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Chapter 110 Qiao Yu of the Future - Qiao Xi's Upper Boundary Theorem!

School has started, and the campus of Yanbei University has become lively, and the Center for Mathematical Research has also become more lively.

Director Tian said that he had not lied to him. For example, some elective courses in the School of Mathematics were taught directly in the research area. In addition, the research center also opened a basic mathematics intensive course for senior undergraduates in the School of Mathematics.

Of course, if Qiao Yu wanted to attend these courses, he could also attend them at any time. Of course, it was far more than just these courses. Whether it was Yanbei University or Huaqing University, as long as it was a mathematics course, as long as he wanted to attend it, he could attend it.

There is no need to go through the trouble of registering for classes online, and he doesn't need those credits and GPAs for the time being anyway.

Tian Yanzhen's requirement for him in the past six months is still to finish reading those books.

Qiao Yu also used practical actions to make Tian Yanzhen feel that he really didn't need to worry too much about his last disciple.

On Sunday night, Qiao Yu would carefully prepare a reading experience and send it to his tutor early on Monday morning. Of course, Qiao Yu would not forget to send a copy to his master on Monday morning. Then he received two comments.

From the notes on his reading experience, we can see that his two math instructors had done in-depth research on these basic math books, and they would remind him of many details that he had not noticed in their notes.

During this period, in order to thank Chen Zhuoyang for his help, Qiao Yu specially invited this senior brother Chen to have a big meal in Huaqing’s cafeteria.

Not only because the small building he lived in finally had hot water, which even allowed him to sneak to the second floor to take a shower at night when no one was around, but also because the various supplementary teaching materials for the college entrance examination that Senior Brother Chen had collected for him cost Qiao Yu more than 300 yuan just for the mailing fee, including many review papers for senior high school students in various subjects from the best high schools in Beijing.

Their scarcity is enough to explain the fact that most of the teachers who set these papers have been selected into the national college entrance examination question-setting group many times.

After that big meal, Senior Brother Chen became more attentive to Qiao Yu.

Because he accidentally noticed that the balance on Qiao Yu's Huaqing Card was a little too scary.

Let's put it this way, if someone stole Qiao Yu's card, the amount in it would cost him at least ten years in prison. Chen Zhuoyang did some random calculations and came to the conclusion that even if Qiao Yu was stuck eating in the Huaqing cafeteria for thirty years from now on, he might not be able to use up the balance on the card.

Money is not everything, but it can really measure the degree of pampering.

The favor from his master was so terrifying that Chen Zhuowen could no longer envy him. He just felt that the gap between people was too big and there was no way to compare them.

He now truly believed that if Qiao Yu took his paper to ask Mr. Yuan to help revise it, Mr. Yuan might really do it himself.

Really, Chen Zhuoyang also wants to find an opportunity to call Teacher Yuan grandpa.

Unfortunately, there is really no chance. Of course, if there was a chance, Chen Zhuoyang felt that he might not be able to call out.

The difference between Qiao Yu's youthful face and his half-bald look is really huge. When Qiao Yu calls "Master Grandpa", one can feel the beautiful relationship between the grandfather and grandson. He may be able to hold back from vomiting when he calls "Master Grandpa", but he can't guarantee how others will look at him.

Not as talented as him, and not having the advantage of age...

In terms of mathematics, it is easy to prove that he should just cling to his junior brother's thighs. It is not shameful for a mathematics doctor who does not want to do scientific research to bow his head in order to graduate!
On the other hand, although school has started and Lao Xue has become busy, he still takes time every day to check on Qiao Yu.

Sometimes I just come to take a look, and sometimes I come to give Qiao Yu some advice, such as helping him plan some necessary courses to attend.

After all, I'm in Yanbei, and it would be a waste of resources if I didn't attend classes at all.

Qiao Yu did listen to advice, but he attended fewer courses in the School of Mathematics, but attended more elective courses in the School of Physics next door, mainly focusing on the two courses of Quantum Mechanics and Mathematical Physics Methods.

It’s not that he wants to develop in the direction of physics, at least for now, but Qiao Yu feels that it would be beneficial for him to broaden his knowledge appropriately.

In particular, some concepts in physics can slightly limit his infinitely divergent thinking. After all, physics does not have the freedom of mathematics.

As we all know, even in mathematical analysis, infinite divergence is very troublesome because it means that the result may be undefined. For example, a divergent series cannot produce a finite sum, which directly leads to the mathematical model losing its practical meaning.

In addition to these daily courses, in the two weeks after school started, Director Tian answered his questions twice, and the master across the street called him over three times.

On one occasion, on the same day, Director Tian helped him answer questions in the morning, and at lunch time, Senior Brother Chen suddenly brought a birthday cake over, and Old Xue also came over to give him a birthday present.

Having a premonition, Qiao Yu was called over by his master in the afternoon, and sure enough, he celebrated his birthday again.

Yes, on February 2rd, Qiao Yu's sixteenth birthday, the first year he came to Beijing, he celebrated his birthday twice, from noon to night. He celebrated it at Yanbei University at noon and at Huaqing University at night.

When he returned to Yanbei University that night, he called Qiao Xi and criticized his mother for not calling him on his birthday. Qiao Xi woke him up with a few words: "How can you be so embarrassed? When did you not celebrate your lunar birthday at home? Do you need me to remind you? You had already celebrated your birthday once before you went to Beijing this year, and Keke even ordered a cake for you!"

Yes, his birthday is on the 29th day of the twelfth lunar month. Because when he was a child, his birthday was always arranged by his grandfather, and his grandfather only recognized the lunar calendar...

So when Qiao Yu was sixteen, he celebrated his birthday three times.

Another time, I was called by my master to go to Peking University and Tsinghua University to send Professor Zhang Shuwen, whom he had met once, back to the United States.

It was at this time that Qiao Yu learned that Professor Zhang was actually a professor and doctoral supervisor at Princeton University. He was just a visiting professor at Huaqing University, and would come to Huaqing University once or twice a year to give some agreed lectures and participate in some academic exchange activities at his master's mathematics research center.

In addition, his master's grandfather introduced him to a professor named Guo Zhenggong, who was also a student of his master's grandfather and currently serves as the director of the School of Mathematics at Huahai University. In terms of seniority, he is Qiao Yu's uncle.

In fact, Qiao Yu had already checked on the Internet the reasons and process of the conflict between his teacher and his master's grandfather.

The details on the Internet are not very detailed, but the general process is available. Probably the biggest gain for Qiao Yu is that he discovered that his master, who was usually kind to him, was actually quite fierce when he was young and had a very hot temper.

However, regarding the things said on the Internet, Qiao Yu felt that it was probably just a dispute of personal feelings, so he showed great respect to his uncle.

Just as Xue Song said, the grudges of the previous generation cannot be blamed on him.

Of course, if either side is uncomfortable with him, then I'm sorry, Qiao Yu feels that if he gets angry, he can actually be quite fierce. Well, he must be as fierce as his master when he was young. If he wants to learn, he must learn the whole set.

Fortunately, both Professor Zhang and Professor Guo were quite friendly to him. However, it seemed that Professor Guo was mostly doing it for Mr. Yuan's sake. That kind of friendly politeness often carried a hint of alienation and disdain. Qiao Yu could feel it, but didn't care.

People are not RMB, and it is impossible to please everyone. In the Morality and Law class, we said that the key is to grasp the main contradiction. The attitude of a senior teacher is irrelevant. On the other hand, Professor Zhang, who was quite strict with him that day, was still quite strict, but he talked to him a lot of things, all of which were practical.

His words were full of protectiveness, and before leaving, he suggested to Qiao Yu that if he was willing, he could go to the Institute for Advanced Study in Princeton for one or two years as an exchange doctoral student, so as to be exposed to more advanced mathematical ideas from abroad and broaden his horizons.

Qiao Yu naturally agreed verbally, but he felt that it might have been necessary in the past, but now that he owns the two major document databases of Yanbei and Huaqing, there is really no need for him to go out and communicate face to face with foreign bigwigs.

In fact, Qiao Yu always felt that paper communication was more efficient, because high-end papers really didn’t have that much nonsense, and all the proofs were clear at a glance, which was enough for him to understand the mathematical thinking of the paper author.

All in all, Qiao Yu felt that his days at Yanbei University were quite comfortable.

I spend most of my time every day reading books and papers, and occasionally go out to attend a few classes.

And this kind of peaceful life brings a lot of benefits.

In terms of learning, Qiao Yu's progress in just two weeks can be said to be amazing. Yes, it really has to be described as amazing. After all, the fact that he could make two academicians feel satisfied, happy and a little surprised at the same time was enough to show how strong Qiao Yu's learning ability was.

Even the two big guys supported him to take more classes in the School of Physics.

In addition, Qiao Yu discovered through observation that Teacher Lan was not lying to him. Whether it was Yanbei or Huaqing, there were really few girls in the School of Mathematics and the School of Physics and Astronomy.

Even if there is, it doesn't seem to fit Qiao Yu's aesthetic.

It’s a good idea to go to the nearby Weiming Lake for a stroll, where you can always see many attractive senior schoolmates.

It seems that there is a reason why many mathematicians around us, such as Teacher Lan, Lao Xue, Senior Brother Chen, etc., are still single at such an old age.

I didn't have much contact with female classmates, and when I was young, I had to focus on boring numbers. It would be strange if I could have a girlfriend.

The only thing that bothered Qiao Yu was probably the scientific research. His research on the topic he had proposed before seemed to have reached a dead end. He thought he could show off to his tutor and master, but now it seemed like a piece of chicken ribs, which made him feel tasteless and a pity to throw away.

But overall, life is quite peaceful and fulfilling.

This peaceful and fulfilling life was suddenly disrupted by my group of friends.

Because Qiao Yu had been too lazy to talk in the friend group for a long time, this group of three people gradually became deserted and no one had popped up for a long time.

After all, everyone is quite busy.

But on Tuesday of the third week of February, Yu Yongjun suddenly started to @Qiao Yu crazily in the group again.

"@喻数临风What the hell, what the hell, what the hell, the first phase of special training this year is really at Yanbei University! Boss, you are invincible!"

"Please, Boss, please come out and let me see your heroic figure."

"Don't abandon me, Boss. Have you forgotten that I once helped you carry a gun? I also helped you fight against that idiot Yu Wei. Really, come out for a moment and say whatever you want. Without your instructions, I can hardly breathe!"

……

I have to admit that the fat boy's hand speed is really fast. In just a few minutes, he sent dozens of messages in the group, half of which were @乔喻.

The direct effect is that the phone vibrates twice after a while.

Unable to bear the annoyance, Qiao Yu finally picked up his phone, quickly flipped through Yu Yongjun's crazy words, and sent an angry expression to the group.

"Boss, you finally came out!"

"I'm busy! I have to study! And do research!" Qiao Yu sent a serious expression with sunglasses.

"No, Boss, you can't just focus on studying and forget that you still have a life! And we! If you immerse yourself in the ocean of knowledge every day and arm your mind with culture, after a long time, what will you have left except that little knowledge!"

It’s been a few months since I last saw him, and this fat guy is still the same as always... shameless and really frustrating.

But you know what, it really works...

Qiao Yu had clearly felt that these days were very fulfilling, but after hearing what the fat man said, she suddenly felt that her life was a little bit empty.

Yes!

During this period of time, he was so busy studying that he forgot that life still needs some simpler and purer happiness. Especially when he was constantly frustrated by scientific research projects, he actually forgot that he was also a top student who could defeat others!

Yes, now he spends most of his time studying on his own, and even the joy of criticizing his classmates has been temporarily deprived.

The most infuriating thing is that when I look around I find that there are no enemies around me for the time being, only friends.

His senior brothers were all very protective of him, but as for people of the same age... well, there seemed to be no one of the same age around him. So he felt unhappy all of a sudden, and the next moment Qiao Yu also started to speed up his hand.

"Don't worry. I'm studying a very important mathematical problem. Do you know Schultz's theory of quasi-complete spaces and the problem of estimating the upper bounds of rational points on curves? Oh, you definitely don't understand, but it doesn't matter. You just need to know that combining these two is my recent research topic.

By the time we all go to IMO together, I will have mastered this topic. By then, you will know that I have not only gained knowledge, but also gained the admiration of the mathematics community and rewards from teachers.

Oh, and I'll probably get tons of envy and jealousy... Well, when I think about it, I'm actually a little jealous of you two. Your life is more fulfilling than mine, and you don't have to experience the loneliness of being at the top, but maybe this is the fate of geniuses."

Yu Yongjun: “!!!”

Chan Buzhixue: “???”

Yes, Yu Yongjun sent nearly a hundred messages in the group, but failed to get Yu Wei out. Qiao Yu directly got Yu Wei out with just one message.

It is obvious that this guy has been peeking at the screen, but refuses to make a sound, and is still as arrogant as usual.

Qiao Yu suddenly felt sorry for Yu Wei, because he suddenly thought of Brother Chen. In the field of mathematics, if you don't have enough talent, it seems that the longer you persist, the greater the blow you will suffer.

"Huh? Yu Wei, you're here again. I thought you had given up on math. Although discussing IQ is a serious topic, have you ever thought about the possibility that even a CMO can't get a perfect score, so he might not be suitable for studying math? (serious face)"

Before Yu Wei could reply, Yu Yongjun jumped out and said, "Brother, your attack is too broad. It has also hit your most loyal brother."

Qiao Yu immediately replied: "It's okay, you can learn computational mathematics in the future. I have found out for you. This thing is very simple. If you know addition, subtraction, multiplication and division, you can do this thing. But Yu Wei is different. He must be a man who wants to get into algebraic geometry. If you don't believe me, you can ask him, but his IQ may not be enough to study this field.

Oh, by the way, Yu Wei, don't think too much. I'm not saying you're stupid. In fact, you're quite smart, as smart as my PhD senior. But being smart is not enough in this field. It requires a higher IQ than being smart. For example, if your IQ is 160, it's already far higher than a normal person, but this field requires an IQ of , understand?"

After sending this message, in order to prove his sincerity, Qiao Yu sent a serious face emoticon to the group.

What can I say? After all, he is a brother in the friend group. Qiao Yu really can't bear to see a rich second-generation brother who does not consider going home to inherit billions of assets, but chooses to jump into the fire pit of mathematics.

But then again, these days he had heard his seniors talk about the life stories of many awesome mathematicians, and most of them were really rich second-generations, the kind whose families owned mines and had no shortage of money.

After all, if you get stuck in the research of basic mathematics and theoretical mathematics, you may end up doing nothing for your whole life...especially in foreign countries, such as the Earth Science and Technology Center of Xi'an University.

A little-known fact is that at Western University, unless one is a particularly well-known scholar, the salary of a professor teaching in a general university is not high. The median annual income of professors is only more than 80,000 US dollars, and this is pre-tax income.

After personal deductions, taxes in the state of residence, and various social security and medical insurance payments, there is probably only over $50,000 left. That works out to an income of less than $5,000 a month, which is considered quite poor.

As for associate professors and assistant professors, their salaries are even lower.

Not being famous means you won’t be invited to give lectures outside often, and it’s even harder to get projects…

Although many Western technology companies know the importance of mathematical theory research, when they want to invest, they naturally give priority to well-known theoretical mathematicians, such as Edward Witten, Peter Schultz, Mary Carter, etc.

If young mathematicians want to get projects, they can only go into the application field. They have to come up with an idea and package it to catch the eyes of investors.

This is the reality. An unknown little professor found Google and said that if he was given one million dollars, he could find the final solution to N-body motion. However, it probably wouldn't even pass the security guard's test.

Without material foundation, it is difficult to go far in this industry relying solely on passion.

So theoretically speaking, Yu Wei's family conditions are really suitable for math, but Qiao Yu thinks it's a pity, after all, low IQ is a fatal flaw...

But it was obvious that Yu Wei did not appreciate it, and only sent two short words in the group: "Hehe..."

From these two words, we can see that there is only anger, no gratitude.

Qiao Yu also began to persuade him: "I understand your obsession with mathematics, but why don't you try another way? For example, you can honestly take the college entrance examination, go to Guanghua College of Yanbei University, and then go home to inherit billions of wealth and run the family business.

When you are able to manage money, you can invest in my future research topics. Then when I produce results, I can add your name to the list. We can both do what we are best suited to. This way, we can not only achieve results, but also allow you to fully participate.”

Chan Buzhixue: "Qiao Yu, that's enough! I admit that you are better than me for now, but I will definitely catch up with you! Whether it's exams or papers! I'm putting this here!"

The momentum was so strong that even Qiao Yu was frightened. He asked weakly in the group: "Oh, what if you can't do what you said in the group?"

Yu Wei didn't reply for a long while, and the group fell silent.

Perhaps because he felt that Yu Wei's anger level had reached its limit today, the fat guy rarely continued to add fuel to the fire in the group. Instead, he started a private chat with Qiao Yu after Qiao Yu asked that question in the group.

"Boss, don't hit Yu Wei too hard! I feel like his little universe is about to explode. Well, I just happened to have accumulated several difficult problems recently. Let him calm down later. You can help me figure out how to solve these problems first. Hey, I asked the teacher but he still can't give me a solution. I know the rules, fifty points for one question, you can keep the money."

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

Looking at the red transfer interface, Qiao Yu sighed in his heart. It turned out that geniuses are lonely and their friends cannot understand them!

I directly clicked on the "Return Transfer" button under "Transfer" and 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 is completely different after bro went there!"

"Well, don't thank me yet. Have you ever heard of this saying? Countless ordinary mathematicians spend their entire lives trying to save a math genius a tea time."

"Boss, you have a vision!"

"Yes, so I won't take your money, but I won't help you solve the problem either. Do you think that 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, how about you apply for my project when you go home to inherit the family property? Hurry up, I still have to study my project!" This time Yu Wei replied quickly: "No need! If I can't catch up with you, I will never marry!"

After seeing Yu Wei's words and thinking of this guy's usually cold temper, Qiao Yu suddenly felt that things had gone a bit too far, so much so that he didn't even bother to remind the other party. The ambiguity in this sentence could make people who didn't know the truth imagine many 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 big-name mentors mainly provide academic magic defense, which cannot defend against physical attacks!

It can be seen that this guy was really angry and confused!
"Stop it. The stakes are so high. What if your father gets angry? Your family's billions of wealth will have no successor. He will definitely fight me to the death!"

"Don't worry, I have two brothers, and I can inherit the family property!"

Oh, so he has two older brothers. No wonder he is so willful.

However, Qiao Yu suddenly thought of what Lang Jie said: the first generation of rich people are much more interesting than the second generation of rich people. So this is what it meant.

After all, the first generation can spend their money however they want, but it is different for the second generation. They have to pay money from the first generation before they can spend it. It is even more complicated if there are two older brothers.

Qiao Yu was still sighing in his heart and was about to reject Yu Wei decisively. After all, he didn't like men, but Yu Yongjun suddenly popped up again.

"Brother, when you need to fight for the family property in the future, remember to tell me and my eldest brother. We will definitely stand firmly on your side... In addition, Lao Yu, although you are indeed quite pretty, before pursuing the eldest brother, you should first ask the eldest brother about his orientation. What if the eldest brother is a normal person? Um, 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 I decisively quit WeChat and set my phone to do not disturb mode.

In just over a week, these two guys will go to Yanbei University for training. He will then naturally be able to see what expression Yu Wei will have. But what is giving him a headache now is the topic he has chosen for himself.

He has already read and almost digested Schultz's five papers on the theory of quasi-complete space. During this period, he also supplemented a lot of basic knowledge and basically completed the proof of his whimsical proposition.

According to his original idea, let X be a high-dimensional algebraic curve defined on the number field K, and X is a closed subset in the p-adic complete algebraic space. Then there exists a constant C that depends on the geometric properties of the curve X, so that the number of rational points on the curve satisfies: N(X)≤C.

This constant C does exist, and Qiao Yu even felt that his proof process was perfect.

And he has also figured out the formula for this constant C.

In other words, the night he came to Yanbei University, the fantastic proposition had actually been proven by him.

If it weren't for Professor Zhang, he might have already started writing the paper with great enthusiasm to announce his discovery to the mathematical community!
But he hasn't started writing yet, because the formula for deriving the constant C looks like this:

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

Three constants A1, A2, and A3 are introduced, representing constants related to modular form, -advanced homology, and quantized homology categories, respectively. α and β represent the exponents related to these geometric constraints, and of course the genus g is still the main factor determining the upper bound.

It doesn't work. It doesn't work at all.

Qiao Yu tried to apply Professor Robert's work and wanted to use his formula to solve some applied problems, but soon found that determining the modular form level k, the selection of prime number P, and the determination of quantized coherence parameter C were all too complicated.

The constants A1, A2, A3 in the formula, as well as the constants α and β related to determining the geometric structure depend on the specific geometric background and curve type. When Qiao Yu actually tried to calculate it, he found out how troublesome it was.

During this period, he has been thinking about how to simplify the formula so that it can be easier to use and the results still hold. He has thought of many ways, but has encountered obstacles everywhere.

He could already roughly understand Brother Chen's feeling of being overwhelmed when facing scientific research. Every time he thought of a way to solve the problem, and then excitedly rushed to the computer and started to solve it, reality would give him a blow.

Every time I tried, the final result was a dead end.

He also specifically asked Lao Xue, who advised him not to hope to find a universal formula, but to directly simplify the specific situation and reduce complexity in specific problems.

This can have a certain application space in practice and can be considered completely worthless.

For example, a simplified formula can be made specifically for a certain type of simple elliptic curve.

This is certainly a method, and Qiao Yu can even use this method to write a number of papers, such as one on elliptic curves, one on parabolas, and one on hyperbolas... If you want to be more impressive, you can also work on algebraic variety projection curves and high-genus hyperelliptic curves...

But Qiao Yu felt that this was meaningless. After all, his original intention was to create a general formula and publish it directly in the four top journals, so that the world mathematics community could directly name it as a paper of the same level as Qiao Yu's Upper Boundary Theorem!
Qiao Yu felt that he could not reach this level and would not be able to bring honor to his teacher and his master.

Moreover, given his current status, if he chooses to write a water-down thesis, it will not only be meaningless to him, but may also lead to a lot of criticism and make Director Tian lose face. It would be better for him to study quietly.

After all, he had no plans to work at a university, where he would need to write papers or get a professional title.

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

Of course, only Tian Yanzhen and Yuan Zhengxin didn’t know what Qiao Ze was thinking, otherwise they would probably scold him. It would be best if they could scold this kid to wake him up, so that he wouldn’t think about messy things every day and waste time!

After all, it was a bit naive to want to name a theorem after oneself at the age of fifteen. Although if Qiao Yu really solved this problem, it was indeed possible.

But how can a concise universal upper bound accurate estimation formula be so simple?

Professor Robert Greene has been researching this topic for many years, and he has only been looking for a more accurate result among various special curves.

But Qiao Yu's idea was obviously different.

Euler graduated with a master's degree at the age of sixteen and proposed a philosophical system comparing Descartes and Newton. Gauss independently discovered a method for finding the roots of cubic equations at the age of fifteen. Why couldn't Qiao Yu propose the upper bound theorem at the age of sixteen?
So naturally, Qiao Yu went straight to the subject, but now he was really frustrated! He had dealt a heavy blow to two good friends, and there was no way to make up for it...

……

At the same time, in a key middle school in Shuangqing, a fat boy with a sad face raised his head and said to the teacher next to him, "Teacher Qu, Qiao Yu suddenly became unethical! He said he would charge 50 yuan per question, but now he refuses to answer me."

The teacher sighed and said, "Well, if you don't understand it, then don't worry about it. Why are you so anxious? Let me study it for two days."

……

In a study room with its own computer and internet at Linhai International Middle School, Yu Wei left the group chat with a livid face. He was really furious. By the time he was reminded by that damn fat guy and realized that his words were ambiguous, it was too late to withdraw...

But after taking three deep breaths, he calmed down, picked up his phone and sent a WeChat message to the teacher.

"Teacher Chen, please help me find a few more papers on the problem of estimating the upper bound of rational number points on a curve and Peter Schultz's papers."

Soon the other party replied: "What do you want these papers for?"

“I want to see how hard this thing is.”

"Professor Schultz's main work at the moment is to solve the Langlands conjecture. To be honest, his paper is just a waste of time and has no meaning if you read it now."

"It's okay, Mr. Chen, I just want to get a general idea. It won't take up too much time."

"Okay, I'll send it to your email in an hour."

Yu Wei put down his phone with a serious expression.

I felt so unconvinced that I became so upset that I lost the mood to do the questions.

During this period of time, he had been intensively practicing various Olympiad questions, and was ready to avenge his previous defeat during the first special training session. However, who would have thought that Qiao Yu, who had gone to Yanbei University, had already started working on his research project.

And this 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 show off in front of him, but Yu Wei knew very well that if he wanted to surpass Qiao Yu, he must first at least determine the gap between them.

Fortunately, he didn't have to wait long before there was a response in his mobile mailbox.

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

Two of them are about the derivation of upper bounds of rational points on curves, and the other is "Perfectoid Spaces: A survey" by Peter Schultz. It was specifically noted in the email that this is the easiest paper by Peter Schultz to understand.

Yu Wei was the first to download Schultz's paper.

After all, Professor Chen said that it was a waste of time for him to read Schultz's paper now, and he was still a little unconvinced.

However, after opening it and reading it, the boy fell silent, and even his inner resentment diminished a lot.

Yu Wei was aware that he had a certain foundation in algebraic geometry, and he had also heard of the name Peter Schultz. He believed that he might not be able to understand this paper very well, but at least he could understand what it said.

But after reading the review, he realized that his understanding of these cutting-edge mathematical research seemed to be a little biased.

This is not something that can be understood by just knowing a little bit of university advanced mathematics.

They are obviously of the same age, is the gap really that big?

He didn't want to believe it was true, but every time Qiao Yu said something that sounded like bragging, he found it was true in the end. And it happened more than once, three or four times... so much so that he didn't dare to trust his own judgment anymore.

Thinking of this, Yu Wei suddenly felt a little uneasy, and before he knew it, his hands had clenched into fists...

There's nothing we can do. People are always like this. When they haven't been beaten, they don't know how painful it is...

……

In Xingcheng, Qiao Xi was sitting at the desk where Qiao Yu used to write, doing his papers calmly.

The sunshine in Star City is just right in winter. Although it doesn't bring much warmth when it shines through the window onto my body, it feels very comfortable.

But what made Qiao Xi feel most comfortable was that looking at the familiar yet unfamiliar textbooks and doing these familiar yet unfamiliar exercises seemed to bring her back to the age when she had infinite longing for the future.

Going to Beijing to attend university...

"Ring..." The sudden ring of the cell phone woke Qiao Xi up from her trance...

He was distracted again. Looking at the math test in front of him which he had already finished most of, Qiao Xi lazily turned his head to look at his cell phone. It was another call from that bad boy at home.

I swiped my finger and selected hands-free.

"Hey, what are you doing?"

"Mom, what are you doing?"

"Do the math test you sent back."

"Oh, is it difficult?"

"It seems a little different from what we learned back then, but it's okay. It's a little hard to do, but it doesn't feel particularly difficult."

"Well, that's normal. The textbooks are changing. If you have questions, you can ask me anytime. This is the privilege you get."

"Come on, what are you calling for?"

"Hey, Mom, I seem to have run into a problem. There's a damn math problem that I can't figure out how to solve no matter how hard I try. What should I do? My teacher and my master's master have high hopes for me, but who would have thought that I would hit a bottleneck just at the beginning."

"Hmm? A difficult proposition?"

"I don't think it's that difficult. In fact, I've already solved the problem, but the result I got is very complicated, with a lot of parameters. I want to simplify the result and throw the complicated things into the proof process, but I've tried every possible way and still can't handle it."

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

"I asked Lao Xue, but he advised me to avoid the most complicated process, which would be meaningless."

"Oh, is it possible that your result is a false proposition?"

"No way! I have a hunch, you know, a hunch? That there must be a way to simplify this result and form a theorem, but I just don't know how to start."

"So you're here to ask for comfort? Hurry up and ask mom to comfort me."

Qiao Xi put down the pen in her hand, stretched out her fair hand, placed the phone in front of her, then propped her chin with one hand, ready to listen to how her own brat complained.

It was a very novel experience. In front of her, Qiao Yu rarely showed such a helpless mentality.

The only pity is that she doesn't seem to be able to help.

"Stop it, Mom, I'm annoyed..."

"Oh, okay, then first tell me why your result has so many parameters?"

"Because this problem is governed by multiple geometric constraints, each geometric tool will have a different set of restrictions after use. And these tools must be used to condense the results into a formula."

"Oh..." Qiao Xi began to ponder, and then asked: "Are all the tools indispensable?"

“Yes, I have tried to reduce the restrictions or improve the tool, but it doesn’t work.”

“So the constraints of these tools have absolutely nothing in common?”

"Commonality?"

"Yes, since every tool must be used and each tool has different restrictions, if you want to simplify it, you have to find the commonalities or the common points between these conditions."

"Hmm? Mom, it seems like what you said makes some sense."

"So you can try to study whether there is any potential connection between those different parameters. If so, maybe you can unify multiple parameters? Isn't math about finding possible logical connections between different conditions?"

Qiao Xi said this irresponsibly. She felt that Qiao Yu should understand this principle better than her...

But the other side was silent for a long time...

"Hey, why aren't you talking?" Qiao Xi was a little surprised.

"Mom, did you give in to that man back then, so he was able to get first place in the exam?"

"Ok?"

"I've been thinking about how to optimize those tools to control the parameters recently. Why didn't I think of unifying these parameters since they can't be controlled? Thank you, Mom, I feel like I've found the direction!"

"No way? Are you serious?"

"Of course! God, I've always envied those mathematicians who can create tools at will. What I'm doing now is also creating tools, but when I was getting stuck on this, how could I forget that in this case, even if there are no ready-made tools, I can still solve the problem by creating tools?!

Thank you, Mom! By the way, if I really solve this problem because of your hint, this theorem will be called the Qiao Yu-Qiao Xi Upper Bound Theorem! And you will be the second author of this paper!"

After saying that, the other party hung up the phone without even waiting for Qiao Xi to speak.

Qiao Xi shook her head in confusion...

This brat, what's wrong with her? Why does she need a second author?! And the Qiao Yu-Qiao Xi upper bound theorem? What the hell!

　Thanks to the book friend 20201028183615004 for the reward and encouragement

　　PS: The 25th day of updating words has been completed!
　　
　
(End of this chapter)