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.
To be continued...