Chapter 142 About the fact that my mother may also be a math genius
It’s still early to finish dinner, only nine o’clock. After Qiao Xi finished her evaluation, she went back to the hotel to rest.
Leave time for two children who are 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. You can enjoy the happy dizziness caused 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 feels that a bunch of stupid women on the Internet don'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 hard, and it would be the saddest thing if you lose the ability to gain happiness from the ordinary.
...
With only two people left, Qiao Yu began to act unscrupulously and directly asked him the strange question that he had been asking for a long time today.
"By the way, why do I feel that you have suddenly become better behaved?"
Yes, for Qiao Yu, this girl seems to have suddenly become much quieter after not seeing her for half a year.
I no longer habitually disagree with him. It 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.
Being an elder brother can be so willful.
"I heard it." Xia Keke responded.
"I just said you became good, and you lost your temper, right?" Qiao Yu glanced at the little girl beside him.
"I'm not losing my temper. I just feel that I can't keep up with you. 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're right. Hey... let me put it bluntly, is there any woman in this world who is worthy of me?
Not long ago, I went to Switzerland Before, there was a girl in the cafeteria who wanted to cheat on my WeChat account, but I ignored her and turned around and left.”
Qiao Yu said boldly.
You can’t even say that he lied, because it 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 emotional 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 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? 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 good enough. On the contrary, when you feel that you are always coming into contact with some garbage people, hey... then you really need to start to be vigilant and reflect. "
Qiao Yu started to preach non-stop.
Fortunately, Xia Keke is used to it. Qiao Yu has been like this since elementary school. Whenever he finds an opportunity, he will talk to her like this.< br>
"So Qiao Yu, how many outstanding girls do you think it takes to be worthy of you in the future?"
Xia Keke asked again fiercely.
"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...
< br>Hey... Anyway, considering how familiar we are, I’ll just give it a try. After all, it’s better to take advantage of someone I don’t even know, right?”
“Bah, Qiao Yu, who is greedy for your body?” The girl's face turned red with embarrassment, like a red persimmon.
"Ah? You're not greedy for my body? Then are you 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 pretended He said in panic.
"Ah... Qiao Yu!"
With this scolding, it was obvious that Xia Keke's mood had been coaxed back to normal.
No way, Qiao Yu knows how to deal with a little girl's emotions after growing up together.
A serious chat might even make her cry. It's better to stimulate and stimulate, it will be better soon.
But the most annoying thing is that she said she didn't want his body, but she took the initiative to hold his hand and refused to let go...
Xia Keke also She opened up the conversation and chattered 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 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 Ke came to attend summer camp. All regulations must be respected, especially the school's management regulations.
Although Qiao Yu knows 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 for people in this kind of matter.
......
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, it's good to be back. Academician Tian invited you to dinner today?"
"No, it was Mr. Yuan who invited us to Huaqing There's food to eat. By the way, I might have to take a leave by then. Mr. Yuan said today that he'll be waiting for summer here. The camp is over, let Qiao Yu take me to Qiuzhai in Huaqing."
"Oh, this is all a trivial matter. Just tell me to go and rest quickly. Don't delay. Tomorrow’s opening event”
“Okay!”
...
On the other side, Qiao Yu hesitated for a moment, and then went to Building 9 of Shaoyuan Hotel.
Qiao Xi came, and her small apartment no longer smelled good. He decided to sleep on the sofa in the hotel for the next few days.
The best thing about summer is that you can sleep anywhere for a night.
Knocked on the door, and soon the door opened. Qiao Xi must have just taken a shower, and her hair was still a little wet.
"Coco has gone back?"
"Yes."
"Are you planning to sleep here tonight?"
"Yes, there is a sofa in the suite anyway."< br>
Qiao Xi looked at Qiao Yu, made some gestures, and said, "Isn't the sofa a little short?"
"Is it short? Let's add another one."
"It's better to change to a double room."
"No, have you forgotten? I loved sleeping on the sofa when I was a child."< br>
"Do you like sleeping on the sofa? You want to watch TV on the sofa."
"Mom, if we see through it but don't tell it, we will still be good friends! Otherwise we will end our friendship."< br>
Qiao Xi sniffed it with disgust and scolded: "Go take a shower, why do you smell so bad? In such a hot day, I wonder if you take a shower every day!"
Qiao Yu said plausibly: "This is the place. In Beijing, who washes every day? Take a shower! Besides, I’m so popular even if I don’t take a shower. What if I wash myself fresh every day?”
……
After the mother and son finished their usual bickering, Qiao Yu said He entered the bathroom honestly.
After quickly dealing with the hygiene problem, he left the bathroom and sat next to Qiao Xi who was scrolling through his mobile phone.
"Stop watching short videos." Qiao Yu said.
“Check it out occasionally, and always keep in touch with the outside world, otherwise it would 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 tell me."
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 is good news. Guess how much the other party 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 only tens of thousands or hundreds of thousands, you have 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 uninterested.
"It's 1.367 million after tax!"
"Wow, Qiao Yu, you are so awesome."
"Next time you praise me, please be more sincere."
Qiao Xi shrugged and said: "I can't be more sincere. Because I have always felt that with your ability and wisdom, it is hard for me to be surprised at what you achieve."
All I can say is Qiao Xi knows how to praise Qiao Yu.
"I have 1.6 million now, and I'll 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. If you use it, I will ask you for it."
Qiao Xi shook her head slightly and rejected Qiao Yu's kindness.
“By the way, Qiao Yu, when I was resting in the past few months, I carefully read the paper you posted. Then I had 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 it?”
“I couldn’t understand it at first, but I used the method you said, first read the documents you cited, and then read After quoting the literature, I read some books and felt that I probably understood it."
Qiao Yu looked at Qiao Xi curiously.
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 be more serious at that time, let Qiao Xi take a look first so that he can tell the truth.
However, Qiao Xi can roughly understand it, which makes Qiao Yu a little strange.
Qiao Yu asked: "Among the documents I cited are Peter Schultz's papers. Are you sure you understand his papers?"
"You mean the PerfectoidSpaces article, right? ? It is to perfect the specified geometric object by constructing a series of different spaces. Is this... difficult to understand? I think it is a tricky method. ”
Qiao Xi said casually.
Qiao Yu became anxious and lectured loudly: "How can you say it's a trick? In the study of p-adic number theory and algebraic varieties, the goal of construction is not to simplify the problem. There is no similar tool before. Use.
Otherwise, the number field is based on the prime number p. What tools can be used to effectively deal with algebraic geometry objects? You must know that the combination of p-adic numbers and algebraic geometry is the most difficult part to deal with! If you talk like this, people will laugh at you. ”
< br>"Oh!" Qiao Xi nodded with a relaxed expression as usual.
Seeing his mother's modest look, Qiao Yu continued to say 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 everyone used to conduct research in the field of real numbers or complex numbers, but if you switch to the field of p-adic numbers, traditional tools cannot be used. It is because the properties of geometric objects in the P-adic number field are more 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 true in p-adic space. You see, this is the value of Schulz’s research.
Okay, let’s not talk about this. 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, I think it's better anyway. After finishing your derivation process, it feels very interesting. If your proof is OK..."
"Wait... I want to correct you. This sentence can be omitted. Of course my proofs are fine! They have been published in top journals and verified by supercomputers."
Qiao Yu is dissatisfied interrupted Qiao Xi again. He had no choice. Even his mother couldn't bear to speak unprofessionally 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 combined with the space you constructed, then between the two There is a potential relationship between the geometry of algebraic curves and the distribution of rational number points. Just wait, I’ll get a pen and paper.”
After saying that, Qiao Xi stood up. There was a ballpoint pen on the table in the room. Along with a stack of manuscript paper printed with Yanbei University.
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 curve genus and geometry The common influence of constraints
Then let f(θ, g) be a and 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 a random As the genus increases, the number of rational solutions gradually approaches a stable upper bound. So I think N(C)≤f(θ,g). ”
Qiao Yu touched his chin, feeling 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 the genus increases, the rational points will not change because they are directly restricted by geometry.
In other words, Qiao Xi put forward 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. Wait...
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, did you really think of this?"
"Well, after all, it was the first paper you sent me. I would take it out and read it when I was bored. Turn. That day I suddenly felt that this might be possible.
Of course, I don’t know if it’s correct, let alone how to verify it. But I thought 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 proved. But the idea is interesting. No, aren’t you still brushing 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 can’t 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 those math books.
Although it is difficult, it is also 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 construct a model first and do numerical experiments and calculation verification. If it is consistent with this result, it will make sense.”< br>
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 algebraic geometry To summarize, it is nothing more than using algebraic equations to describe geometric objects, curves, surfaces, high-dimensional algebraic varieties, rational point distributions, singular point structures, and the relationship between modulus spaces.
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 way, the space can be made. The research objects in it can 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 she was 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 world-famous now. Beautiful mathematician!
Frank be damned!
Wait, but if this didn't happen, Qiao Xi would have nothing to worry about if she became a mathematician.
Well Frank damn +1!
"Mom, is it possible that you are also a mathematical genius?"
"Me? Stop joking."
As he said that, 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."
It's true Don't really 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 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, the one I told you before Brother Chen, he told me that he couldn't understand Schulz's papers at all, and he couldn't fully understand those abstract things, so can you feel the despair of not being able to learn?"
Qiao Yu? Taking the manuscript that Qiao Yu had just written, he 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 other materials. Hmm ...No, he must have learned those things before, right?”
This did make Qiao Xi a little surprised.
Although Qiao Yu called him many times, he rarely talked about academic issues.
When we chat occasionally, we just 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 it, I can understand it a little bit...< br>
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 correct. You know 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 mathematics. Conjecture. Because being able to come up with a valuable conjecture in mathematics is an extraordinary achievement in itself.
It requires not only deep insight and creativity, but also an extremely high level of understanding and intuition in the field of mathematics. The above are Mr. Yuan’s original words. I said this when I started to solve the geometric Langlands conjecture. "
Qiao Xi tilted her head, speechless because of Qiao Yu's stubbornness.
"Okay, so what? What do you think this means? Then I can become a mathematician because I feel that there is 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 received 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 this year! I was even a layman when it came to mathematics, and I had never wanted to be a mathematician. So it makes absolutely no sense to me.
My thoughts are your thoughts, if that makes sense to you. You can use it directly. Stop making trouble, go to sleep if you have nothing to do. I took the high-speed train 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 yours. Just give it away? Is there any more rigor? You go to sleep and I'll send your thoughts to Grandpa. Listen to what my grandpa said. "
As he spoke, Qiao Yu picked up his phone and took a photo 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. Door.
Too lazy to pay attention to Qiao Yu.
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 for a long time.
It’s a real curse, 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 can’t stand the fact that the old man has this hot temper his whole life. I can only listen to Mr. Yuan's words...
There is no way. Although Yuan Zhengxin is not his mentor, he was once kind to him. I can only endure it.
Finally I have 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 is more famous and rich, But at least he didn't do anything excessive on this point, right? Even if we get into trouble, the younger generation can still cooperate.
He never stopped me! He treated me the same even if he got good grades. This at least shows that Yan Zhen still has a big heart. "
Tan Luyuan could only smile bitterly. He responded: "Yes, what you are saying is that I am not as good as him in this regard."
Of course, I can't help but feel guilty. If their circumstances were different, even if Qiao Yu was his student, he would be more generous than Tian Yanzhen.
Well, after hearing this, Mr. Yuan felt that it was almost done. I didn't want to say anything more and was just about to take a rest when my phone vibrated many times in succession.
Yuan Zhengxin picked up his phone and looked at it. Several messages from Qiao Yu popped up in the system.
Click in and you will see a photo of a manuscript with very graceful 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 taken after my mother read my paper on the upper bound of the rational point of a curve. A guess given.”
"She feels that in an algebraic curve that satisfies the prescribed 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 proven comes out, 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 estimate this upper bound based on the geometric properties of the specific curve. ."
"She is very I can even understand Professor Schultz's paper independently! I think this is a sign of mathematical talent. But instead of admitting it, she even said that I was making a big fuss."
"If You also think she is talented in mathematics, so you must scold her for me! Of course, 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 argue with her, so please!”
The old man can see that Qiao! Yu was very excited, otherwise he would have sent five text messages in less than two minutes.
But after watching it, the old man did become interested. If nothing else, being able to independently understand Schulz's paper is already very powerful.
As for this conjecture...
The old man clicked on the photo, then zoomed in and looked at it very carefully.
Tan Luyuan next to him was a little confused. Why did the old man pick up his mobile 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 handed over by 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 right, even a certain type of curve can satisfy this condition.
It means that as long as the analysis is The geometric properties of this type of curve can be used to derive an upper bound regardless of its complexity. When it comes to high dimensions...
< br>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 doesn't like to talk much today? I think this proposition can be applied for a natural science fund, right?"
It’s really a question mark on his face. If this was the conclusion that Qiao Yu's mother came up with independently after reading Qiao Yu's paper, then this mathematical intuition would be too scary.
Although it is not yet certain whether it is correct. But luckily, you can use supercomputing to do a simple verification first. If there is a big difference, this topic can really be approved.
No... Can mathematical talent be inherited in the family? Really, this made Tan Luyuan very doubtful about life.
After all, his son really didn’t show any talent in mathematics. I don't even have any talent for science, so I could only choose liberal arts in high school. This is probably one of the pains in his life.
Even now his son is actually developing pretty well. But he was a great professor of mathematics, but his son chose liberal arts, which made him embarrassed to talk to anyone about it.
"Do 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. In this case, I'll call him, I'll put it on speakerphone, and you can listen."
Tan Luyuan could hear the old man's excitement when he said this.
Then I suddenly thought of a possibility...
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 along.
"Grandpa, you haven't slept yet."
"Well, I haven't slept. I was chatting with Professor Tan just now. Let me ask you, is this guess really made by your mother's independent thinking? Conclusion?"
"Yes, wait, Grandpa, I will ask her to get up and tell 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 about to scold him. The worry-free boy said a few words and saw the mobile phone raised in Qiao Yu's hand, showing that he was on a call...
He could only take a deep breath and took the mobile 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?"
< br>"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 is a bit rough.
You It is 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 supercomputer calculation result is still there. It is 6 rational number points. Of course, 6 is indeed less than 8, and it does satisfy the result of N(C)≤C(θ)=θ^g.
Therefore, it cannot be said that Qiao Yu’s argument is wrong. But this was obviously not precise enough, so I wondered if I could make the result more detailed.
After carefully reading Qiao Yu’s paper several times, I guess there is a connection between the geometric properties of curves and rational number solutions. 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 increased, the deviation between the supercomputer calculation results and the theoretical formula gradually narrowed. Especially in 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 have this guess. Of course, I really don’t know if this is 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. 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...will I won’t 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."
......< br>
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 so late at night?"
"I told you, it was grandpa who called me."
"But I really have no talent for mathematics! And I still know how to I often get distracted!" Qiao Xi said, rubbing her head.
"But what if there is? Let grandpa verify it. If there is, I support you personally going to the battle to tear up the scumbag. Think about it, he is just a small mathematics professor at Berkeley That’s it. It costs nothing to try!
If you become a great mathematician in the future and can give a special lecture at the World Congress of Mathematicians, he will be so scared that he will wet his pants when he sees you. ?”
Qiao Yu said nonchalantly.
Well, Qiao Yu does have the confidence.
Probably he is the only one who can waste a great academician’s valuable time with such confidence.
Thanks to the banana-loving cat for the reward and encouragement!
(End of this chapter)