Chapter 146 If you want to apply, apply for a key research project!

"Is your modal dependency design too arbitrary?"

"Grandpa, how can you be so random? This leaves enough room for future expansion. Integers can also be generalized to P-radical numbers. So the structure of modal numbers is the same.

As long as it is defined systematically using specific modal mapping or directly making modal equations, the consistency and interpretability of the mathematical structure can be maintained..."

…

"Isn't your definition of modal volume operator complicated? Please show me how to operate it in detail!"

"No, grandpa, this just looks complicated. It is actually a generalization of classic convolution. For elements that generally satisfy rotational symmetry, the convolution operation will not change with the position in space.

For another example, for the modal space on the unit circle, the uniform measure dμ(x,y)=dθ in polar coordinates can be used, and convolution no longer relies on complex multivariable measures.

If it is in a symmetric modal space, since the convolution maintains symmetry, the calculation of the convolution can be simplified through Fourier transform. Just convert the convolution operation into a product in the frequency domain.

Come on, let me give you an example, but don’t worry, let’s do it one by one. Let’s start with the symmetric modal convolution formula. We translate the two functions directly from the classic convolution and sum them up..."

As he said that, Qiao Yu picked up the paper and pen.

One old and one young, one question and one answer. It's just that the questions are few and the answers are many...

When Mr. Yuan asked a question, Qiao Yu had to answer a lot, and occasionally write a lot of explanations on paper with a pen.

Tian Yanzhen and Zhang Yuantang lost interest in chatting next to them and simply moved behind the old man and Qiao Yu to see Qiao Yu's derivation.

Just like that, three big-shot figures came together and surrounded Qiao Yu.

This is what Tian Yanzhen's assistant, Xiao Li, who has yet to be named, saw when he opened the office door with Qiao Xi.

Xiao Li was still hesitating whether to say something, but fortunately Tian Yanzhen heard the noise and looked up.

I was surprised, but I reacted immediately.

"Qiao Xi is here, please come in."

Qiao Yu, who was doing the derivation, immediately looked up when he heard Qiao Xi's name, and said in surprise: "Mom."

Mr. Yuan glanced at Qiao Xi and said seriously: "Qiao Xi, sit down casually for now, and wait a while for Qiao Yu to explain some of his thoughts."

Zhang Yuantang looked confused at the woman who looked like a celebrity standing at the door.

Is Qiao Yu's mother so young?

Noticing that an old professor whom he had never met before was looking at him, Qiao Xi smiled and nodded as a greeting.

"Okay, Mr. Yuan, Professor Tian. Qiao Yu, please feel free to explain."

He said softly, looked at Qiao Yu curiously, and then shook his head slightly. Qiao Yu lowered his head, but the derivation of the manuscript was a little faster.

Qiao Xi randomly found a seat and sat down, curiously watching the three old people surrounding Qiao Yu, looking serious and thoughtful.

There were no empty seats around Qiao Yu, so she was too lazy to go over and join in the fun. Seeing how the two academicians were listening so carefully, she probably didn't understand.

Qiao Xi even suspected that Qiao Yu deliberately chose today to show off in front of her.

Qiao Xi has long been used to it. The way Qiao Yu showed off in front of her grandfather and her since childhood was different from other children.

In the words of this kid: "Language is the palest, weakest and most worthless thing in the world."

Qiao Xi didn't even know where Qiao Yu, who was still young at the time, got these messy views.

She suspected that it was Grandpa Qiao Yu who taught him. This old man liked to talk to children about things that children should not understand at all, but Grandpa Qiao Yu would never admit it as long as he was not caught in the act.

Well, for Qiao Xi, spending time alone is not difficult. There will be no mess of negative emotions such as loneliness, boredom, embarrassment, or not being taken seriously, and there will be no random speculation about other people's thoughts.

Because as long as you sit there quietly and let yourself go, the difficult time will pass in a daze.

"This is all I can think of now. I think this framework is feasible. I feel that as long as I complete this axiom system, I will definitely be able to solve the twin prime conjecture in the future."

Qiao Yu finally concluded.

After saying that, he glanced at Qiao Xi, who was sitting opposite. Then he showed a boyish smile.

In fact, given Qiao Yu's age - a sixteen-year-old boy, as long as he smiles, he should feel like a teenager.

But if it wasn't in front of Qiao Xi, Qiao Yu's smile would rarely be so pure.

"Well, it's interesting, very interesting. If you actually make this, it will be included in the textbook."

Yuan Zhengxin took Qiao Yu's manuscript and said something.

"Yes, let's not mention other meanings. With the current level of confusion in the symbols of the mathematical system, the emergence of such a programmatic system can at least reunify the mathematical symbols.

In a paper I was reviewed last time, both sharp and flat were used. If this continues, I suspect that even the high and low clefs in mathematics papers will be used in the paper."

Zhang Yuantang echoed from the side.

Tian Yanzhen shook his head and said: "This idea cannot be described by a single framework. It is a highly inclusive research platform.

In particular, the significance of contextualizing number theory geometry and disassembling number theory problems into geometric spaces for analysis will not be discussed in detail. The purpose of inviting you here is to discuss how to do this project."

After all three people expressed their opinions, Qiao Yu said, "Well, how about I take my mother out for a walk first?"

Before Tian Yanzhen could answer, Yuan Zhengxin smiled and patted his shoulder, saying, "Go, go, but Qiao Xi, don't let Qiao Yu run too far away. We'll go have dinner together after we finish talking."

"Okay, Grandpa Shi."

After saying that, Qiao Yu stood up, came to Qiao Xi, and said, "Mom, let's go and let the professors discuss things. I'll take you around first."

"Yes." Qiao Xi stood up, nodded to her tutor, her son's tutor, and Professor Zhang Yuantang opposite, and then took Qiao Yu's hand and walked out of Tian Yanzhen's office.

…

"Are there any results again?" Qiao Xi asked her son beside her as she walked out of Tian Yanzhen's office.

"Yes, it's a big achievement." Qiao Yu said seriously without the exaggeration and extravagance when reporting to Mr. Yuan.

"Oh." After agreeing, the two of them had already walked out of the small building. Qiao Xi felt that communicating with Qiao Yu today was a bit strange.

Last time she came here just to see Qiao Yu, but this time she will settle in the capital for a while and officially start her college life.

Qiao Yu also changed from her son to something like a classmate or even a fellow student.

"Why don't you ask me what my great achievement is?" Qiao Yu finally couldn't help but turned to look at Qiao Xi and said.

Qiao Xi said confidently: "Because I definitely don't understand what you said."

Qiao Yu felt that this was probably one of the reasons why Mr. Yuan fell in love with his mother.

He even suspected that Qiao Xi herself didn't know that she had the ability to get to the bottom of any problem, leaving him helpless every time.

However, this did not affect Qiao Yu's arrogant explanation: "I have constructed an axiom system that can discuss number theory and geometry under the same system.

In other words, I will study number theory in the future, and you will study geometry, and we can still study the topic together. I will break down the number theory problems that need to be solved.

At that time, I will be able to appoint you to my team to be responsible for the analysis and proof of the geometry part. So Qiao Xi, you should seize the time and study hard."

"Qiao Yu!" Qiao Xi stopped and looked at her dear son.

"What?" Qiao Yu, who felt that he was performing well, glanced at his mother who was always very gentle.

"What did you call me just now?"

"Qiao Xi, what's wrong? The world is dynamic, and of course the names can change. For example, of course I should call you mom at home, but we are at school now.

Well, isn't our current relationship in school just like... Ouch...Mom, Mom, stop twisting, your ears will really fall off, they hurt..."

"Oh, what should you call me in school from now on?"

"Mom, it must be mom."

"Well, Qiao Yu, you are still the same as when you were a child, so well behaved!"

…

The professors who were still in the office naturally didn't care about the little incident between mother and son in the courtyard.

After all, they know better than Qiao Yu what this wild idea means to the world of mathematics.

From the Langlands Program to the Geometry Langlands Program... what the Western mathematical community has always hoped to do is to build a bridge between different research directions in mathematics.

The Langlands Programme, in particular, has always been recognized as one of the most ambitious and far-reaching theories in modern mathematics.

The core idea is to try to establish deep connections between two seemingly unrelated fields in mathematics: number theory and representation theory.

And through this connection, it provides a new unified perspective and builds a bridge between different branches of mathematics.

Qiao Yu geometrizes number theory by building a geometric environment and using geometric tools such as modal distance and modal convolution.

Although Qiao Yu did not propose multiple interrelated sub-conjectures like the Langlands program, trying to clarify the correspondence between Galois representation, automorphic forms and specific conjectures of the L function, etc.

But Qiao Yu has achieved a de facto conceptual unification. If it succeeds, no, it should be said that once it succeeds, it will completely rewrite the way of studying all number theory problems in the world.

And in a sense, the sub-conjectures of the Langlands program can also be included in the framework of metaphor construction for study.

Obviously this will be a milestone in the history of mathematics.

So for many people, coming to this ordinary day may be witnessing and participating in history.

…

"This subject must apply for a national foundation project." After Qiao Yu left the office, Tian Yanzhen said directly.

Yuan Zhengxin nodded, and then said unceremoniously: "Qiao Yu was jointly trained by us."

Zhang Yuantang couldn't help but ask: "Qiao Yu is already a graduate student? If I remember correctly, in the past, Huaxia required at least a graduate student's subject to apply for the National Foundation, right?"

Tian Yanzhen explained with a smile: "That was before. Since the year before last, we have started a trial program where outstanding undergraduate students can apply for national foundation projects.

There are currently eight universities in China that outstanding undergraduate students can apply for the National Natural Science Foundation of China. Yanbei University and Huaqing University happen to be among these eight universities."

Zhang Yuantang opened his mouth, but didn't say anything.

Good guys, you can apply for national foundation projects as an undergraduate.

Of course, Zhang Yuantang is not saying that Qiao Yu’s idea is not worthy of applying for a national foundation. The main reason is that he feels that Qiao Yu is completely a special case.

However, if it is only tried out in eight universities, there is nothing wrong with it.

After Yuan Zhengxin patiently listened to Tian Yanzhen's explanation, he said: "In this case, this will be submitted as a joint project of the two major mathematical research centers of Huaqing and Yanbei.

The person in charge of the project should still be Qiao Yu. You should guide Qiao Yu to write out the project book as soon as possible. In addition, it is not just about applying for a national foundation. I think this project needs to be submitted to the national key research and development plan."

Tian Yan really laughed. He specially made a phone call to invite Yuan Zhengxin for this purpose.

For other undergraduates, applying for Natural Science Foundation projects may be difficult.

But if it's Qiao Yu, it's actually not that difficult. Don't say he is Qiao Yu's mentor.

Even if he is not Qiao Yu's mentor, just because Qiao Yu gave a 60-minute report at the World Congress on Algebraic Geometry this year, the judges of the Natural Science Foundation Review Committee will have some ideas.

But it's not that simple to apply for a national key research and development program. Ultimately, Qiao Yu is too young.

The sixteen-year-old person in charge of a key research and development project will undoubtedly cause great controversy.

As the saying goes, where there are people, there are rivers and lakes. Who can guarantee that Qiao Yu will be able to create this framework?

As long as people give some reasonable doubts, or even say Qiao Yu is still young and don't be so anxious, this matter can be delayed.

It would be a bit reluctant to rely on him or Yanbei University alone to promote this matter. But if Huaqing, represented by Mr. Yuan, promotes it together, the situation will be different.

"Sir, I think so too. No matter what, we must submit it. After all, once this project is successful, it will be helpful for analysis, optimization, gaming and regulation of various complex systems.

We at Yanbei University will set up a special class to take the lead in promoting this matter, and I will need your help and cheers. Of course, it will be in the name of joint research between the two parties."

Tian Yanzhen followed Yuan Zhengxin's words.

Yuan Zhengxin glared at Tian Yanzhen, but thinking that Qiao Yu's current student status was still at Yanbei University, he swallowed the words that came to his lips.

However, he added: "Yes, but since it is a joint research, the number of personnel participating in this project in Huaqing must be roughly the same as that in Yanbei."

Tian Yanzhen nodded, and then added: "I think Qiao Yu will also consider this. And since he is the proposer and person in charge of the project, why not let him decide. We will each provide him with a How about letting him choose from the list?"

Yuan Zhengxin nodded. At least Tian Yan had no selfish motives for this proposal. Even if he had selfish motives, it was for Qiao Yu, so he could accept it.

Not to mention that Qiao Yu has always called him grandpa, just because Qiao Xi is his student now, when making a choice, Qiao Yu will definitely not deliberately exclude the names reported by Huaqing.

"Ahem..." Zhang Yuantang next to him finally couldn't bear it anymore and coughed twice, and then successfully attracted the attention of the two of them.

"Actually, I have a suggestion. Why don't I go back and promote this cooperation. I think the University of Santa Barbara will also be interested in participating in this basic mathematics research work.

I mean, if it succeeds, it can also increase the attention paid to this basic mathematics project. Cross-border cooperation can help this research."

Tian Yanzhen and Yuan Zhengxin looked at each other, and then Tian Yanzhen pondered for a moment and replied sincerely: "Professor Zhang, to be honest, I very much hope to promote this cooperation.

But at this time, I think your thinking is still too simple. The problem is probably not on our side, but on your side."

This answer made Zhang Yuantang not sure how to answer for a while, and he was even a little frustrated.

Because what Tian Yanzhen said is actually correct, it does not mean that the two sides cannot cooperate at all now, especially in this basic mathematics, there are still channels for communication.

But if we really want to cooperate, there are many things that need to be reviewed now, which are very detailed and may even cause trouble for the school.

Therefore, for schools, many times they adopt the attitude that doing more is worse than doing less.

Who would have thought that after decades of shouting for global integration, the world would become more and more closed. It has even affected the field of basic academic research.

For people who are devoted to academic studies, this is obviously abnormal. But unfortunately, they can't change anything.

However, Tian Yanzhen changed the subject and said, "But I have a suggestion. If you are also interested in this project, why not cooperate in your own name?"

While Zhang Yuantang was still thinking, Yuan Zhengxin suddenly said: "By the way, will the Natural Science Foundation review team meeting be held next Tuesday?"

"Yes, Mr. Yuan." Tian Yanzhen replied.

"I'll go there too this time." Yuan Zhengxin said immediately.

Tian Yanzhen nodded.

The old man is also one of the leaders of the expert team of the review committee. He was too lazy to participate in the past. If he wanted to participate, he would definitely have a seat.

"By the way, I took the child's manuscript." Yuan Zhengxin said confidently.

The old man neatly organized Qiao Yu's handwritten manuscript yesterday and what he wrote during today's explanation.

"Well, this..."

"You want him to write another one." Yuan Zhengxin said without refusal.

Tian Yan really stopped talking.

…

Dinner was at Yanbei University.

Qiao Yu was in a bad mood.

Facts have proved that for a filial child, bloodline suppression is almost an unsolvable problem.

We are classmates, and my mother can pull his ears without hesitation. This means that even if the two of them really have a teacher-student relationship, my mother will still pull his ears without hesitation.

He still had no place to reason.

Okay, Qiao Yu admits that he is still naive. Unless he can treat Qiao Xi the same way he treats outsiders, otherwise he will always be eaten to death by his mother.

Professor Zhang Yuantang also looked a little preoccupied. However, Mr. Yuan and Director Tian were in high spirits. Although they did not drink, it could be seen from their attitude towards Qiao Xi.

In fact, compared to the three professors, Qiao Xi can be considered a young person. Even compared to Tian Yanzhen and Zhang Yuantang.

But everyone was very polite, and we didn't talk about mathematics at the dinner, only the local customs of Star City.

A new generation of internet celebrity city always has something to talk about.

After dinner, Tian Yanzhen took Qiao Yu and Professor Zhang to put Yuan Zhengxin and Qiao Xi in the car.

Qiao Yu actually wanted to see Qiao Xi's accommodation arrangements at night, but Tian Yanzhen didn't allow him.

Yuan Zhengxin didn't make the decision for him, and even joked before leaving: "Don't worry, grandpa promises to arrange everything for your mother. If you feel dissatisfied when you come to Huaqing tomorrow, you can trouble grandpa."

…

After watching Mr. Yuan leave, Tian Yanzhen took Qiao Yu to send Professor Zhang to the hotel, and then took Qiao Yu back to the research center.

"Come to the office with me."

"Ah? Director Tian, ​​it's so late today, why don't you go back?"

"What? You still want to sneak away to Huaqing after I leave? Don't think about it, I'm not free tonight."

"Um... the mathematician still has to work overtime?"

"What do you mean? Mathematicians only need brains to do scientific research. You have been to a chemical laboratory. People do not only need brains but also physical strength to do scientific research! So don't worry, there will be more opportunities for you to work night shifts in the future. Very good!"

…

After obediently following Tian Yanzhen into the office, Qiao Yu discovered that two stools had been placed at the instructor's desk.

"Come, sit next to me."

Well, it seems that I really want to accompany him.

Qiao Yu sat down obediently, and then saw Director Tian open the computer and bring up a bunch of files.

"Tonight I will guide you to fill in some formatted content. You can go back and fill in some technical related content. Leave it to me tomorrow."

"Application form for the National Natural Science Youth Foundation?"

"Yes, fill in the major research project as the first funding category."

"Um...this...are you sure it's a major research project?"

"If you are asked to fill it in, just fill it in."

"Oh, what about the description of this subcategory?"

"Mathematical logic."

"oh……"

Qiao Yu stopped talking nonsense and filled out the application form carefully as Tian Yanzhen asked. However, his mind couldn't help but think of what Lao Xue once said to him...

"You just need to find a good mentor who can handle the situation..."

The experience of people who have been there is really useful.

A different supervisor might not have had the courage to ask him to apply for a major research project directly...

Doesn't this sound very noble?

Tian Yanzhen was still murmuring in his ears: "The auxiliary instructions should be based on the guide. You will not only apply this time in the future, but you must remember it and check it."

There is also a research team that has not been established yet, but a list will be given to you in the next two days. The team members are from Yanbei and Huaqing. It is up to you to choose..."

"Ahem... Well, Director Tian, ​​let me ask, can I choose Professor Xue?"

"I will put him on the list. The unit will include us and the Huaqing Mathematical Research Center... You should have no problem with the abstract. It is best to be more concise than the abstract of the paper..."

…

Just like that, when Qiao Yu came out of Tian Yanzhen's office, it was already past ten o'clock in the evening.

However, only a small part of the application form has been filled in. The larger parts have not yet been filled out.

For example, the basis for project establishment, research content, project features and innovations, annual research plan and expected research results, etc. are all filled in.

Especially since the two parties jointly established the project, he also specifically explained the reasons...

In addition, he also needs to write a beautiful resume for himself.

Unfortunately, he is only sixteen years old and is already old enough to write a resume.

However, Tian Yanzhen had already given him a complete explanation of the key points for filling in these contents. Qiao Yu basically knew how to write them.

To be honest, Qiao Yu actually had nothing to be dissatisfied with.

To be able to have a big-name academician mentor spend more than two hours instructing him to fill out this kind of project document is definitely a blessing that takes several lifetimes to acquire.

It is no exaggeration to say that if Chen Zhuoyang dared to make such a request, Tian Yanzhen's words of "go away" would be a compliment to him.

Qiao Yu suddenly felt sorry for this senior brother.

Why are you in such a hurry to graduate? Otherwise, maybe you can take him to participate in this major national research project. When this project is completed, won't your resume be beautiful?

On the way back to the room, Qiao Yu was still thinking about various thoughts, but when he sat down in front of the computer, he no longer thought about these.

Director Tian and Mr. Yuan gave him the opportunity, so he naturally had to make good use of it. Anyway, he wasn't feeling sleepy yet, so he planned to write out the basis for the project, the research content, and the characteristics of the project while his mind was still clear.

In Director Tian’s words, these are the top priority. He even hinted to him that there is no need to be afraid. Even if you brag about your awesomeness, he and Mr. Yuan will help you find out...

What a coincidence...

He's quite good at this.

Just after writing 2,000 words in the project book, the phone suddenly rang.

Qiao Yu thought it was Qiao Xi who called him after she settled down, but when he picked it up, he saw that it was Professor Xue.

"Hello……"

"Qiao Yu, Academician Tian wants to apply for a national key project for you?"

"Um... did the news spread quickly or were you particularly well-informed? Professor Xue, to be honest, I knew this news less than three hours ago."

"Nonsense, Academician Tian just asked me if I am interested in joining this research group. What other projects do you want to do?"

"Ah, you refused to join this project?"

"How is it possible?! How could I refuse a national key project?"

"Director Na Tian didn't tell you the details of the project?"

"I didn't have time to ask, Academician Tian just asked for my opinion and hung up the phone. Maybe he had to rush to ask other people."

"Well, it doesn't really matter. It's just that Professor Zhang Yuantang is here. After talking with him, I felt that it is too inconvenient to study number theory problems now, so I designed an axiom system by myself.

I originally planned to discuss the rationality of this system with Professor Zhang and Director Tian today. Who knew that after hearing this, Director Tian called Mr. Yuan to Yanbei. Then I don’t know what they talked about.

Anyway, after dinner, Director Tian pulled me into his office and made sure that I apply for this thing in front of him. Hey, Professor Xue, you don’t know how troublesome it is to fill out the application form for this project!

There are dozens of pages of information to fill in, not including the thousands of words of research content that need to be written. Director Tian is very urgent. Normally I would be asleep at this time, but now I can only seize the time to write these things out... "

Qiao Yu began to complain.

There is no way. Although Yanbei University is big, there are not many people who can complain and are willing to listen to him.

But Xue Song is definitely one of them. After all, the friendship between the two of them, both as teachers and as friends, has been established in the past six months.

However, Qiao Yu soon felt something was wrong. The other party seemed to be listening, and after listening, there was no sound...

"Hey, Professor Xue, are you still there?"

"Yes...but since you still have to fill in the information, I won't disturb you for now. I'm just calling you to confirm this matter. Qiao Yu...well, come on."

"Oh, okay, hang up first."

Listening to the busy signal from the phone, Qiao Yu thought for a while and clicked on Senior Brother Chen's WeChat.

Although Senior Brother Chen has graduated, Qiao Yu feels that the friendship between the two still exists. When good things happen, you should think of yourself first.

And if you think about it carefully, although Senior Brother Chen is a bit bad at scientific research, he is cautious and meticulous, and he is still good at doing some auxiliary work.

So I simply took a picture of the cover of the information and sent it to him on WeChat.

In less than three seconds, Senior Brother Chen replied, but the message was a bit simple.

"???"
Chapter completed!