Chapter 144 About the axiom system of generalized modal number theory on multiple transcendental spaces
After the meal, Qiao Yu took Qiao Xi to play in the capital for three days. Then Qiao Yu was informed that he could not return to Star City 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 will be a Natural Science Foundation scientific research review meeting in late August. Tian Yan really hopes that Qiao Yu can also attend to gain experience.
Going home in this situation is a waste of time. So when we go back, it can only be Qiao Xi and Xia Keke.
Mr. Yuan asked Qiao Xi to come to Huaqing to report in mid-September.
Unlike Qiao Yu's situation, Qiao Xi may enroll in Huaqing in a 3+2+3 way.
So she needed to go back to Star City to prepare a series of documents and corresponding certificates.
Then come to Huaqing and take basic courses honestly with the leading class. Because Qiao Xi's foundation in advanced mathematics is a little worse than Qiao Yu's.
However, in Mr. Yuan's view, these don't matter. It's just a matter of substitute lecturers and professors working hard to do more small things.
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 Qiao Xi's arrival would cause those professors who were not too old to be single and not single to get excited.
Some people's excellence requires in-depth understanding to know. But some people's excellence can be seen on the outside. It's unfair, but there is no way. This world has never been truly fair since the day society was born.
At 34 years old, in the world of mathematics, he is no longer young from a research perspective, but in terms of age alone, he is actually not too old.
Those who have not yet graduated with a Ph.D. at this age cannot be counted as an exception. Huaqing already has one.
Even if Qiao Xi has a child, it's Qiao Yu. This is even a bonus.
Mr. Yuan even felt that he had to keep a close eye on Qiao Xi. Those professors who were careful and thoughtful had to keep them away from Qiao Xi.
…
As for Qiao Yu, if Mr. Yuan hadn't asked Qiao Xi to come to Huaqing to study, he would probably have resisted Tian Yanzhen's arrangement a little.
It's finally summer vacation, but it's still a bit too much to not let him go home. Even a donkey in the production team needs to rest properly, right?
However, considering that Qiao Xi will come to the capital in September and will be able to see her every day from now on, the young man's restless heart has been healed.
It doesn't matter anymore.
If you can't go back, don't go back. Anyway, he's not the only one at the Mathematics Research Center who can't go back.
Qiao Yu felt that nothing was wrong, and the most depressed person was Xia Keke.
On the last day of the summer camp, Qiao Yu took Xia Keke to visit Mr. Yuan again.
One thing to say, Xia Keke performed well. But with Qiao Xi Zhuyu in front, she seemed a bit ordinary.
So Mr. Yuan only gave a few words of encouragement.
The general meaning is that you still have to study hard, and you still have to 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 has been cultivated, children with slightly less talent are somewhat looked down upon. After all, ordinary intelligence and genius intelligence are two types of intelligence.
If it must be explained, it is probably that the upper limit of the former can be roughly estimated, while the upper limit of the latter cannot be estimated at all.
Mr. Yuan even muttered a few words when parting, saying that Qiao Xi had wasted more than ten years. If he had met him ten years earlier, his achievements would have been limitless.
Qiao Yu likes to hear this sentence. But even if we push it back ten years, Qiao Xi is only forty-four years old. Qiao Yu feels that she is actually quite young.
As for Xia Keke, she was probably shocked.
She actually understood why Qiao Yu was admitted to Yanbei University in advance without taking the college entrance examination. 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 a young person’s outlook on life has been subverted.
She knew that Aunt Qiao was also very powerful, but she really didn't expect that she could be so powerful.
The only pity is that Qiao Xi repeatedly told her not to tell anyone about it for the time being.
She could only hold it in her heart, which really depressed Xia Keke. Forget about being unable to 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 wasn't long before this matter inevitably spread.
There is no way that it is not as easy for adults to apply for student status as it is for school students.
You need to deal with the community and various administrative departments in the area, such as the district education bureau, police station, etc., and you also need to go to Qiao Xi's alma mater to go through some procedures.
Thanks to Qiao Yu, Qiao Xi happens to be a celebrity in the area, and the head of the district education bureau happens to be Principal Zhang, who has just been promoted from Xingtie No. 1 Middle School...
So although Xia Keke was tight-lipped during the summer vacation and felt uncomfortable, Lao Xia and Liu Lu still learned the news from other people.
No way, there are too many sources of information.
…
"Keke, Qiao Yu's mother is going to Huaqing to study? Do you know about this?"
"Hey, how did you know?"
"I heard what your Aunt Wang said when I was on duty. She also said that the news spread among the parents of Tieyi Middle School."
"Ha, let me tell you. Of course I know. Not only do I know that Aunt Qiao is going to Huaqing to study, but I also know that Academician Yuan wants 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 go search it on Baidu? He is a very powerful mathematician, the mentor of Professor Qiao Yu, and the winner of the Fields Medal? Well, do you know about the Fields Medal?"
"Is this... the reason for Qiao Yu?"
"It must not be just because of Qiao Yu. Academician Yuan arranged the exam for Aunt Qiao. As a result, Aunt Qiao passed. Hey, in fact, Qiao Yu also helped me fight for the opportunity, but unfortunately I failed.
But Academician Yuan also told me that as long as I maintain my current grades, it will not be difficult to get into Yanbei or Huaqing in the college entrance examination..."
While eating, they heard Xia Keke talk a lot, which completely shocked the two of them.
They had always felt sorry for the mother and son downstairs. One had gone to Yanbei and the other was about to go to Huaqing. The future achievements of the two were probably beyond their reach.
It would be understandable if Qiao Yu was suddenly discovered. After all, he is still a genius who is studying. You can often see this kind of thing in the news.
But after all, Qiao Xi is in her thirties, and she is not a student... Really, it seems that there are no movies like this.
This makes people feel somewhat unreal.
The most important thing is that these two people are neighbors they have been in contact with since childhood, and they are people living around them.
So much so that when they went to bed at night, the two of them were still talking about it.
"Qiao Xi is also a math genius? I can't tell."
"Nonsense. Can we see it? Have you seen that Qiao Yu is a genius before?"
"That's right, but is this a good thing? Qiao Xi likes Keke very much. When Keke takes the college entrance examination and goes to the capital in the future, she will have someone to take care of her."
"Yes, during the parent-teacher conference, the teacher said that Keke really hopes to be admitted to Yanbei or Huaqing, hehe..."
"Okay, stop giggling and go to sleep."
…
When everyone in Lao Xia's family knew about this, it basically meant that the entire community already knew about it.
The specific manifestation is probably that more and more people go out to say hello to her...
There is no doubt that the reputation of the Qiao family among the neighbors has reached its peak, but for Qiao Xi, this is undoubtedly a very troublesome thing.
In fact, it is not just the railway communities that are affected.
Qiao Xi’s high school alma mater, Xingcheng No. 1 Middle School, was actually very confused. It was very inexplicable. A student who graduated more than ten years ago was suddenly admitted to Huaqing?
And it is said that he is also the student appointed by Mr. Yuan...
Of course, for Xingcheng City No. 1 Middle School, the news is more than that simple.
After all, Qiao Yu has become a legend in the Star City education system. Even the current leaders of the city's No. 1 Middle School didn't expect that Qiao Yu's mother actually attended their own school sixteen years ago.
And Qiao Xi’s situation is quite special.
I have been unemployed since graduating from high school. After my school records were sealed for a period of time, they were transferred to the local talent management center.
So the situation that 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 adjust his position.
But when Qiao Xi went to consult on how to handle the matter, the school sent two teachers in charge of student status to contact the Talent Center to help find Qiao Xi's student status.
Coupled with the cooperation of the education department and teachers specially sent from Huaqing to help with various matters, the whole process went very smoothly.
And according to Zhang Tiejun, in order to facilitate this matter, Mr. Yuan rarely called the ministry directly. It is said that he begged the leaders to make an exception for the development of Chinese mathematics.
In short, this August has been more fulfilling for Qiao Xi than ever before, and she also found that she really can't stay in Xingcheng...
After all, she really couldn't adapt to a life where she would be watched every day when she went out, and someone would invite her to her almost every day.
Even the principal of No. 1 Middle School tentatively asked if he was willing to be interviewed...
When Qiao Yu was interviewed, Qiao Xi only found it interesting, but asking her to be interviewed... Qiao Xi felt that she would definitely mess everything up.
So, after completing all the procedures in Star City, 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 Lao Xia and his family to have a meal at a better restaurant in Star City, and boarded the high-speed train to the capital the next day.
…
While Qiao Xi was busy processing her student registration, Qiao Yu was also busy in the capital.
In fact, Qiao Yu was also very excited during this period. It should be said that he was always in a state of excitement.
Qiao Xi actually came to Huaqing to study, which was undoubtedly the biggest surprise at this stage of life for Qiao Yu.
So naturally I am very motivated.
The proposal report on solving the twin prime conjecture has already been submitted to Director Tian.
However, Qiao Yu did not think about this issue during this period, but instead supplemented the relevant knowledge of number theory and the content of the Langlands Program.
Although Qiao Yu does have a high self-esteem, he is still a little in awe of this kind of world-wide problem.
As Tian Yanzhen said, if these problems were really that simple, a mathematician would not spend his whole life on them and get nothing.
For example, the Riemann Hypothesis, although it is one of the seven major conjectures listed in the millennium, was only proposed by Riemann in 1859.
A century and a half has passed now, and God knows how many studies and papers over the years have been based on its establishment.
Although the twin prime conjectures are two independent problems from the perspective of number theory, their commonality is that they are closely related to the distribution of prime numbers.
It can be said that if the twin prime conjecture can be proven, then the mathematical tools and techniques used will most likely also help prove the Riemann Hypothesis.
Qiao Yu wanted to prove himself as soon as possible. If telling Tian Yan that he really wanted to solve this problem directly was a bit of bragging, now he was really thinking about it.
On August 17, after lunch, Qiao Yu was reading papers in his small study room as usual.
What Qiao Yu is studying today is "Langlands' Fundamental Lemma and Its Applications".
This is a paper by a Vietnamese mathematician, Ngo Bao Chau, which is very interesting. He used geometric methods when proving the fundamental lemma of automorphic forms in the Langlands program.
This breakthrough was rated as one of the top ten scientific advances in 2009 by Time magazine, which had some credibility at the time.
It was precisely because of this achievement that the Vietnamese mathematician won the Fields Medal in 2010.
Of course, this mathematician also became the first and only Fields Medal winner in the entire Southeast Asia region.
Just when he saw the wonderful point, Qiao Yu received a call from Tian Yanzhen.
"Come to my office quickly."
After saying that, Tian Yanzhen hung up the phone without waiting for Qiao Yu's response.
Qiao Yu couldn't refuse the mentor's call.
After standing up and stretching, he hurried downstairs and came to Tian Yanzhen's office.
In fact, Tian Yanzhen is somewhat elusive in Qiao Yu's opinion.
Most of the time, he didn't know whether his mentor was at the research center.
His study and research are now increasingly in a free-range mode.
In the initial stage, half a day was set aside every week to answer questions for him. However, the time for answering questions has been canceled recently.
The reason given by Director Tian is that he now has a clearly targeted topic and no longer needs the tutor to answer questions for him.
The only thing left now is the study and research progress report on Monday. This is not what Tian Yanzhen requested, but what Qiao Yu took the initiative to do.
Of course, as a tutor, you can 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 read it yet, it will embarrass the instructor.
After all, such a good seedling will make the instructor worry about gains and losses.
You can't just respond casually with satisfaction without even looking at it.
With Qiao Yu's cleverness, he can definitely tell that the instructor has not read these things at all. Then will this kid start perfunctory in the next week?
So in a sense, Qiao Yu continued to PUA his dear mentor in a very conscious way.
The two academicians Tian Yanzhen and Mr. Yuan, no matter how busy they are, must spare one or two hours every week to understand what Qiao Yu did last week.
Of course, this method is not suitable and cannot be popularized. Let's put it this way, because if the big boss is really an academic master and does not have the talent to dare to play like this, not only will he not be taken seriously, but he may also be directly blacklisted.
The reason is also very simple. When talking about gains, if it is not handled well, many times the results that make students feel proud will be ridiculous in the eyes of well-informed bosses.
To paraphrase what a well-known tutor from Yanbei said when teaching students: "You are really amazing. You can always come up with 10,000 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 another person in the office today.
"You're here, let me introduce you..."
"No need, Director Tian. I know Professor Zhang Yuantang. I have seen Professor Zhang's photo on the Internet. Hello Professor Zhang, I have read your paper, it is very exciting."
Qiao Yu answered quickly.
"Cousin Yuan, you see, this guy 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 more importance to Professor Zhang than him introducing him.
After Zhang Yuantang looked at Qiao Yu, he also laughed and sighed: "She is indeed very young. Stop standing and sit down."
After speaking, Zhang Yuantang patted the sofa next to him.
Qiao Yu immediately sat over obediently.
Of course he knew that Director Tian specially invited this professor here because he chose the twin prime conjecture.
After all, the professor in front of me is one of the top mathematicians in this field in the world.
It was precisely after this mathematician proved for the first time that there are infinitely many finite intervals between prime numbers that the number theory community launched a large-scale collaborative project.
Reduces his spacing cap from 70 million to 246.
This is all the information that Qiao Yu has recently accessed.
Mathematics is like this. Once someone gives a direction and breaks through a certain bottleneck, others will soon be able to take a big step forward.
Until the next bottleneck appears.
Although Qiao Yu did not think that Professor Zhang's method could really completely solve the twin prime conjecture and the situation where the distance was 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 a few pleasantries, Zhang Yuantang got to the point: "I heard from your instructor 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. Why did you stop focusing on the Langlands Conjecture in geometry? I have also read your paper and always thought that you might be more interested in algebraic geometry."
Qiao Yu opened his mouth without hesitation: "Because I have studied your paper and feel that the twin prime conjecture and Riemann Hypothesis cannot be fully proved with the existing tools, whether it is the sieve method or the automorphic form.
I think the Langlands Program may be a breakthrough in solving this problem. Starting from symmetry and the properties of invariants, try to build a new algebraic geometry framework, and even use geometric language to express the characteristics of prime numbers.
So you see, my previous research was actually the foundation for the final solution to the prime number problem. As for helping Professor Dennis’ team improve the proof of the geometric Langlands conjecture, it was an accident.”
"Accident?" Zhang Yuantang was startled, then shook his head and nodded again.
Then he glanced at Tian Yanzhen who was drinking tea. He finally knew what it means for a newborn calf to not be afraid of tigers.
I couldn't help but ask: "Then do you know what a new framework represents?"
Qiao Yu nodded and replied: "You know, for example, this means that I have to build a new axiomatic system from scratch. I also need to make this system at least recognized by the mainstream mathematics community."
After studying these days, Qiao Yu felt more confident when talking to Zhang Yuantang.
Zhang Yuantang subconsciously glanced at Tian Yanzhen, who was drinking tea silently next to him, and smiled, and continued to ask: "So you plan to do this work alone? Build 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, actually it doesn't have to be one person. If necessary, I may invite my mother to join my team. "
"Your mother?" Zhang Yuantang was stunned, probably because he couldn't understand where Qiao Yu's confidence came from.
In fact, if he hadn't been studying twin prime numbers, maybe he wouldn't have such doubts.
"Qiao Yu's mother Qiao Xi is currently a student of Mr. Yuan Zhengxin." Tian Yanzhen explained next to her.
After saying that, Tian Yanzhen glared at Qiao Yu.
If he didn't explain this sentence, he was afraid that Zhang Yuantang would think that Qiao Yu was fooling around.
"Oh?" Zhang Yuantang glanced at Tian Yanzhen, a little confused. He had heard of Qiao Yu's name, but Qiao Xi...
Wait, Zhang Yuantang suddenly thought of the paper Qiao Yu had just published on Ann.Math not long ago. There seemed to be a second author with such a name.
Mother and son co-authored a paper?
"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."
After saying that, the other person actually hung up the phone.
Listening to the "beep" sound coming from the receiver of the mobile phone, Qiao Yu almost became angry...
The tutor is inviting people to a big dinner, and my mother is also inviting people to a big dinner, but no one cares about him.
Very good, Qiao Yu went straight out of the yard, swept the car, rushed to the cafeteria to have a quick meal, and then rushed back to his small study.
The reason why he wanted to go to dinner with Tian Yanzhen was of course not because he was missing the meal, but because today's discussion with Zhang Yuantang really gave him some inspiration.
Without taking him to dinner, I just want to summarize some of his thoughts first.
Turning on the computer, Qiao Yu quickly typed a title on the newly created document.
"Modal axiom system on multiple spaces."
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 axiom system of generalized modal number theory on multiple transcendental spaces."
"One of the core issues in number theory is to understand the distribution and regularity of prime numbers. However, classical number theory methods still lack effective tools for some key conjectures. For example, the twin prime conjecture, Riemann's conjecture, etc.
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. He reminded himself that if the framework was successfully built, he would like to thank Professor Zhang, who had chatted with him for a long time.
But I thought I didn’t take him to dinner, so forget it, I won’t write it now. I’ll talk 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-multiple transcendental space is composed of countless modal spaces (α, β). Each modal space corresponds to a set of modal parameters (α, β). These parameters affect the properties of the numbers in this space.
Definition 1.2: The value range of modal parameters - the modal parameters (α, β) can take any value within the definition domain, which allows the modal space to continuously change in multiple transcendental spaces.
2. The existence of modal mapping.
In multiple transcendental spaces, define modal mappings
Represents the transfer of objects from modal space (α, β) to modal space (γ, δ).
Definition 2.1: Modal mapping properties - Modal mapping has nonlinear and irreversible characteristics, and its behavior can change with changes in modal parameters.
Definition 2.2: Invariance condition of modal mapping - If the modal mapping satisfies certain symmetry conditions, the modal object maintains its modal characteristics unchanged after transformation.
…
After writing these contents on the document, Qiao Yu stopped and started thinking.
Professor Zhang Yuantang's words today made him make up his mind.
"To study prime numbers, you do not necessarily have to study the prime numbers themselves first, but you can start with the structure of the numbers."
So he decided to simply extend the traditional numerical system to the framework of different modal spaces.
Directly allow different mathematical objects to 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.
Qiao Yu didn't know whether this big idea would succeed, but he planned to take advantage of Professor Zhang's two days in Yanbei to lay out the framework first, and then do some targeted discussions.
After all, Director Tian finally invited people here, and he had to make them feel that their visit was worthwhile.
At this moment, Zhang Yuantang, who had followed Tian Yanzhen to the restaurant, suddenly sneezed several times.
"Professor Zhang, please pay attention to your health. Are you too tired? Go to bed early tonight."
Tian Yanzhen said with concern next to him.
Completed the 10th day of November 10,000-word punch-in!
Chapter completed!