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.
To be continued...