Chapter 142 About the fact that my mother may also be a math genius

It was still early after dinner, but it was only nine o'clock. After Qiao Xi finished her evaluation, she went back to the hotel to rest.

She left time for her two children who were half-old in her eyes.

Unlike other parents who worry about puppy love, Qiao Xi is most worried about Qiao Yu not falling in love.

Although Qiao Xi does not think love is a necessity in life, if you put aside those messy interest entanglements, love itself should be beautiful.

Well, Qiao Xi hopes that her son can at least truly experience pure love once. He can enjoy the dizzy feeling of happiness brought about by the instantaneous secretion of hormones.

This seems to be impossible on the Internet, but it should still be possible in reality.

Qiao Xi even felt that a bunch of stupid women on the Internet didn't understand the truth. For those rich men, love is just a way of life.

For countless ordinary people, it is life itself.

Life is already very bitter, and it would be the saddest thing if we lose the ability to gain happiness from the ordinary.

…

There were only two people left, and Qiao Yu began to act unscrupulously, directly asking him questions that had been strange for a long time today.

"Speaking of which, why do I feel that you have suddenly become better behaved?"

Yes, for Qiao Yu, this girl seemed to have suddenly become much quieter after not seeing her for half a year.

I no longer habitually disagreed with him, which made him feel quite uncomfortable.

The girl lowered her head and walked on the path beside Weiming Lake without speaking.

"Hey, are we talking to you? Why are your ears not so good at such a young age?" Qiao Yu said arrogantly.

A brother can be so willful.

"I heard it." Xia Keke responded.

"I just said you became good, so you lost your temper, right?" Qiao Yu glanced at the little girl beside him.

"I'm not losing my temper, I just feel like I can't keep up with you anymore. For example, I don't understand what you talked about with Professor Tan today."

After taking two steps in silence, Xia Keke suddenly said this.

Qiao Yu blinked, probably understanding why this girl suddenly became so weird.

"That's right, then you are right. Hey... let me put it bluntly, is there any woman in this world who is worthy of me?

Not long ago, before I went to Switzerland, there was a girl in the cafeteria who tried to trick me into using my WeChat ID, but I ignored her and turned around and left."

Qiao Yu said boldly.

We can't even say that he lied, because such a thing is true. It's just that this sentence is somewhat narcissistic and shameless.

But the effect is obvious.

The little girl next to him was obviously in a mood and couldn't help but roll her eyes at him.

"Right, so you are still the girl closest to me, so don't panic. Besides, how old are you? What are you thinking about every day?

Whether they are worthy or not! You will know when you come to Yanbei or Huaqing in the future. There will be a bunch of high-quality young men around you, and you can't wait to line up to pick from them.

So the most important thing is to improve yourself. No matter how high you can reach in the future, suitable people will naturally appear. What did the ancients say? People flock together!

When you find that the people around you are excellent, don't feel discouraged, because it means that you are also good enough. On the contrary, when you feel that you are always exposed to some rubbish people, hey...then you really need to start to be vigilant and review.

"

Qiao Yu started preaching nonstop.

Fortunately, Xia Keke is also used to it. Qiao Yu has been like this since elementary school. Whenever he finds an opportunity, he will talk to her like this.

"So Qiao Yu, how good a girl do you think it takes to be worthy of you in the future?"

Xia Keke asked again abruptly.

"What did I just say to you, and you didn't listen carefully? How can any girl be worthy of me? So, when you grow up, if you are still greedy for my body...

Hey... Anyway, since we are so familiar, I will consider you. After all, instead of taking advantage of those I don’t even know, it’s better to take advantage of my own family, right?"

"Bah, Qiao Yu, who covets your body?" Qiao Yu's words made the girl blush with embarrassment, like a red persimmon.

"Ah? You're not greedy for my body? Then you're greedy for my money? That won't work. Let me tell you, you can give me your body, but not your money! I'm useful!"

Qiao Yu said pretending to be panicked.

"Ah...Qiao Yu!"

With this scolding, it was obvious that Xia Keke's mood was coaxed back to normal.

There is no way, Qiao Yu knows how to deal with little girls' emotions after growing up together.

A serious chat might even make her cry. It's better to stimulate her and she'll be fine soon.

But the most annoying thing is that she said she didn't want his body, but she took the initiative to grab his hand and refused to let go...

Xia Keke also started chatting, chattering with Qiao Yu about her high school life during the separation.

"By the way...Chen Xiwen, do you remember? I told you that she and I have the best relationship in the dormitory. She had a fight with another classmate in the dormitory last month..."

Qiao Yu listened silently all the way, and then sent Xia Keke back to Shaoyuan Hotel before ten o'clock.

After all, Xia Keke is here to participate in the summer camp. All regulations must be respected, especially the school's management regulations.

Although Qiao Yu knew very well that when a person reaches a certain status, he doesn't need to pay too much attention to these formal things, and the leading teacher won't care too much.

But there is absolutely no need to cause trouble to others on this matter.

…

Before going back to her room, Xia Keke followed Qiao Yu's instructions and went to talk to Teacher Yang.

"Teacher Yang, I'm back."

"Well, it's good to be back. Is Academician Tian treating you to dinner today?"

"No, Mr. Yuan invited us to have dinner in Huaqing. By the way, we may need to take a leave by then. Mr. Yuan said today that when the summer camp here is over, he asked Qiao Yu to take me to Huaqing.

’s Qiuzhai.”

"Oh, this is all a trivial matter, just tell me when the time comes. Go and rest quickly, don't delay the opening of the camp tomorrow."

"OK!"

…

On the other side, Qiao Yu hesitated for a moment, then went to Building 9 of Shaoyuan Hotel.

Qiao Xi came, and his small suite no longer smelled good. He decided to sleep on the sofa in the hotel for the next few days.

That's the best thing about summer, you can sleep anywhere for a night.

Knocking on the door, the door opened soon. Qiao Xi must have just taken a shower, and her hair was still a little wet.

"Coco has gone back?"

"Um."

"Are you going to sleep here tonight?"

"Yeah, there's a sofa in the suite anyway."

Qiao Xi looked at Qiao Yu, made some gestures, and said, "Isn't the sofa a little short?"

"Is it short? Then add one more."

"It's better to change to a double room."

"No, have you forgotten? I loved sleeping on the sofa when I was a kid."

"Do you like sleeping on the sofa? You want to watch TV on the sofa."

"Mom, if you see through something but don't tell it, we will still be good friends! Otherwise we will end our friendship."

Qiao Xi sniffed it with disgust and scolded: "Go take a shower, why do you smell so bad? In such a hot day, I doubt you take a shower every day!"

Qiao Yu said plausibly: "This is the capital, who takes a shower every day! Besides, I'm so popular even if I don't take a shower. What if I wash myself fragrantly every day?"

…

After the mother and son finished their usual bickering, Qiao Yu went into the bathroom obediently.

After quickly dealing with the hygiene issues, he left the bathroom and sat next to Qiao Xi who was scrolling through her cell phone.

"Stop watching short videos." Qiao Yu said.

"Look around once in a while, but always keep in touch with the outside world, otherwise it will feel silly if you don't know anything."

Qiao Xi put down her phone.

"Then why don't you listen to me tell you about my trip to Paris to attend the meeting."

"Okay, you say."

Qiao Yu began to talk about his experiences in Paris, and the focus inevitably fell on that man.

From the meeting at breakfast to the final departure...it was told vividly.

Qiao Xi just listened quietly, fully satisfying the little guy's desire for expression.

"By the way, there's good news. Guess how much the other side paid me when I went to the chemical laboratory to help people as a consultant?"

After talking about Paris, Qiao Yu looked at Qiao Xi with a mysterious face and said.

Qiao Xi looked at Qiao Yu's expression, thought for a moment, and said, "One million?"

"Huh? Why do you think there are so many?" Qiao Yu asked.

"If it's just tens of thousands or hundreds of thousands, you've made it before, so you shouldn't be like this."

Qiao Xi analyzed.

Qiao Yu actually didn't think he was very shy, but Qiao Xi could always see through it, which made him feel a little unmotivated.

"It's 1.367 million after tax!"

"Wow, Qiao Yu, you are so awesome."

"Next time you compliment me, please be more sincere."

Qiao Xi shrugged and said, "I can't be more sincere. Because I've always felt that with your ability and wisdom, it's hard to be surprised at what you achieve."

It can only be said that Qiao Xi knows how to praise Qiao Yu.

"I have 1.6 million now, and I will give you half of it later." Qiao Yu said.

"No, I can't even spend all the money. You know, I don't like those luxury goods, I don't like makeup, and I don't know how to manage money. Why do I need so much money? I really have no money. I will find it.

You want it."

Qiao Xi shook her head slightly and rejected Qiao Yu's kindness.

"By the way, Qiao Yu, during my break in the past few months, I carefully read the paper you posted. Then I came up with some ideas. I don't know if they are right or not."

"Huh? About the derivation of the upper bound of rational numbers on curves?"

"That's right. You only sent me that paper, right?" Qiao Xi said softly.

"Um, can you understand?"

"I couldn't understand it at first, but I used the method you mentioned. I first read the documents you quoted, then read the documents that cited the documents, and then read some books, and I felt that I probably understood it."

Qiao Yu looked at Qiao Xi strangely.

He originally thought this paper was easy to understand, but his senior brother Chen found it difficult to understand, which made him realize that what he thought was simple might not be that simple.

At that time, I sent it to Qiao Xi not only because I wanted to show off in front of my mother, but also because Qiao Xi was also the second author of this paper.

If someone really wants to take it seriously at that time, let Qiao Xi take a look first so that he can tell the truth.

However, Qiao Xi could roughly understand it, which still made Qiao Yu a little surprised.

Qiao Yu asked: "Among the documents I quoted are Peter Schulz's papers. Are you sure you understand his documents?"

"You're talking about the Perfectoid Spaces article, right? It's about constructing a series of different spaces to perfect a specified geometric object. Is this... hard to understand? I think it's just a tricky way to deal with it."

Qiao Xi said casually.

Qiao Yu became anxious and lectured loudly: "How can it be said that it is a trick? In the study of p-adic number theory and algebraic varieties, the purpose of the construction is not to simplify the problem, but because there has been no similar tool that can be used before.

Otherwise, what tools can be used to effectively handle the algebraic geometry objects in the number field based on the prime number p? You have to know that the combination of p-adic numbers and algebraic geometry is the most difficult part to handle in algebraic geometry! If you go out and talk like this, people will

It’s a joke on you.”

"Oh!" Qiao Xi nodded with a relaxed expression as usual.

Seeing his mother's modest look, Qiao Yu continued to speak earnestly: "One of the core issues of algebraic geometry is the study of the geometric properties of algebraic varieties.

It was also when I was doing this proposition that I realized that in the past, everyone had conducted research on the field of real numbers or complex numbers, but if you switch to the p-adic number field, traditional tools cannot be used. This is because the properties of geometric objects in the P-adic number field are more complex.

special.

Let me give you an analogy. The tools in traditional complex geometry rely heavily on continuity and smooth structures, but these structures do not hold in p-adic space. Understand, this is the value of Schulz’s research.

.

Okay, let’s not talk about this anymore. Just tell me what you think after reading that paper?”

Qiao Yu waved his hand magnanimously. Seeing that his mother admitted her mistake so humbly, he decided not to criticize anymore.

"Well, anyway, after I read your derivation process, I found it very interesting. If your proof is OK..."

"Wait... I want to correct you. This sentence can be omitted. Of course my proof is fine! It has been published in the top journal and has been verified by supercomputer."

Qiao Yu interrupted Qiao Xi again with dissatisfaction. He had no choice but to tolerate his mother's unprofessional speech in mathematics.

"Okay, okay, your proof is fine. Then the geometric properties of the curve seem to have a direct impact on the distribution of rational numbers.

If you combine the space you constructed, then there is a potential relationship between the algebraic curve geometry and the distribution of rational number points between the two. Wait a minute, I'll get a pen and paper."

After saying that, Qiao Xi stood up. On the table in the room was a ball pen and a stack of manuscript paper with Yanbei University printed on it.

Qiao Yu also took it seriously, stood up from the sofa and came to Qiao Xi's side.

"Your previous conclusion is that N(X)≤C(θ)=θ^g, that is, for any algebraic curve C, the number of rational points N(C) on it is affected by the genus of the curve and the geometric constraints.

So assuming that f(θ,g) is a function related to the geometric characteristics of the curve, in an algebraic curve that satisfies this geometric condition, is it possible that the function f(θ,g) tends to a limit?

"In other words, there is an upper bound where the number of rational solutions gradually becomes stable as the genus increases. So I think N(C)≤f(θ,g)."

Qiao Yu touched his chin and felt very interesting.

If this is proved, it means proving that there is an inevitable relationship between the natural upper bound of the algebraic curve solution and its geometric properties.

Because this means that as the genus g increases, the number of solutions may tend to some stable limit.

In words that ordinary people can understand, there is a threshold. When this threshold is reached, no matter how much the genus is increased, the rational points will not change anymore because they are directly restricted by geometry.

In other words, Qiao Xi came up with a very interesting mathematical conjecture.

If it can be proven, Qiao Yu feels that it can provide a new mathematical perspective at the intersection of algebraic curve theory, number theory and geometry.

etc……

What is a new perspective, not a new perspective? Did Qiao Xi really understand his paper?!

What kind of fairy mother is this?!

"Um...Mom, is this really what you think about?"

"Well, after all, it was the first paper you sent me. I would take it out and look through it when I was bored. That day I suddenly thought that there might be such a possibility.

Of course, I don’t know if it’s right or not, let alone how to verify it. But I think you might be interested. If you have time, you can find a way to verify it.”

Qiao Xi pointed to the inequality she wrote down casually.

"I don't know. This needs to be proven. But the idea is very interesting. No, aren't you still studying papers every day? When did you start studying algebraic geometry?"

Qiao Yu still felt a little unbelievable.

Even if this is just a conjecture, if you can't understand his paper, you won't be able to propose it at all.

For example, if he asked his senior brother Chen to read his paper a hundred times, he probably wouldn't be able to come up with this kind of insight.

"You work so hard every day, so I thought it would be good to help you in the future, so I have been very diligent recently. In addition to brushing up on physics problems, I have been reading math books.

Although it is difficult, it is also quite interesting. Is this difficult to prove?" Qiao Xi answered casually and then asked.

"This involves the relationship between geometric constraints and algebraic curves, which is more troublesome. However, you can first construct a model and conduct numerical experiments and calculation verification. If it is consistent with this result, it will make sense."

Qiao Yu first analyzed the conjecture professionally, and then criticized: "But you are too ambitious! Have you finished high school mathematics? Are you starting to read Schultz? Study algebraic geometry?"

Qiao Xi shook her head and said: "I have already gone through the high school mathematics textbook. And didn't you send this paper to me? Didn't you send it for me to read?

And to summarize, algebraic geometry is nothing more than using algebraic equations to describe geometric objects. Curves, surfaces, high-dimensional algebraic varieties, rational number point distribution, singular point structures, and the relationship between modulus spaces and so on.

As for Schulz's paper, I don't need to fully understand it. I just need to understand it. And the essence of the perfect space he proposed is nothing more than ensuring a good geometric structure.

This allows the research objects in the space to be fully described. In fact, they are all connected, and the ultimate goal is to facilitate calculation and classification."

Qiao Yu didn't know what to say.

But I felt a little more resentful towards that man...

Look, with Qiao Xi's understanding, if she hadn't encountered this incident and gone to school, she might be a world-famous beautiful mathematician now!

Frank be damned!

Wait, but if this didn't happen, Qiao Xi would have nothing to do if he became a mathematician.

Well Frank damn +1!

"Mom, is it possible that you are also a math genius?"

"Me? Stop joking."

With that said, Qiao Xi stretched, stood up, and sat back on the sofa.

Then he said casually: "As you said before, learning is the simplest thing in the world. Math genius... let's forget it."

I really don't care.

In fact, the only person in this world that Qiao Xi cares about is Qiao Yu. If it weren't for having a son, she probably wouldn't even care about life or death.

As for the mathematical genius, it should be Qiao Yu.

"It is true that learning is the simplest thing in the world. At least it is easier than making money. But it was only after I came to Yanbei University that I realized that it is not that simple to achieve this level.

For example, Brother Chen, whom I told you before, told me that he couldn't understand Schulz's paper at all. He couldn't fully understand those abstract things. So can you feel the despair of not being able to learn? ?」

Qiao Yu took the manuscript that Qiao Yu had just written and chased him to the sofa and said.

"Your senior brother, the student of Director Tian, ​​wouldn't be able to understand Schulz's paper? He lied to you, right?

You may not be able to understand it if you read it directly, but you can read it with the help of other materials. Hmm... No, he should have learned those things before, right?"

This indeed surprised Qiao Xi.

Although Qiao Yu called him many times, he rarely discussed academic issues.

Occasionally, we chat, just to complain about the difficulties we encounter.

"What could he possibly lie to me about? You have no idea what the situation was like at that time. He was so anxious to come up with something new for his graduation thesis, and then I asked...forget it, it was too troublesome to explain, and he really couldn't understand it anyway. "

Qiao Yu said seriously.

Seeing Qiao Yu's anxious look, Qiao Xi believed Qiao Yu's explanation, then smiled and said, "Okay, even if your senior brother can't understand, I can understand a little bit...

But that doesn’t seem to mean anything. I just think it’s possible. And I don’t know if it’s right or even how to verify it. So don’t get excited.”

Qiao Yu became more serious and said: "Old Yuan once said to me that only talented mathematicians can come up with valuable mathematical conjectures. Because being able to come up with a valuable conjecture in the field of mathematics is an extraordinary achievement in itself. Achievement.

It not only requires profound insight and creativity, but also requires extremely high understanding and intuition in the field of mathematics. The above are Yuan's original words. They were said when I started to solve the geometric Langlands conjecture. "

Qiao Xi tilted her head, feeling speechless due to Qiao Yu's stubbornness.

"Okay, so what? What do you think this means? Then I can become a mathematician because I feel like there's some possibility?

Do you know? Qiao Yu, when you said you wanted to win the Fields Medal in the future, I checked it out. This award can only be won before the age of forty because it is difficult for mathematicians to be creative after the age of forty. .

And I am thirty-four years old! I am even a layman when it comes to mathematics, and I have never thought about becoming a mathematician. So this makes no sense to me.

If you think it makes sense, then my thoughts are your thoughts. You can just use them. Stop making trouble and go to sleep if you have nothing to do. I took the high-speed rail all day today."

After saying that, Qiao Xi stood up and planned to go back to the room to sleep. After one night, Qiao Yu probably wouldn't be so entangled.

"Academic things are given away as you say. Are there any more rigors? Go to sleep and I will send your thoughts to grandpa. Listen to what my grandpa has to say."

As he spoke, Qiao Yu picked up his phone and took a photo of Qiao Xi's manuscript.

Qiao Xi turned her head and rolled her eyes at Qiao Yu, then walked into the room and closed the door.

Too lazy to pay attention to Qiao Yu.

Ever since this kid came into contact with mathematics, he has become more and more stubborn.

…

Huaqing, Qiuzhai.

Yuan Zhengxin is still in the office, and Tan Luyuan has not left either.

There was no other way. After eating and happily sending Qiao Yu and his party away, the old man scolded him vigorously for a long time.

It was a real scolding, without any curse words. To be honest, Professor Tan was very wronged. He really had no objection to Qiao Yu, let alone any idea of ​​flattering him.

But I couldn't stand the fact that the old man had such a hot temper all his life. I could only listen to Mr. Yuan's words...

There was no other way. Although Yuan Zhengxin was not his mentor, he had been kind to him. He could only endure it.

I have finally calmed down now, but I am still talking about it.

"I know you have always had opinions about Yan Zhen, but everyone has their own circumstances. The grudges of the previous generation cannot be placed on the next generation, right?

Although Yan Zhen has gained a lot of fame and fortune, at least he hasn't done anything excessive at this point, right? No matter how tense we are, the younger generation will still be able to cooperate.

He never stopped me! Even if I get good grades, I will be treated the same. This at least shows that Yan Zhen is still open-minded. You should learn from him on this point!"

Tan Luyuan could only respond with a wry smile: "Yes, you are saying that I am not as good as him in this regard."

Of course, I still couldn't help but feel slanderous in my heart. If their circumstances were different, even if Qiao Yu was his student, he would be more magnanimous than Tian Yanzhen.

Well, after hearing this, Mr. Yuan felt that it was almost over. He didn't want to say anything more and was just about to take a rest when his phone vibrated many times in succession.

Yuan Zhengxin picked up the phone and looked at it. Several messages from Qiao Yu popped up in the system.

When you click in, you will see a photo and a manuscript with very beautiful handwriting.

However, the old man did not rush to read the content of the manuscript in the photo, but first read the series of words that followed.

"Grandpa, are you asleep? Excuse me. If you are asleep, you can come back tomorrow. The photo just now was a guess made by my mother after reading my paper on the upper bound of the rational point of a curve. "

"She felt that in an algebraic curve that satisfies the prescribed geometric conditions, the function f(θ,g) may approach a limit, indicating that as the genus increases, the number of rational solutions gradually approaches a stable upper bound."

"I think if this conjecture can be proven, it means that as long as there is a suitable functional form, this can be described by f(θ,g). Even if the curve may not have a clear closed form, we can still use it according to the specific form. The geometric properties of the curve estimate this upper bound."

"She can even independently read Professor Schultz's paper! You commented on it. I think this is a sign of mathematical talent. But instead of admitting it, she even said I was the one making the fuss."

"If you also think that she is talented in mathematics, you must help me scold her! Although if I take it seriously, she will definitely not be able to quarrel with me, but you know, she is my mother after all! I can't help her She fights for it, so I’m begging you!"

The old man could tell that Qiao Yu was very excited, otherwise he would have sent five text messages in less than two minutes.

However, after reading it, the old man did become interested. If nothing else, it is already very powerful to be able to independently understand Schulz's paper.

As for this conjecture...

The old man clicked on the photo, then zoomed in and looked at it carefully.

Tan Luyuan next to him was a little confused. Why did the old man pick up the phone and suddenly stay there?

Just as he was about to speak, Mr. Yuan suddenly waved to him and said, "Lu Yuan, you also read Qiao Yu's paper today. Come over and take a look at this one."

Tan Luyuan quickly stood up and walked over, took the mobile phone from the old man, took off his glasses, and looked at it carefully.

"This... means that the upper bound is determined by the geometric characteristics of the curve? If this is correct, even a certain type of curve can satisfy this condition.

This means that as long as the geometric characteristics of this type of curve are analyzed, there is no need to worry about its complexity, and an upper bound can be obtained. How to involve high dimensions...

That’s right, it would be better if the expressions of the function could also be listed.”

Tan Luyuan frowned and thought for a while, then looked up at Mr. Yuan with a question mark on his face, and said: "Is this what Qiao Yu's mother thought of? The one who is not very talkative today? I think this proposition can be applied for a natural science fund. ?」

There is really a question mark on his face. If this is the conclusion that Qiao Yu's mother came to independently after reading Qiao Yu's paper, then this mathematical intuition is too terrible.

Although it is not yet certain whether it is correct or not. Fortunately, you can use supercomputing to do a simple verification first. If the difference is correct, this topic can really be approved.

No... can mathematical talent be inherited in the family? Really, this makes Tan Luyuan very doubtful about life.

After all, his son really didn't show any talent in mathematics. He didn't even have any talent in science. He could only choose liberal arts in high school. This was probably one of the pains in his life.

Even though his son is actually doing well now, he is a great professor of mathematics, but his son chose liberal arts, which makes him embarrassed to talk to others about this matter.

"You also think this conjecture is interesting? It should be true. My grandson will not lie to me. And do you think it is necessary for him to lie to me?

If you understand mathematics, you understand it; if you don’t understand it, you don’t understand it. Just ask him and you will know. In this way, I will call him and put him on speaker phone, and you will listen."

Tan Luyuan could hear that the old man was a little excited when he said these words.

Then suddenly a possibility occurred to me...

I couldn't help but feel a little dazed again.

If it really happened, then the mother and son...

The call was quickly connected, and Qiao Yu's voice came.

"Grandpa, you haven't slept yet."

"Well, I didn't sleep. I was chatting with Professor Tan just now. Let me ask you, is this conclusion really your mother's independent thinking?"

"Yes, please wait, grandpa, I will ask her to get up and talk to you now."

…

In the hotel room, Qiao Yu walked directly to the bedroom door and started knocking.

"Mom, Grandpa Yuan called and asked you to talk to him."

Soon, the door was opened, and Qiao Xi glared at Qiao Yu. Just as she was about to scold this careless boy, she saw the mobile phone raised in Qiao Yu's hand, showing that she was on a call...

He could only take a deep breath and take the phone from Qiao Yu's hand.

"Hello, Mr. Yuan."

"Qiao Xi, right? Professor Tan and I both find your idea very interesting. Can you tell us how you came up with it?"

"Okay, Qiao Yu showed me his paper. I think Qiao Yu's treatment of the impact of genus and geometric constraints on the number of rational points was a bit rough.

Especially the supercomputer verification report at the end of the paper. Although the results are correct, some results are actually biased.

For example, there is a line in the verification data where θ^g is equal to 8, but the actual result calculated by the supercomputer is 6 rational number points. Of course, 6 is indeed less than 8, and it does satisfy N(C)≤C(θ)=θ^g. result.

So it cannot be said that the result of Qiao Yu's argument is wrong. But it is obviously not precise enough, so I thought about whether the result could be made more detailed.

After carefully reading Qiao Yu's paper several times, I guessed that there is a connection between the geometric properties of the curve and the rational number solution. But I couldn't find it, so I took a trick and counted all the data given by the supercomputer at the end of the paper.

Then it was found that when the genus increases, the deviation between the supercomputer's calculation results and the theoretical formula gradually decreases. Especially in the curves with higher genus.

So this seems to indicate that although θ^g provides an effective upper bound, the actual number of rational number points does not seem to grow according to this power function, but tends to a relatively stable value.

So I came up with this guess. Of course, I really don’t know if this is correct, and I don’t know how to prove it, let alone verify it. I can’t even think of the expression of this function.”

Qiao Xi explained slowly. She simply thought that there might be such a function. If so, she would be a mathematical genius. Qiao Xi felt that mathematical geniuses were probably dead.

"Well, Qiao Xi, it's too late today. If you have nothing to do tomorrow morning, how about you come to my Qiuzhai to sit down?"

"Ah...this...wouldn't it bother you too much?"

"I don't have anything to do tomorrow morning, so I'll call Qiao Yu and let's chat casually without any pressure."

"Okay, Mr. Yuan, then I will take Qiao Yu to visit you tomorrow."

"Well, Qiao Yu knows where my office is. I usually arrive at eight o'clock. You have a good rest, I'll hang up."

"Good night, Mr. Yuan."

…

After hanging up the phone, Qiao Xi glared at Qiao Yu angrily. Qiao Yu looked at Qiao Xi with his head raised.

The word "unyielding" seems to be written on his face.

"Is it appropriate for you to alarm Mr. Yuan at night?"

"As I said, it was grandpa who called me."

"But I really have no talent for math! And I still get distracted a lot!" Qiao Xi said, rubbing her head.

"But what if there is? Let grandpa verify it. If there is, I support you to go to the battle and tear up the scumbag yourself. Think about it, he is just a small mathematics professor at Berkeley. There is nothing wrong with trying. cost!

What if you become a great mathematician in the future and can give a special lecture at the World Congress of Mathematicians? If he sees you, won’t he be so scared that he wets his pants?”

Qiao Yu said nonchalantly.

Well, Qiao Yu does have the confidence.

He is probably the only one who can waste a great academician's valuable time with such confidence.

Thanks to the cat who loves bananas for the reward and encouragement!
Chapter completed!