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Chapter 142: My Mom Might Also Be a Mathematical Genius

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

She left time for the two half-grown children in her eyes.

Unlike other parents who worry about premature love, Qiao Xi is most worried that Qiao Yu will not fall in love.

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

Well, Qiao Xi hoped that her son could at least experience pure love for once, and enjoy the dizzy feeling of happiness brought by the instant secretion of hormones.

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

Qiao Xi even felt that a bunch of silly women on the Internet didn't understand one thing at all: love is just a spice of life for those rich men.

For countless ordinary people, it is life itself.

Life is already bitter enough, and the most tragic thing is to lose the ability to find happiness from the ordinary.

……

There were only two people left, and Qiao Yu began to act without restraint, directly asking the question that had puzzled him for a long time today.

"Why do I feel like you've suddenly become obedient?"

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

I didn't habitually contradict him anymore, which made him feel quite uncomfortable.

The girl lowered her head and walked along the path beside Weiming Lake without saying a word.

"Hey, I'm talking to you. How come your hearing is still not good at such a young age?" Qiao Yu said arrogantly.

Being an older brother can be so willful.

"I heard it." Xia Keke responded.

"Just when I said you had become a good boy, you're throwing a tantrum, right?" Qiao Yu glanced at the little girl beside him.

"I'm not angry, I just feel like I'm losing track of you. For example, I couldn't understand what you were talking about with Professor Tan today."

After walking two steps silently, Xia Keke suddenly blurted out these words.

Qiao Yu blinked and roughly understood why this girl suddenly became so weird.

"I see, then you're right. Well... let me be frank, is there any woman in this world who is worthy of me?
Not long ago, before I went to Switzerland, a girl in the cafeteria tried to trick me into giving her my WeChat ID, but I ignored her and just walked away.

Qiao Yu said shamelessly.

You can't even say he's lying, because it really happened. It's just that this statement is a bit narcissistic and shameless.

But the effect is obvious.

The little girl next to him was obviously upset 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?
What is the difference between a good match and a bad match! When you come to Yanbei or Huaqing in the future, you will know that there will be a bunch of high-quality young men around you, and they will be lining up for you to choose.

So the important thing is to improve yourself. Whatever height you can reach in the future, people who are suitable for you will naturally appear. What did the ancients say? Birds of a feather flock together!
When you find that the people around you are excellent, don’t feel discouraged, because that means you are also excellent enough. On the contrary, when you feel that you always come into contact with rubbish people, hey... then you really need to start to be alert and reflect on yourself. "

Qiao Yu began to preach incessantly.

Fortunately, Xia Keke was used to it. Qiao Yu had been like this since elementary school, and he would tell her the same thing whenever he found an opportunity.

"So Qiao Yu, how outstanding a girl do you think she has to be to be worthy of you in the future?"

Xia Keke suddenly asked again.

"What did I just say to you? Didn't you listen carefully? How could any girl be worthy of me? So, when you grow up, if you still want my body...

Well... Anyway, since we are so familiar with each other, I will consider you. After all, it is better to give it to my family than to give it to people I don't even know, right?"

"Bah, Qiao Yu, who wants your body?" Qiao Yu's words made the girl blush with shame, like a persimmon that has been turned red by premature ejaculation.

"Ah? You're not after my body? Are you after my money? No, I'm telling you, I can give you my body, but not my money! I'm useful to you!"

Qiao Yu said in pretended panic.

"Ah...Qiao Yu!"

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

There's no way. Having grown up together, Qiao Yu knows too well how to deal with the little girl's emotions.

If you talk to her seriously, she might cry. It's better to stimulate her, and she will feel better immediately.

But the most infuriating thing was 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 opened up and chattered with Qiao Yu about her high school life during the time they were apart.

"Oh, right... you still remember Chen Xiwen, right? I told you that she and I have the best relationship in the dormitory. She had a quarrel 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 attend the summer camp. She must respect all regulations, especially the school's management regulations.

Although Qiao Yu knew very well that once people reached a certain status, they didn't need to pay too much attention to these formalities, and the teacher in charge would not care too much about it.

But there is absolutely no need to cause trouble to others over such matters.

……

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

"Teacher Yang, I'm back."

"Well, I'm glad you're back. Academician Tian is inviting you to dinner today?"

"No, it was Master Yuan who invited us to Huaqing for dinner. By the way, I may have to ask for leave by then. Master Yuan said today that after the summer camp is over, he would let Qiao Yu take me to Qiuzhai in Huaqing."

"Oh, these are all small matters. Just tell me when the time comes. Go and have a rest quickly, so as not to delay the opening activities of the camp tomorrow."

"Ok!"

……

On the other side, Qiao Yu hesitated for a moment, then went to Building No. 9 of Shaoyuan Hotel.

With Qiao Xi here, his own small suite is no longer attractive. He decided to sleep on the sofa in the hotel for the next few days.

The good thing about summer is that you can sleep anywhere for a night.

I knocked on the door and it opened soon. Qiao Xi must have just finished taking a shower and her hair was still a little wet.

"Has Coco gone back yet?"

"Ah."

"Are you planning on sleeping here tonight?"

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

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

"Is it short? Then add another one."

"Then we might as well get 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 can see through it but don't say it, we can still be good friends! Otherwise, our friendship will end."

Qiao Xi sniffed it with disgust and scolded, "Go take a shower, why do you stink so badly? It's so hot, I doubt if you take a shower every day!"

Qiao Yu argued: "This is the capital, who takes a bath every day! Besides, I am so popular even if I don't take a bath, what will happen if I take a bath every day and smell good?"

……

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

He quickly dealt with the hygiene issue, then left the bathroom and sat next to Qiao Xi who was browsing on her phone.

"Watch less short videos." Qiao Yu said.

"You can take a look occasionally. You have to keep in touch with the outside world. Otherwise, it would feel silly not to know anything."

Qiao Xi put down her phone.

"Then why not let me tell you about my trip to Paris to attend the conference."

"Okay, you say."

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

From the breakfast meeting to the final departure...it was described vividly.

Qiao Xi just listened quietly, fully satisfying the little guy's desire to perform.

"Oh, there's some good news. Guess how much money I was paid by someone in a chemistry lab as a consultant?"

After talking about Paris, Qiao Yu looked at Qiao Xi mysteriously 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 only tens or hundreds of thousands, you've made that much before, so you wouldn't be so cocky."

Qiao Xi analyzed.

Qiao Yu actually didn't think he was very cocky, but he felt a little bored because Qiao Xi always saw through him.

"It's 136.7 million after tax!"

"Wow, Qiao Yu, you are amazing."

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

Qiao Xi shrugged and said, "I can't be more sincere. Because I always feel that with your ability and wisdom, I won't be surprised by any achievements you make."

All I can say is that Qiao Xi knows how to praise Qiao Yu.

"I have 1.6 million now. I'll transfer half of it to you later," Qiao Yu said.

"No, I have more money than I can spend. You know, I don't like luxury goods, I don't like makeup, and I don't know how to manage money. Why do I need so much money? If I really run out of money, I'll ask you for it."

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

"By the way, Qiao Yu, during my rest period these past few months, I carefully read the paper you published. Then I had some ideas, but I don't know if they are correct."

"Hmm? About the derivation of the rational upper bound of the curve?"

"Yes. You only sent me that paper, right?" Qiao Xi said softly.

"Well, can you understand it?"

"I didn't understand it at first, but I used the method you told me. I first read the literature you cited, then read the literature that cited the literature, and then flipped through some books. I think I roughly understand it now."

Qiao Yu looked at Qiao Xi with some surprise.

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

I sent it to Qiao Xi at that time 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 be serious about it, let Qiao Xi take a look first, and then he can explain the whole thing.

However, Qiao Yu was still a little surprised that Qiao Xi could roughly understand it.

Qiao Yu asked: "Among the references I cited, are there any papers by Peter Schultz? Are you sure you understand his references?"

"You mean the Perfectoid Spaces paper? It's about perfecting a given geometric object by constructing a series of different spaces. Is this... hard to understand? I think it's just a tricky way of dealing with it."

Qiao Xi said casually.

Qiao Yu was anxious and loudly taught him, "How can you say it's a trick? In the study of p-adic number theory and algebraic clusters, the goal of the construction is not to simplify the problem, but because there were no similar tools available before.

Otherwise, what tools can be used to effectively deal with algebraic geometry objects in number fields based on prime numbers p? You should know that the combination of p-adic numbers and algebraic geometry is the most difficult part of algebraic geometry! If you say this in public, people will laugh at you. "

"Oh!" Qiao Xi nodded calmly as usual.

Seeing his mother's humble look, Qiao Yu continued to say earnestly: "One of the core problems of algebraic geometry is to study the geometric properties of algebraic sets.

It was only when I was working on this topic that I realized that everyone used to conduct research in the field of real numbers or complex numbers, but if we switch to the field of p-adic numbers, traditional tools will not work. This is because the geometric objects in the field of p-adic numbers have more special properties.

Let me give you an example. The tools in traditional complex geometry rely heavily on continuity and smooth structures, but these structures do not hold in p-adic space. You see, this is the value of Schultz'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. Since his mother admitted her mistake so humbly, he decided not to criticize her anymore.

"Well, anyway, I found your derivation process very interesting. If your proof is correct..."

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

Qiao Yu interrupted Qiao Xi again with dissatisfaction. There was nothing he could do. Even if it was his mother, he couldn't tolerate her unprofessional remarks on 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, there is a potential relationship between the two in terms of algebraic curve geometry and the distribution of rational number points. Wait a minute, I'll get a pen and paper."

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

Qiao Yu also became serious, 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 suppose f(θ, g) is a function related to the geometric properties of the curve. In the algebraic curve that satisfies this geometric condition, is it possible for the function f(θ, g) to tend to a limit?

"That is to say, there is an upper bound at which the number of rational solutions gradually stabilizes as the genus increases. So I think N(C)≤f(θ,g)."

Qiao Yu touched his chin and felt it was very interesting.

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

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

To put it in terms that ordinary people can understand, there is a threshold value. When this threshold value is reached, no matter how much the defect increases, the rational point will not change because it is directly restricted by geometry.

In other words, Qiao Xi proposed a very interesting mathematical conjecture.

If it can be proven, Qiao Yu thinks it can provide a new mathematical perspective for the intersection of algebraic curve theory, number theory and geometry. And so on...

What new perspective? What’s 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 wanted?"

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

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

Qiao Xi pointed to the inequality she had written down.

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

Qiao Yu still felt a little bit unbelievable.

Even if this is just a guess, it cannot be proposed if you cannot understand his paper.

For example, if you ask his senior brother Chen to read his paper a hundred times, he probably won't be able to come up with such an 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 doing physics questions, I have been reading those 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 rather complicated. However, we can first construct a model and do numerical experiments and calculation verification. If they all conform to this result, then it makes sense."

Qiao Yu first analyzed the conjecture very professionally, and then criticized: "But you are too ambitious! Have you finished high school mathematics? You started reading Schultz? Studying algebraic geometry?"

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

And algebraic geometry is nothing more than using algebraic equations to describe geometric objects, such as curves, surfaces, high-dimensional algebraic clusters, distribution of rational points, singular point structures, and the relationship between them and modular spaces.

As for Schultz's paper, I don't need to fully understand it. Just roughly understand it. And the perfect space he proposed is essentially nothing more than ensuring a good geometric structure.

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

Qiao Yu didn't know what to say.

But I felt even more angry towards that man...

Look, with Qiao Xi's comprehension ability, if she hadn't encountered this incident back then and had gone to school, she might have become a world-renowned beautiful mathematician now!

Damn Frank!
Wait, but if this didn’t happen, it seems like there would be nothing for him to do if Qiao Xi became a mathematician.

Well, +1 for Frank!

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

"Me? Don't be ridiculous."

As he spoke, Qiao Xi stretched, stood up, and sat back on the sofa.

Then he said casually: "Like you said before, learning is the easiest thing in the world. Mathematical genius... forget it."

I really don't care.

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

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

“It’s true that learning is the easiest thing in the world, at least easier than making money. But I only realized after coming to Yanbei University that learning to this level is not that easy.

For example, the senior brother Chen I told you about before told me that he couldn't understand Schultz'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 he had just written and chased after him on the sofa and said.

"Your senior, the student of Director Tian, ​​couldn't understand Schultz's paper? Did he lie to you?

You may not 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 did surprise Qiao Xi.

Although Qiao Yu called him many times, they rarely talked about academic issues.

Occasionally we chat and complain about the difficulties we encounter.

"Why would he lie to me? You have no idea what was going on at the time. He was so anxious to come up with something new for his graduation thesis, and then I asked him to... Never mind, it's too much trouble to explain. Anyway, he really couldn't understand it."

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 doesn't understand, I can understand a little bit...

But this doesn’t seem to mean anything, I just think there is such a possibility. And I don’t know if it is right, or even how to verify it. So don’t get excited. ”

Qiao Yu became more serious and said, "Mr. Yuan once told me that only talented mathematicians can come up with valuable mathematical conjectures. Because coming up with a valuable conjecture in the field of mathematics is itself an extraordinary achievement.

It requires not only deep insight and creativity, but also a high level of understanding and intuition in the field of mathematics. These are all Yuan Lao’s original words. He said this when I started to solve the geometric Langlands conjecture.

Qiao Xi tilted her head, speechless at Qiao Yu's stubbornness.

"Okay, so what? What do you think this means? That I can become a mathematician because I feel that there is some possibility?
Do you know? Qiao Yu, when you said you were going to win the Fields Medal, I checked it out. This award can only be won before the age of 40 because it is difficult for mathematicians to be creative after the age of 40.

And I'm thirty-four years old! I'm still a complete layman when it comes to math, and I've never thought about becoming a mathematician. So this doesn't make sense to me.

If you think it makes sense, then my idea is your idea. You can use it directly. Stop it, go to sleep if you have nothing to do. I have been sitting on the high-speed train all day today. "

After saying that, Qiao Xi stood up and planned to go back to her room to sleep. After a night, Qiao Yu would probably not be so entangled.

"You can just give academic stuff away as you say? Is there any rigor in it? Go to sleep. I'll send your thoughts to grandpa. Let's hear what my grandpa has to say."

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

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

I'm 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 was still in the office, and Tan Luyuan also stayed there and hadn't left.

There was no way out. After the meal, after happily seeing Qiao Yu and his group off, the old man scolded him for a long time with great anger.

It was a real scolding, without any curse words. To be honest, Professor Tan was wronged, he really had no opinion on Qiao Yu, and he had no intention of flattering him.

But the old man has always had this hot temper. I can only listen to what Yuan Lao said...

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

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

"I know you have always had a problem with Yan Zhen, but everyone has their own experiences. The grudges of the previous generation can't be placed on the next generation, right?
Although Yan is really more fame-seeking, at least he didn't do anything excessive in this regard, right? Even if we are in a bad situation, the younger generation can still cooperate.

He never stopped me! He treated me the same regardless of my achievements. This at least shows that Yan Zhen is broad-minded. You should learn from him in this regard!"

Tan Luyuan could only smile bitterly and replied: "Yes, you are right. I am not as good as him in this respect."

Of course, he couldn't help but complain in his heart. If the two of them had their circumstances reversed, even if Qiao Yu was his student, he would be able to show more open-mindedness than Tian Yanzhen.

Well, after hearing this, Yuan Lao also felt that it was about enough. He didn't want to say anything more and was about to take a rest when his phone vibrated several times in a row.

Yuan Zhengxin picked up the phone and took a look. Several messages from Qiao Yu popped up on the system.

When you click on it, you will see a photo of a manuscript with very beautiful handwriting.

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

"Grandpa, are you asleep? Sorry to bother you. If you are asleep, you can come back tomorrow. The photo just now is a conjecture my mother made after reading my paper on the upper bound of rational points on curves."

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

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

"She can even understand Professor Schultz's paper on her own! Please judge for yourself. I think this is a sign of mathematical talent. But she not only refused to admit it, but also said that I was making a fuss."

"If you also think she has a talent for math, please help me scold her! Although if I get serious, she will definitely not be able to argue with me, but you know, she is my mother after all! I can't argue with her, so please!"

The old man could see that Qiao Yu was very excited, otherwise he wouldn't have sent five text messages in two minutes.

But after reading it, the old man did become interested. Apart from anything else, being able to understand Schultz's paper independently is already very impressive.

As for this conjecture...

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

Tan Luyuan next to him was a little confused. Why did the old man pick up his phone and suddenly stay there?
Just as he was about to speak, Mr. Yuan suddenly waved at him and said, "Lu Yuan, you also read Qiao Yu's paper today. Come over and take a look at this."

Tan Luyuan quickly stood up and walked over, took the phone handed to him by the old man, took off his glasses, and looked at it carefully.

"This... does it mean that the upper bound is determined by the geometric properties of the curve? If this is correct, then only a certain type of curve can satisfy this condition.

This means that as long as we analyze the geometric properties of this type of curve, we can get an upper bound regardless of its complexity. If we talk about high dimensions...

That’s right, it would be even better if the function expression 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 doesn't talk much today? I think this proposition can be applied for a natural science fund, right?"

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 we cannot be sure whether it is correct or not, it is a coincidence that we can use supercomputers to do a simple verification. If it is roughly correct, this project can really be established.

No...mathematical talent can be inherited from family? Really, this made Tan Luyuan doubt his life.

After all, his son really didn't show any talent in mathematics. He didn't even have any talent for science, so he had to choose liberal arts in high school. This was probably one of his lifelong pains.

Even though his son is doing quite well now, he is a mathematics professor, but his son chose liberal arts, which makes him embarrassed to talk about it with others.

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

If you know math, you know it, and if you don’t know it, you don’t know it. Just ask and you’ll know. So, I’ll call him, I’ll put him on speakerphone, and you can listen too.”

Tan Luyuan could tell that the old man was a little excited when he said this.

Then a possibility suddenly occurred to me...

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

If this really happened, then this mother and son...

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

"Grandpa, you haven't slept yet."

"Well, I haven't slept yet. I was just chatting with Professor Tan. Let me ask you, is this conjecture really the conclusion your mother came to through independent thinking?"

"Yes, wait a minute, Grandpa, I'll let her 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. Qiao Xi glared at Qiao Yu. Just as she was about to scold this troublesome boy, she saw the phone in Qiao Yu's hand, which showed that he was on a call...

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

"Hello, Mr. Yuan."

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

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

Especially the supercomputing verification report at the end of the paper. Although the results are all correct, some of them actually have deviations.

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

So we can't say that Qiao Yu's argument is wrong. But it's obviously not detailed enough, so I wondered if I could make the result more detailed.

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

Then it was found that when the genus increased, the deviation between the supercomputer's calculation results and the theoretical formula gradually narrowed, especially in the curve with higher genus.

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

So I made this guess. Of course, I really don’t know if it’s right, 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, and if so, then she would be a mathematical genius. Qiao Xi felt that mathematical geniuses were probably everywhere.

"Well, Qiao Xi, it's too late today. If you have nothing to do tomorrow morning, why don't you come to my Qiuzhai and sit down? How about that?"

"Ah... this... will it bother you too much?"

"I happen to have nothing to do tomorrow morning, so I'll call Qiao Yu over and we can chat casually without any pressure."

"Okay, Mr. Yuan, I'll bring Qiao Yu to visit you tomorrow."

"Well, Qiao Yu knows where my office is. I usually arrive at eight o'clock. Have a good rest. I'm hanging up now."

"Good night, Mr. Yuan."

……

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

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

"Is it appropriate for you to disturb Mr. Yuan in the middle of the night?"

"I told you, it was my grandfather who called me."

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

"But what if there is? Let me verify it. If there is, I support you to personally go and tear the scumbag apart. Think about it, he is just a small math professor in Berkeley. There is no cost to try!
What if you become a great mathematician in the future and give a special lecture at the World Congress of Mathematicians? Wouldn't he be so scared that he would pee his pants when he sees you?"

Qiao Yu said nonchalantly.

Well, Qiao Yu does have the confidence.

Perhaps only he could so confidently waste the precious time of a great academician.

　Thanks to the cat who loves bananas for the tip and encouragement!

　　
　
(End of this chapter)