qiao Yu's response.

Qiao Yu had no way of refusing the mentor's call.

After standing up and stretching, he hurried downstairs and came to Tian Yanzhen's office.

In fact, Tian Yanzhen seemed somewhat elusive to Qiao Yu.

Most of the time, he didn't know whether his mentor was in the research center.

The study and research on him are now tending towards a free-range mode.

In the initial stage, I would set aside half a day every week to answer his questions, but recently I simply cancelled the time.

The reason given by Director Tian was that he now had a clearly-directed topic and no longer needed a tutor to answer his questions.

The only thing left now is the study and research progress report on Monday. This was not requested by Tian Yanzhen, but was done by Qiao Yu on his own initiative.

Of course, as a mentor, you can just ignore the content of Qiao Yu’s weekly reports.

But if there is no reply for a long time, Qiao Yu will ask: "Are you satisfied with my study and research results this week?"

If you don't look at it, it will embarrass your tutor.

After all, such a good seedling will make the tutor feel anxious and worried.

You can't just reply with a "satisfaction" without even looking at it.

With Qiao Yu's cleverness, he could definitely tell that the instructor hadn't read these things at all. So would this kid start to be perfunctory in the next week?
So in a sense, Qiao Yu continuously and reversely PUAs his dear mentor in a very conscious way.

No matter how busy they are, Academicians Tian Yanzhen and Yuan Lao must take out one or two hours every week to find out what Qiao Yu did last week.

Of course, this method is not suitable and cannot be popularized. Let's put it this way, if the big boss is really an academic master, he doesn't have the talent to do this, not only will he not be taken seriously, but he may also be directly blocked.

The reason is very simple. When talking about gains, if it is not handled properly, many times the results that students feel very proud of will seem ridiculous in the eyes of knowledgeable bigwigs.

To paraphrase what a famous Yanbei teacher said when teaching his students: "You are really amazing. You can always come up with ten thousand ways to make people feel that I am really useless in the field of education."

……

Arriving at Director Tian's office, Qiao Yu knocked on the door as usual and went straight in. To his surprise, there was someone else in the office today.

"Now that you are here, let me introduce you..."

"No need, Director Tian, ​​I know him, Professor Zhang Yuantang. I have seen Professor Zhang's photo online. Hello, Professor Zhang. I have read your paper, it is very interesting."

Qiao Yu answered quickly.

"Cousin Yuan, you see, this kid is not honest at all." Tian Yanzhen shook his head, pointed at Qiao Yu and said with a smile.

Of course, I'm not really angry.

Tian Yanzhen knew Qiao Yu's little thoughts and recognized him directly, which obviously showed that she valued Professor Zhang more than if he had introduced him himself.

After Zhang Yuantang looked at Qiao Yu, he also laughed and sighed, "You are indeed very young. Don't stand anymore, sit down."

After saying that, Zhang Yuantang patted the sofa next to him.

Qiao Yu immediately sat over obediently.

Of course he knew that Director Tian specifically invited this professor because he chose the twin prime conjecture.

After all, the professor in front of him is one of the top mathematicians in this field in the world.

It was after this mathematician first proved that there are infinitely many finite gaps between prime numbers that the number theory community launched a large-scale collaborative project.

Reduce his spacing limit from 246 million to .

These are the information that Qiao Yu has recently looked up.

Mathematics is like this, once someone gives a direction and breaks through a bottleneck, it will soon allow others to push it forward by a big step, until the next bottleneck appears.

Although Qiao Yu did not think that Professor Zhang's method could completely solve the twin prime conjecture and also solve the case where the spacing is 2, the accumulated experience of these older generation professors on this issue was indeed what he needed most.

And these experiences will not be fully reflected in the paper.

After exchanging a few pleasantries, Zhang Yuantang got to the point: "I heard from your advisor that you plan to do research on the twin prime conjecture?"

Qiao Yu nodded and said, "Yes, Professor Zhang, I have always been interested in the distribution of prime numbers."

"Oh?"

Zhang Yuantang smiled and asked, "You are interested in the distribution of prime numbers, so why did you focus on the geometric Langlands conjecture before? I have also read your paper and have always thought that you might be more interested in algebraic geometry."

Qiao Yu spoke without hesitation: "Because I have studied your paper, and I feel that the existing tools, whether it is the sieve method or the automorphic form, cannot fully prove the twin prime conjecture and the Riemann conjecture.

I think the Langlands Program may be a breakthrough in solving this problem. Starting from the properties of symmetry and invariants, we try to build a new algebraic geometry framework and even use geometric language to express the characteristics of prime numbers.

So you can see that my previous research was actually laying the foundation for the ultimate solution to the prime number problem. As for helping Professor Dennis's team to improve the proof of the geometric Langlands conjecture, that was an accident. "

"Accident?" Zhang Yuantang was stunned, then shook his head and nodded.

Then he glanced at Tian Yanzhen who was drinking tea, and he finally understood what it meant to be a newborn calf that is not afraid of a tiger.

I couldn't help but ask, "Do you know what a new framework represents?"

Qiao Yu nodded and replied, "I know. For example, this means that I have to build a completely new axiomatic system from scratch. And I have to make sure that this system is at least recognized by the mainstream mathematics community."

After these days of study, Qiao Yu became more confident when he talked about these things with Zhang Yuantang.

Zhang Yuantang subconsciously glanced at Tian Yanzhen who was quietly drinking tea next to him, smiled, and continued to ask: "So you plan to do this work alone? Construct a new axiomatic system, and then prove the twin prime conjecture?"

Seeing Zhang Yuantang's smile, Qiao Yu also smiled and replied, "Why not, Professor Zhang. Well, it doesn't have to be just one person. If necessary, I might invite my mother to join my team."

"Your mother?" Zhang Yuantang was stunned, probably unable to understand where Qiao Yu's confidence came from.

In fact, if he had not been studying twin prime numbers, he might not have had such doubts.

"Qiao Yu's mother, Qiao Xi, is currently a student of Mr. Yuan Zhengxin." Tian Yanzhen explained.

After saying that, Tian Yanzhen glared at Qiao Yu.

If he didn't explain this sentence, he was afraid that Zhang Yuantang would think Qiao Yu was joking.

"Oh?" Zhang Yuantang looked at Tian Yanzhen and was a little confused. He had heard of Qiao Yu's name, but Qiao Xi...

Wait, Zhang Yuantang suddenly thought of the paper that Qiao Yu had just published in Ann.Math not long ago. It seemed that there was a second author with the same name.

Did mother and son co-author a paper?
"Well...if it's a new axiom system..."

After a long silence, 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 compared with your new system, the twin prime conjecture is not that important."

Qiao Yu nodded seriously and said seriously: "Yes, solving the twin prime conjecture is just the beginning. Because everyone says 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 in the future that all non-trivial zeros of the zeta function are distributed on the critical line in the complex plane. "

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

"Gödel said that before proving the Riemann hypothesis, we need to find a new cornerstone for mathematics. I always thought that Grothendieck was the person who came closest to solving the cornerstone. If he hadn't been obsessed with it before.

How should I put it, Qiao Yu, I also have high hopes for your ability and admire your courage. But I hope you can keep a calmer mindset. The Riemann hypothesis has driven many mathematicians who studied it into a state of obsession.

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, I am very interested in your research.

Because to be honest, I have thought of many ways during this period. But I haven't figured out a specific entry point yet. "

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

"If you want my advice, it's that when you can't find a way in, put the question of prime numbers aside. Don't worry about prime numbers, but study the structure of numbers itself.

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

Prime numbers are just one phenomenon in the structure of numbers, and what you first need is to understand the more general behavior of numbers, their distribution laws, and their relationship to each other in different structures.

When you have done this and come back to the prime number problem, you may be able to find a natural path in this axiomatic framework to explain their distribution and properties..."

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

This made him very happy.

For a mathematician like Zhang Yuantang, discussing mathematical problems with a junior is not just about giving the junior a face or listening to the junior bragging, and he is willing to answer the questions carefully.

The key lies in the fact that the questions raised by Qiao Yu make him feel that the answers are meaningful.

This is actually the same principle as teachers teaching students.

If a student always asks the teacher questions that are so simple that they are obviously knowable, the teacher will not think that the student is studious.

I will only doubt in my heart whether the student is serious in class or whether he listens carefully. Naturally, he will not be passionate in answering, and may even be perfunctory.

However, if the questions raised by students are valuable and thoughtful, teachers can be motivated and even willing to spend some time discussing with such students.

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

That means that this student's questions not only motivated the teacher, but also made the teacher feel that discussing with this student could inspire his research.

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

As the two continued their discussion on twin prime numbers, many of Qiao Yu's questions directly touched Zhang Yuantang's sore spots. Even Tian Yanzhen, who was standing next to them, listened with great interest and could not help but occasionally interject a few words.

For example, Qiao Yu proposed whether it is possible to define a basic set, in which the elements are neither individual integers nor prime numbers, but are embedded in a space with topological and algebraic structures.

Each of these numbers is considered a point in this framework, and the relationship between points is defined by a specific mapping.

For example, by constructing a new moduli space in which the points are different pairs of prime numbers, we try to transform the existence of twin primes into a closed-loop problem in geometry...

I can only say that Qiao Yu's idea is indeed wild and unrealistic. But if you think about it carefully, it seems to be a good approach.

This continued until Tian Yanzhen felt that Zhang Yuantang was no longer able to handle it...

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

Because Zhang Yuantang's answers were getting slower and slower, and he took longer and longer to think, until he started looking at him from time to time, Tian Yanzhen finally reacted.

I subconsciously glanced at the time and it was already 6:30 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, let's discuss them tomorrow."

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

Then he looked at his instructor innocently, blinked, and said, "Um, Director Tian, ​​I haven't eaten yet either. 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 told you that the instructor is responsible for the students' meals? Can't you go to the cafeteria by yourself if you haven't eaten? Professor Zhang is already tired today. If you have any questions, we can 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 work."

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

"You're welcome. Your question is actually very insightful." Zhang Yuantang praised.

Qiao Yu smiled politely, then walked out, looking back every few steps.

He was also hoping that Professor Zhang would be polite so that he could shamelessly eat with the two professors.

To his disappointment, neither Tian Yanzhen nor Zhang Yuantang had any intention of keeping him.

so awkward……

……

After seeing Qiao Yu leave, Tian Yanzhen smiled and said, "My student is not bad, isn't he?"

Zhang Yuantang smiled bitterly: "More than good. I really can't handle his questions. At first I thought he was a little eccentric.

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

But I'm not sure if this idea will work. But if he can really do it according to this idea..."

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

"Haha, don't think about it, go eat first. You just got over the jet lag, you still need to rest. That kid has a lot of wonderful ideas, maybe he will have a lot of ideas tomorrow."

Tian Yanzhen said with a big laugh.

This was actually the reason why he canceled his half-day weekly tutoring session with Qiao Yu.

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, I can only provide some insights, but it can’t really fully answer Qiao Yu’s question.

If he had to go through an afternoon like this every week, Tian Yan really felt that his sense of mystery as a mentor would soon fade away...

Some students just can't be stared at all the time.

Zhang Yuantang shook his head, then stood up and made a joke: "Really, if I had known that you were such a difficult student, I would not have come."

……

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

The mentor who always loved him didn't even take him out to dinner... He planned to complain to Qiao Xi.

In terms of seniority, Qiao Xi is now Tian Yanzhen's junior sister. When Qiao Xi goes to Huaqing, she can mention this to Master Yuan...

It would be best to let his master's teacher talk to his own tutor. It is inappropriate to chase students away at dinner time.

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

"Mom, are you outside?"

"Well, I'm inviting 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! Look at what you are capable of... I haven't eaten yet! You should eat more and try to grow fat..."

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

“Okay, Keke, stop making trouble and let your Aunt Qiao answer the phone.”

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

"Did Mr. Yuan tell you that I'm going to Huaqing tomorrow?"

"Ah? You're coming tomorrow?" Qiao Yu was a little surprised when he heard this.

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

"You don't know? Then why did you call?"

"Why come tomorrow?"

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

Some people are born to adapt to life under the spotlight. In fact, Qiao Xi should have been able to adapt to it before.

But anyone who has been talked about behind their back for a few years would probably instinctively resist receiving too much attention.

Especially when the attention now overlaps with 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 find time to pick you up tomorrow. Director Tian has specially invited a professor to give a lecture, also tomorrow."

"You don't have to pick me up. Mr. Yuan said he has already arranged everything for me. Tell me what you want to talk about."

"Hey, Director Tian has been talking to Professor Zhang, who will give a lecture tomorrow, until now. Then he took Professor Zhang out for dinner and wouldn't let me go. When you come tomorrow, help me talk to Professor Yuan and find a chance to criticize Director Tian."

"Okay, I get it. You're itching for trouble, right? When I go to the capital tomorrow, I'll definitely beat you up tonight. Is there anything else? I'm hanging up now."

After saying that, the person on the other end really hung up the phone.

Listening to the "beep" sound coming from the phone receiver, Qiao Yu almost laughed out loud...

The tutor invited everyone to a big dinner, and his mother was also inviting everyone to a big dinner, but no one was interested in him.

Very good, Qiao Yu went straight out of the yard, picked up a car, rushed to the cafeteria to eat a quick meal, and then rushed back to his small study.

He wanted to go out to dinner with Tian Yanzhen, not because he missed the meal, but because today's discussion with Zhang Yuantang did give him some inspiration.

Not taking him out for dinner is a good opportunity for me to summarize some of his ideas first.

After turning on the computer, Qiao Yu quickly typed a title on the newly created document.

"A system of modal axioms on multiverses."

After thinking about it carefully, I suddenly felt that this definition of multiple spaces was not very accurate, so Qiao Yu changed it to "the generalized modal number theory axiom system on multiple transcendental spaces"

"One of the core problems of number theory is to understand the distribution of prime numbers and their regularity. However, classical number theory methods still lack effective tools for some key conjectures, such as the twin prime conjecture and the Riemann conjecture.

In order to break through the difficulties in these conjectures, this paper proposes a new mathematical axiom system - the generalized modal number theory system, which provides a new method for exploring the modal structure in number theory. "

Qiao Yu originally planned to write some acknowledgments here, reminding himself that if the framework was successfully built, he should thank Professor Zhang, with whom he had talked for a long time.

But thinking about not taking him out for dinner, I decided not to write about it for now. I'll write about it next time.

After thinking about it, Qiao Yu began to define his multiple transcendental spaces.

1. The definition of multiple transcendental spaces.

Definition 1.1: Modal space - multitranscendental space consists of countless modal spaces (α, β), each of which corresponds to a set of modal parameters (α, β) that affect the properties of numbers in the space.

Definition 1.2: Domain of modal parameters - The modal parameters (α, β) can take any value within the domain, which allows the modal space to change continuously in multiple transcendental spaces.

2. Existence of modal mapping.

In the multi-transcendental space, define the modal mapping

It means transferring the object from the modal space (α, β) to the modal space (γ, δ).

Definition 2.1: Modal mapping properties - Modal mapping has nonlinear and irreversible characteristics, and its behavior can change with the change of modal parameters.

Definition 2.2: Invariance conditions for modal mappings: If a modal mapping satisfies certain symmetry conditions, then the modal objects retain their modal properties unchanged after transformation.

……

After writing these on the document, Qiao Yu stopped and began to think.

A word from Professor Zhang Yuantang today made him make up his mind.

“To study prime numbers, you don’t have to study the prime numbers themselves first, but you can start with the structure of numbers.”

So he decided to simply expand the traditional numerical system into the framework of different modal spaces.

Directly make different mathematical objects have precisely defined modal structures and behaviors in the modal space, and build a generalized modal number theory system.

Then a series of number theory conjectures are transformed into problems in modal space.

This is a big idea, and Qiao Yu doesn't know whether it will succeed, but he plans to take advantage of Professor Zhang's stay in Yanbei for the next two days to build a framework and then do some targeted discussions.

After all, Director Tian has worked hard to invite people here, so he has to make them feel that their visit is worthwhile.

At this moment, Zhang Yuantang, who had followed Tian Yanzhen to the restaurant, suddenly sneezed a few times.

"Professor Zhang, please take care of your health. Are you overworked? Go to bed early tonight."

Tian Yanzhen next to him said with concern.

　The 11th day of November’s 10-word check-in is completed!
　　
　
(End of this chapter)