Although many technology companies in the West know the importance of mathematical theoretical research, when they want to invest, they naturally give priority to well-known theoretical mathematicians, such as Edward Witten, Peter Schulz, Mary Carter, etc. .Generally, if young mathematicians want to get projects, they can only go into the application field. Only by thinking of an idea and packaging it can they impress investors.

This is the reality. An unknown young professor came to Google and said that if he was given one million dollars, he could develop the final solution to N-body motion. He probably couldn’t even pass the security guard level. Without a material foundation, he could just rely on love. , it is difficult to go far in this industry.

So in theory, Yu Wei's family conditions are really suitable for playing mathematics, but Qiao Yu thinks it's a pity. After all, his low IQ is a flaw... But obviously Yu Wei didn't appreciate it and only posted a brief message in the group Two words: "Haha..."

From these two words, we can see that the emotion is only anger, not gratitude.

Qiao Yu also began to continue to persuade: "I understand your obsession with mathematics, but why don't you change your approach? For example, you can take the college entrance examination honestly, then go to Guanghua College of Yanbei University, and then go home and inherit billions of wealth. , run a family business. When you can manage money, you can invest in my future research projects. In this way, when I produce results, I will also give you a name. We will all do what we are most suitable for. In this way, we will not only achieve results, but also Keep you fully engaged."

Cicada Zuzuxue: "Qiao Yu, that's enough! I admit that you are better than me for the time being, but I will definitely catch up with you! Whether it is an exam or a paper! I put my words here!" The momentum was very strong, and Qiao Yu was stunned. They were all frightened, and weakly asked in the group: "Oh, what should you do if you can't do this in the group?"

Yu Wei didn't reply for a while, and the group became quiet.

Probably because he felt that Yu Wei's anger level was full today, the little fat man rarely continued to be angry in the group. Instead, after Qiao Yu asked that question in the group, he started chatting privately with Qiao Yu.

"Boss, don't hit Yu Wei too hard! I feel like his little universe is about to explode. In this way, I happened to have accumulated several difficult problems recently. I will let him calm down later. Please help me look at these problems first. How do I solve this problem? Hey, I asked the teacher but he still couldn’t tell me how to solve the problem. I understand the rules, one problem is fifty, and you can keep the transfer."

As he said that, the little fat man directly sent a document to Qiao Yu, and he also transferred three hundred yuan directly.

Looking at the red transfer interface, Qiao Yu sighed in his heart. Sure enough, geniuses are lonely, and friends can't understand him!

He directly clicked the return transfer under the transfer, and then said: "Don't you understand? Don't send money directly like this in the future. It's not easy for you to save some pocket money." "Damn, thank you boss! Yanbei University is really awesome. , the situation has changed since eldest brother left!"

"Well, don't thank me in a hurry. Have you heard a saying? Countless ordinary mathematicians have spent their entire lives trying to save a math genius an afternoon tea." "Boss, you have a plan!"

"Yes, so I won't charge you, but I won't help you solve the problem either. Do you think fifty dollars per problem can reflect the value of countless ordinary mathematicians' lifelong efforts?"

After saying that, Qiao Yu closed the dialog box with Yu Yongjun and switched to the friend group. When he found that Yu Wei had not replied yet, he took the initiative to @ him and said: "How about this, if you really can't catch up with me in the future, reply How about taking part in my project after inheriting the family property? Hurry up, I still have to study my project!"

This time Yu Wei quickly replied: "No need! If I can't catch up with you, I will never marry you!"

Seeing Yu Wei's words, and thinking of this guy's usually cold temperament, Qiao Yu suddenly felt that this was a bit too much, so much so that he didn't even bother to remind the other person that the ambiguity in this sentence made people who didn't know the truth. After watching it, people can imagine N number of unorthodox one-sided love stories!

He even thought of Yu Wei's father, who rushed towards him with a kitchen knife after seeing these words... After all, the two boss-level mentors mainly provided magical defense in academia, and could not prevent physical attacks. Stay!

It can be seen that this guy is really confused!

"Don't make trouble. The bet is so big. What should you do if your father is anxious? Your family's billions of wealth has no heir, so don't try to fight me!" "Don't worry, I have two brothers who will inherit the family property." Just me!"

Oh, it turns out there are two older brothers, no wonder he dares to be so willful.

But Qiao Yu suddenly thought of Lan Jie's words, the rich generation is much more interesting than the rich second generation, so that's what it meant.

After all, the first generation can spend their money however they want, but the second generation is different. The first generation has to give it first before they can spend it. It is even more complicated if you have two brothers. Qiao Yu was still sighing in his heart, and was about to make a decisive decision. After rejecting Yu Wei, after all he didn't like men, Yu Yongjun suddenly showed up again.

"Brother, remember to tell me and my eldest brother when you need to fight for family property in the future. We will definitely stand on your side... Also, Lao Yu, although you are indeed somewhat pretty, but Before chasing the boss, you have to ask him about his orientation. What if the boss is normal? Well, I took a screenshot..."

Well, after seeing this sentence, Qiao Yu knew that the two of them were going to quarrel again, because he couldn't help but beat up the fat man! So he decisively quit WeChat and set his phone to do not disturb mode.

In more than a week, these two guys will go to Yanbei University for training. Then he will naturally be able to see what Yu Wei will look like, but what gives him a headache now is the one he found for himself. Topic.

He has read and digested all five of Schultz's papers on the theory of nearly complete space. During this time, he has also supplemented a lot of basic knowledge, and has basically completed the proof of his whimsical propositions.

According to his original idea, assume that Make the number of rational points on the curve satisfy: N(X)≤C.

This constant C does exist. Qiao Yu even felt that his proof process was perfect, and he had also figured out the formula for this constant C.

In other words, the night he came to Yanbei University, his fantastic proposition was really proved by him.

If there hadn't been Professor Zhang, he might have started writing a paper with great interest and announced his findings to the mathematical community! But he hasn't started writing yet, because the formula for the constant C looks like this:

Finally, after C1, C2, and C3 are solved, the specific expression looks like this:

Three constants A1, A2, and A3 are introduced, which respectively represent constants related to modular form, p-adic homology and quantized homology norm, while a represents the exponent related to these geometric constraints. Of course, the number grid g is still determined. The main factors of the upper bound are unusable, completely unusable.

Qiao Yu tried to get involved in Professor Robert's work, hoping to use his formulas to solve some application problems, and soon discovered that determining the modular form level k, selecting the prime number P, and determining the quantization homology parameter C , are all too complicated. The constants A1, A2, A3 in the formula, as well as the constants a and β related to determining the geometric structure depend on the specific geometric background and curve type. When Qiao Yu actually calculated it, he realized how troublesome it was.

During this time, he has been thinking about how to simplify the formula so that it can be used easily and the result is still valid. He has thought of many ways, but he has hit a wall everywhere.

He can already roughly understand the feeling that Senior Brother Chen feels when faced with the overwhelming challenge of scientific research. Every time he thinks of a way to potentially solve this problem, and then rushes to the computer excitedly and starts to solve it, the reality is They would give him a stick. Every time he tried, the final result was that the road would not work.

He also asked Lao Xue specifically. The advice Lao Xue gave him was not to hope to find a general formula, but to simplify it directly for specific situations and reduce complexity in specific problems. In this way, it can also be achieved in practice. It has a certain application space and is of no value if it can be considered complete.

For example, make a simplified version of the formula specifically for a certain type of simple elliptic curve.

This is of course a method, and even Qiao Yu can use this method to write papers on numerical bias, such as one on elliptic curves, one on parabolas, one on hyperbola... He must be more formal and do algebra. Cluster projection curves, high genus ellipses... But Qiao Yu felt that this was meaningless. After all, his original intention was to make a general formula and publish it directly in the four top journals, so that it could be directly named by the world's mathematical community in the future. It’s a paper as good as Qiao Yu’s upper bound theorem!

Qiao Yu felt that if he couldn't reach this level, he wouldn't be able to bring glory to the teachers and grandpa Shi's faces.

And with his current status, if he chooses the water thesis, it will not only be meaningless to him, but may also attract a lot of criticism, which will make Director Tian lose his face. He might as well study quietly. After all, he has no intention of going.

To get a job in any university, you need to get a thesis evaluation title or something.

I just said in the group that the results can be produced before the IMO competition, which can be regarded as giving myself a limited time.

Of course, neither Tian Yanzhen nor Yuan Zhengxin knew what Qiao Ze was thinking, otherwise the other person would probably scold him. It would be best to scold this kid to wake him up, so as not to waste time thinking about messy things every day! After all,

It is somewhat naive to want to name a theorem after himself at the age of fifteen. Although it is indeed possible if Qiao Yu really solves this problem.

But where is a concise universal upper bound exact estimation formula so simple?

Professor Robert Greene has been studying this direction for many years, just looking for a more accurate result among various special curves. But Qiao Yu's idea is obviously different.

Euler was able to graduate with a master's degree at the age of sixteen and proposed a philosophical system comparing Descartes and Newton. Gauss independently discovered the method of finding the roots of cubic equations at the age of fifteen. Why couldn't Qiao Yu propose an upper bound at the age of sixteen?

Reason? So naturally, Qiao Yu directly tackled this topic, but now he is really frustrated! It has hit two good friends, the kind of frustration that cannot be compensated...

At the same time, in a key middle school in Shuangqing, a fat man looked up and looked at the teacher next to him with a sad face. He raised his head and said to the teacher next to him: "Teacher Qu, this guy Qiao Yu suddenly doesn't respect martial arts! We agreed to fifty

I just asked a question, but now you won’t pay attention to me.” The teacher sighed and said, “Hey, if you don’t understand it, then you can’t understand it. Why are you in such a hurry? I’ll study it for two days.”

In a study room with its own computer and network in Linhai International Middle School, Yu Wei withdrew from the group chat with a livid face. He was indeed furious. When he was reminded by that damn fat man, he realized that there was an ambiguity in that sentence.

, it was impossible to withdraw... But after taking three deep breaths, he calmed down, then picked up his phone and chose to send a WeChat message to the teacher.

"Mr. Chen, please help me find some more papers on the problem of upper bound estimation of rational number points on curves and Peter Schulz." Soon the other party responded with a message: "What do you want these papers for?"

"I want to see how difficult this thing is."

"Professor Schultz's current main work is to solve the Langlands conjecture problem. To be honest, his paper is just a waste of time and it is meaningless." "It's okay, Teacher Chen. I just want to have a general understanding. It won't delay too much.

time."

"Okay, I'll send it to your email in an hour." Yu Wei put down the phone with a serious expression.

I was so unconvinced that I felt restless and even lost my mood to answer the questions.

During this period of time, he had been studying various Olympiad questions with high intensity, and was ready to avenge his shame in the first period of special training, but who would have thought that Qiao Yu, who went to Yanbei University, had already started doing research on the project. And this

The guy seems to be serious about doing scientific research.

Because the first special training was actually held at Yanbei University.

He really didn't want that guy Qiao Yu to continue to sing in front of him, but Yu Wei knew very well that if he wanted to surpass Qiao Yu, he had to at least determine the gap between the two. Fortunately, he didn't have to wait long. There is movement in the mailbox.

Yu Wei did not log in with his mobile phone, but directly logged in to his email on the computer. Coach Chen helped him download three papers.

Two articles are about the derivation of the upper bound of rational points on curves. The other article is "Perfectoid Spaces: A survey" by Peter Schulz. It was also noted in the email that this is the easiest to understand by Peter Schulz. A paper. Yu Wei was the first to download Schulz’s paper.

After all, Teacher Chen said that it was a waste of time for him to read Schulz's paper now, and he was still a little unconvinced. But after opening it and reading it, the young man became silent, and even his inner dissatisfaction was much less.

Yu Wei felt that he had a certain foundation in algebraic geometry. He had also heard of Peter Schulz's name. He believed that he might not be able to understand this paper, but at least he could understand what it said. But when After reading the review, he knew that his understanding of these cutting-edge mathematical research seemed to be a little off.

This is not something that can be understood with a little knowledge of advanced college mathematics. We are obviously the same age, but is the gap really that big?

He didn't want to believe it was true, but it seemed that every time Qiao Yu sounded like he was bragging, he found out in the end that it was true. And it happened more than once, three or four times... As for him, he didn't dare Trusting his own judgment. Thinking of this, Yu Wei suddenly felt a little uneasy. Unknowingly, his hands had clenched into fists.

There is no way, people are always like this, until they are beaten, they have no idea how painful it is to be beaten...

In Star City, Qiao Xi is sitting at the table where Qiao Yu once used to write, calmly doing papers.

The sunshine in Star City in winter is just right, and although it doesn't bring much warmth to my body through the window, I feel very comfortable.

But what makes Qiao Xi feel most comfortable is that looking at familiar yet unfamiliar textbooks and studying these familiar yet unfamiliar exercises seems to bring her back to the age when she had infinite longing for the future. Going to university in the capital... .

"Ring..." The cell phone ringtone that suddenly came to mind woke Qiao Xi out of her trance...

She was distracted again and glanced at the math paper in front of her that she had already completed. Qiao Xi lazily turned her head and glanced at her phone. It was another call from the brat at home. She swiped it casually and chose hands-free.

"Hey, what are you doing?" "Mom, what are you doing?"

"Do the math paper you sent back." "Oh, is it difficult?"

"It seems a little different from what we learned at that time, but it's okay. It's a bit difficult to do, but it doesn't feel particularly difficult." Well, that's normal. If the textbook changes again, feel free to ask me any questions you don't understand. , this is how you can enjoy this treatment."

"Stop talking nonsense, why are you calling?"

"Hey, Mom, I seem to be in trouble. There's a damn mathematical proposition that I can't even figure out how to solve. What should I do? Both the teacher and Grandpa Shi have high hopes for me. Who would have thought that I just had to solve it? It’s been a bottleneck since the beginning.” “Huh? A difficult proposition?”

"I don't think it's very difficult. In fact, I have already solved this proposition, but the result is very complicated, with a bunch of parameters. Now I want to simplify the result and throw the complicated things into the proof process, but I have tried all the ways. , still can’t deal with it. "

"Then why don't you ask the instructor? Why are you calling me? I can't help you solve it."

"I asked Lao Xue, but the advice Lao Xue gave me was to avoid the most complicated process. That would be meaningless." "Oh, is it possible that your result is a false proposition?"

"It's impossible! I have an intuition. Do you know your intuition? There must be a way to simplify this result and form a theorem, but I just don't know how to start." "So you are here to seek comfort? Please tell me quickly. Please mom comfort me."

Qiao Xi put down the pen in her hand, stretched out her white hand, put the phone in front of her face, and then propped up her chin with one hand, preparing to listen to her brat's complaints. It was a very novel experience. Qiao Yu rarely showed this in front of her. A helpless state of mind.

The only pity is that she seems to be unable to help. "Don't make trouble, Mom, I'm bothered."

"Oh, okay, then tell me first, why does your result have a bunch of parameters?"

"Because this problem is controlled by multiple geometric constraints, each geometric tool will have a different set of constraints after use. These tools must be used to condense the results into a formula." "Oh..." Qiao Xi Begin to meditate and then ask, "Are all tools indispensable?"
To be continued...