After saying that, Qiao Yu closed the dialog box with Yu Yongjun and switched to the friend group. When he found that Yu Wei had not replied, he took the initiative to @ him and said, "How about this? If you really can't catch up with me in the future, what if you go home and inherit your family property, you will invest in my project? Hurry up, I still have to study my project!"

This time Yu Wei replied quickly: "No need! If I can't catch up with you, I will never marry you!"

Seeing Yu Wei's words and thinking of this guy's cold-hearted temperament on weekdays, Qiao Yu suddenly felt that he was playing a little too much now, so he didn't even bother to remind the other party that the ambiguity in this sentence made people who didn't know the truth read it and could even imagine N rebellious unilateral love stories!

He even thought of Yu Wei's father in his mind. When he saw this sentence, he rushed towards him with a kitchen knife... After all, the two big-name mentors mainly provide the academic magic defense, and physical attacks cannot be prevented!

It can be seen that this guy is really confused by the anger!

"Don't make a fuss, what should you do if your father is anxious? Your family has billions of wealth and no one can come to me for the best of their lives!" "Don't worry, I have two brothers, and it's not a matter of inheriting the family property!"

Oh, it turns out that there are two older brothers, no wonder they dare to be so willful.

However, Qiao Yu suddenly thought of Lanjie's words: The rich generation is much more interesting than the rich second generation, so it turns out that this is what it means.

After all, spend the money of the first generation as he wants. The second generation is different. If the first generation gives it first, it will be more complicated. If there are two brothers, it will be even more complicated. Qiao Yu was still sighing in his heart, intending to decisively reject Yu Wei. After all, he doesn't like men, so Yu Yongjun suddenly jumped out again.

"Brother, when you need to compete for family property in the future, remember to tell me and my elder brother, we will definitely stand firmly on your side... In addition, Lao Yu, although you are indeed a bit handsome, you have to ask about the boss's orientation before chasing him. What if the boss is a normal person? That, I took a screenshot..."

Well, after seeing this sentence, Qiao Yu knew that the two of them would start arguing again next, because he couldn't help but beat the fat man up! So he decisively quit WeChat and set his phone to the non-disturbance mode.

In more than a week, these two guys will go to Yanbei University to participate in the training camp. At that time, he will naturally see what Yu Wei will look like, but what makes him headache now is the topic he found for himself.

He has read all five papers on the theory of perfect space and has almost digested them. He has also made up a lot of basic knowledge during this period, and has basically completed the proof of his whimsical propositions.

According to his initial idea, X is a high-dimensional algebraic curve defined on the number domain K, and X is a closed subset of p into complete algebraic space. Then there is a constant C that depends on the geometric properties of curve X, so that the number of rational points on the curve satisfies: N(X)≤C.

This constant C does exist. Qiao Yu even feels that his proof process is perfect, and he has also found the formula for this constant C.

In other words, the night he came to Yanbei University, his wonderful propositions had really been proven.

If it weren't for Professor Zhang, he might have begun to write papers with great enthusiasm and announce his discoveries to the mathematical community! But he hasn't started writing yet, because he has introduced the formula C of the constant to look like this:

Finally, after solving C1, C2, and C3, the specific expressions will look like this:

Three constants A1, A2, and A3 are introduced, representing the modular form, p-to-coordinate and quantum-coordinate constants, and a, respectively, representing the indices related to these geometric constraints. Of course, the grid g is still the main factor that determines the upper bound, and is completely useless.

Qiao Yu tried to bring it into Professor Robert's work, and wanted to use his formula to solve some application problems. Then he soon discovered that determining the modulus format level k, the selection of prime number P, and the determination of quantum co-modulation parameter C are all too complicated. The constants A1, A2, A3 in the formula, and the constants a and β related to the geometric structure depend on the specific geometric background and curve type. Qiao Yu actually found out how troublesome it was when he actually calculated it manually.

During this period, he has been thinking about how to simplify the formula so that it can be useful, and the result is still valid. He has thought of many ways, but he has encountered walls everywhere.

He could probably feel the feeling of Senior Brother Chen's extremely ardent faced with scientific research. Every time he thought of a way to solve this problem, and then rushed to the computer with great enthusiasm and started to solve it, reality would give him a stick. Every time he tried, the final result was that this road was blocked.

He also specifically asked Lao Xue, and Lao Xue’s advice to him was that he could not hope to find a general formula, but simplify it directly based on specific situations and reduce complexity in specific problems. This would also have a certain amount of application space in practice and would be completely valuable.

For example, a simplified formula is made specifically for a certain type of simple elliptic curve.

This is of course a solution. Qiao Yu can even use this method to use water and numbers to disparate papers, such as one article for elliptic curves, one article for parabolas, and one article for hyperbolas... It must be more precise, and can also make algebraic cluster projection curves, and high-deficiency elliptic curves... But Qiao Yu thinks this is meaningless. After all, his original intention is to make a general formula and directly publish it in the four top journals. In the future, it can be directly named by the world mathematics community as a paper of the degree of definition theorem of Qiao Yu!

Qiao Yu felt that it was not enough to reach this level, so he could not add luster to the teacher and grandpa.

Moreover, with his current identity, if he chooses a water thesis, it will not only be meaningless to him, but may cause many criticisms, making Director Tian lose his face, and it is better to study quietly. After all, he does not plan to go to a university and needs to review his thesis and professional title.

I just said in the group that I can achieve results before the IMO game, which is to give myself a limited time...

Of course, neither Tian Yanzhen nor Yuan Zhengxin knew Qiao Ze’s idea, otherwise another person would probably scold him, and it would be better to curse this kid awake, so as to avoid thinking about messy things every day and wasting time! After all, it would be a bit naive to want to name a theorem after his own name at the age of fifteen. Although if Qiao Yu really solved this problem, there was indeed such a possibility.

But where is a simple general upper bound accurate estimation formula that is that simple?

Professor Robert Green has been studying this direction for many years, and he is just looking for a relatively accurate result in various special curves. But Qiao Yu's ideas are obviously different.

Euler was able to graduate from a master's degree at the age of sixteen and proposed a philosophical system that compared Descartes and Newton. Gauss independently discovered the root-finding method of cubic equations at the age of fifteen. Why couldn't Qiao Yu propose the upper definition theorem when he was sixteen? So it was natural that Qiao Yu directly hit this topic, but now it's really frustrating! The frustration that both good friends can't be compensated...

At the same time, in a key middle school in Shuangqing, a fat man was crying and holding his cell phone, raising his head to the teacher next to him, saying, "Teacher Qu, Qiao Yu suddenly didn't talk about martial ethics! He agreed to have a question of fifty yuan, but now he refuses to pay attention to me." The teacher sighed and said, "Hey, if you don't understand, you can't understand. What are you anxious about? Wait for me to study for two days."

In a room with its own computer and online study room at Linhai International Middle School, Yu Wei left the group chat with a pale face. He was indeed furious. When he was reminded by the damn fat man and realized that the sentence was ambiguous, he had already withdrawn it. However, after three deep breaths, he calmed down, and then picked up his phone and chose to send a WeChat message to the teacher.

"Teacher Chen, please help me find a few more papers on the upper boundary estimate of curve rational number points and Peter Schultz." The opposite side replied: "What do you want these papers to do?"

"I want to see how difficult this thing is."

"Professor Schultz's main job is to solve the problem of Langlands' conjecture. To be honest, you can read his thesis now without wasting time." "It's okay, Teacher Chen, I just want to understand it roughly and not waste too much time."

"Okay, I'll send it to your email in an hour." Yu Wei put down his phone with a serious expression.

I was dissatisfied, so I was restless and I lost my mood to do the questions.

During this period, he has been doing various Olympic questions at high intensity, so he is preparing to avenge his previous shame during the first special training period. But who would have thought that Qiao Yu, who went to Yanbei University, had already started to do research on the topic. And this guy seems to be serious about doing scientific research.

Because the first special training was actually held at Yanbei University.

He really didn't want that guy Qiao Yu to continue singing in front of him, but Yu Wei knew very well that if he wanted to surpass Qiao Yu, he had to at least determine the gap between the two. Fortunately, he didn't ask him to wait for a long time, the email address of his mobile phone was moving.

Yu Wei did not log in with his mobile phone, but logged in to his email directly on his computer. Coach Chen helped him download three papers.

Two articles are about the derivation of the upper boundary of the rational point of curves, and the other is a Peter Schultz article "Perfectoid Spaces: A survey", which was also specifically stated in the email that this is the easiest paper for Peter Schultz to understand. Yu Wei took the lead in downloading Schultz's paper.

After all, Teacher Chen said that reading Schultz's paper is a waste of time now, and he is still a little dissatisfied. However, after opening it, the boy fell silent, and even felt much less indignation in his heart.

Yu Wei felt that he had a certain algebraic geometry foundation. He had also heard of Peter Schultz's name. He believed that he might not be able to understand this paper, but at least he could understand what the paper said. But after reading the review, he knew that his understanding of these cutting-edge mathematical research seemed to have some deviation.

This is not something that can be understood by understanding a little bit of advanced mathematics in college. It is obvious that people of the same age, is the gap really so big?

He didn't want to believe that this was true, but Qiao Yu seemed to sound like a bragging thing every time, but in the end he found that it was true. And more than once, three or four times... As for him, he didn't dare to believe his judgment. Thinking of this, Yu Wei suddenly felt a little uneasy, and before he knew it, his hands were already clenched into fists...

There is no way, people are always like this. When you don’t have a blow, you don’t know how painful it is to be beaten...

In Xingcheng, Qiao Xi was sitting at the table where Qiao Yu once wrote, calmly working on the paper.

The sunshine in Star City in winter is just right. Although it doesn’t bring much warmth when it comes to your body through the window, it feels very comfortable.

But what made Qiao Xi feel most comfortable was that looking at the familiar and unfamiliar textbooks and brushing these familiar and unfamiliar exercises seemed to bring her back to the age of having infinite longing for the future. She went to Beijing to go to college...

"Ring..." The ringtone of the cell phone that suddenly remembered woke Qiao Xi from her trance...

He was distracted again and looked at the math test papers that had been done in front of him. Qiao Xiqing turned her head lazy and looked at her phone. It was another call from the stinky brat at home. He swiped casually and then chose to be hands-free.

"Hey, what are you doing?" "Mom, what are you doing?"

"Make the math paper you sent back." "Oh, is it difficult?"

"It seems a little different from what we learned at that time, but it's okay. It's a bit difficult to do, but it doesn't feel particularly difficult." Well, that's normal. If the textbooks change, please ask me any questions you don't know. This means you can enjoy this treatment."

"Stop talking nonsense, what are you doing when you call?"

"Hey, mom, I seem to be in trouble. There is a damn math proposition that I have broken my mind and don't know how to solve. What should I do? The teacher and the teacher have high expectations for me. Who would have thought that I was just starting out? " "Hmm? A very difficult proposition?"

"I don't think it's very difficult. Actually, I've solved this proposition, but the results I got are very complicated, with a bunch of parameters. I want to simplify this result and throw the complex things into the proof process, but I think about it all, but I still can't handle it."

"Then why don't you ask the tutor? Why call me? I can't help you with it."

"I asked Lao Xue, but Lao Xue's advice was to let me avoid the most complicated process, so that would be meaningless." "Oh, is it possible that your result was a false proposition?"

"Impossible! I have a kind of intuition, you know it, right? There is definitely a way to simplify this result and form a theorem, but I just don't know how to start." "So you are here to ask for comfort? Hurry up and say please mom to comfort me."

Qiao Xi put down the pen in her hand, stretched out her white hand, put her phone in front of her, and then supported her cheek with one hand, ready to listen to her own stinky brat complaining. A very novel experience, in front of her, Qiao Yu rarely showed this helpless mentality.

The only shame is that she doesn't seem to be helping. "Stop messing around, mom, I'm annoyed."

"Oh, okay, then let's talk about it first, why do you have a bunch of parameters in your result?"

"Because this problem is subject to multiple geometric constraints, each geometric tool will have a different set of restrictions after use. These tools must be used to condense the results into a formula." "Oh..." Qiao Xi began to ponder and asked, "All tools are indispensable?"

"Yes, I've tried reducing the restrictions or improving the tools, but it's useless." "So do these tools have no common characteristics?"

"Common nature?"

"Yes, since every tool must be used and each tool has different restrictions. If you want to simplify it, you have to find the commonality or the similarity between these conditions." "Hmm? Mom, it seems that you are saying something is reasonable."

"So you can try to study whether there are potential connections between different parameters. If so, maybe you can unify multiple parameters? Isn't math problems just looking for possible logical connections between different conditions?" Qiao Xi said casually, thinking that Qiao Yu should understand this principle better than her.

But the opposite side didn't say anything for a long time...

"Hey, why don't you talk?" Qiao Xi was a little surprised.

"Mom, did you give in to that man back then, so he can get the first place in the exam?" "Hmm?"

"I have been thinking about how to optimize those tools and control parameters recently. Why didn't I think that since I can't control, why don't I unify these parameters? Thank you, mom, I feel like I've found the direction!" "No? Are you serious?"

"Of course! Oh my God, I have been jealous of the mathematicians who can create tools as they please. What I am doing now is also a creation tool, but how did I forget this situation when I was in a stubborn manner? Can there be no ready-made tools to solve it?!

Thank you, mom! By the way, if I really solve this problem because of your prompt, this theorem will be called Qiao Yu-Qiao Xi’s definition theorem! You are the second author of this paper!" After saying that, before Qiao Xi could speak, the opposite person hung up the phone.

Qiao Xi shook her head inexplicably...
Chapter completed!