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.
To be continued...