The school year has started, and the campus of Yanbei University has begun to become lively, and even the Mathematics Research Center has become more lively.

Director Tian didn't lie to him when he said that, for example, some elective courses in the School of Mathematics are directly related to research. Moreover, the research center has also specially opened an intensive basic mathematics course for senior undergraduates in the School of Mathematics.

Of course, if Qiao Yu wants to go to these courses, he can also attend them at any time. Of course, it is not just these courses. Whether it is Yanbei University or Huaqing University, as long as it is a mathematics course, he can attend it as long as he wants to. . There is no need to go through the trouble of registering online to take classes. Anyway, he doesn’t need those credits and grade points for the time being.

Tian Yanzhen's request for him in the past six months is still that he only needs to finish reading those books.

Qiao Yu also used practical actions to make Tian Yanzhen feel that he did not need to worry too much about his closed disciple.

On Sunday night, Qiao Yu will carefully prepare a copy of his reading experience, and then send it to his tutor early on Monday morning. Of course, Qiao Yu will not forget to send one copy to his master's grandfather on Monday morning. Then he will receive two comments. From then on. It can be seen from the annotations on his reading experience that his two mathematics tutors have done in-depth research on these basic mathematics books. Many details that he has not noticed will be reminded in the annotations.

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

Not only because the small building he lives in finally has hot water, but it even allows him to secretly run to the second floor to take a shower at night when no one is around. It is also because Senior Brother Chen helped him collect various college entrance examination teaching aids. The cost of mailing it back alone cost Qiao Yu more than three hundred yuan, including many internal review papers for senior high school subjects from the best high schools in Beijing.

Their scarcity can be explained by the fact that most of the teachers who wrote these papers have the experience of being selected into the national college entrance examination question group many times. After that big meal, Senior Brother Chen also became more attentive to Qiao Yu.

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

Let's put it this way, if someone steals Qiao Yu's card, the amount of money in it will lead to a starting sentence of more than ten years. Chen Zhuoyang did the math casually and concluded that even if Qiao Yu eats three meals a day in the Huaqing cafeteria from now on, In ten years, you may not be able to use up the remaining balance in your card.

Money is not everything, but it can really measure a degree of favor.

The favor from Grandpa Shi is so terrifying that Chen Zhuowen can no longer envy him. He just feels that the gap between people is too big and there is no comparison at all. He now really believes that if Qiao Yu holds his thesis Ask Mr. Yuan to help me change it. Maybe Mr. Yuan will take action himself.

Really, Chen Zhuoyang also wants to find a chance to call Teacher Yuan "Grandpa".

It's a pity that there is really no chance. Of course, if there is a chance, Chen Zhuoyang feels that he may not be able to shout out.

The difference between Qiao Yu's youthful face and his half-bald appearance is really big. When Qiao Yu calls him Grandpa, people can feel the beautiful relationship between grandfather and grandson. He calls out Grandpa Shi, I may be able to hold back from vomiting, but I’m not sure what others will think of me.

The talent is not comparable, and there is no age advantage..

In terms of mathematics, it is easy to prove that he should just cling firmly to his younger brother's thigh. A doctor of mathematics who does not want to engage in scientific research lowers his head in order to graduate and does not complain! On the other hand, although school has started, Lao Xue has also started to be busy. Even though I got up, I still took time to check on Qiao Yu every day.

Sometimes I just come to take a look, and sometimes I come to give Qiao Yu some advice, such as helping him plan some courses that he needs to attend every day. After all, I am in Yanbei, and it would be a waste of resources not to attend the classes at all.

Qiao Yu did listen to the advice, but there were fewer courses in the School of Mathematics, and more elective courses in the School of Physics next door. They were mainly concentrated on the two courses of quantum mechanics and mathematical physics methods. Not that Qiao Yu has no plans to develop in the direction of physics, at least for the time being, but Qiao Yu feels that broadening his knowledge appropriately will be beneficial to him.

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

As we all know, even in mathematical analysis, infinite divergence is a headache, because it means that the result may not be defined. For example, the divergence series cannot produce a finite sum, which directly causes the mathematical model to lose its practical meaning. In addition to these daily In addition to the courses, in the two weeks after the school started, Director Tian asked him twice to clarify his doubts, and the teacher from across the street called him three times.

One of them was on the same day. In the morning, Director Tian was helping him solve his doubts. During lunch, Senior Brother Chen suddenly brought a birthday cake, and Lao Xue also came over specially to give a birthday gift. Qiao Yu, who had a premonition, was called over by Senior Senior in the afternoon. , and sure enough, I celebrated his birthday again.

Yes, in the first year of coming to the capital, on February 3rd, Qiao Yu’s sixteenth birthday, he had two birthdays in a row from noon to evening. He spent the noon at Yanbei University and the evening at Huaqing University. Graduated from college.

When he returned to Yanbei University in the evening and called Qiao to criticize his mother for not calling him on his birthday, Qiao Xi scolded him and woke him up with a few words: "Are you sorry? How often have you not been at home? You have a lunar birthday? Do you want me to remind you? You have already celebrated your birthday this year before going to the capital, and I even ordered a cake for you!"

Yes, his birthday on the lunar calendar is on the 29th day of the twelfth lunar month. Because when he was a child, his birthdays were always arranged by his grandfather, and his grandfather only recognized the lunar calendar... So Qiao Yu had three birthdays in the year when he was sixteen.

The other time I was asked by Grandpa Shi to go to the north of Qing Dynasty to send Professor Zhang Shuwen, who had met him once, back to the United States.

It was also at this time that Qiao Yu learned that Professor Zhang was actually a professor and doctoral supervisor at Princeton University. He only had the title of visiting professor in Huaqing. He would come to Huaqing about once or twice a year to complete some agreed lectures. As well as doing some academic exchange activities at Grandpa Shi’s Mathematics Research Center.

In addition, Grandpa Shi also introduced Professor Guo to him. Professor Guo Zhenggong was also a student of his Grandpa. He currently serves as the director of the School of Mathematics at Huahai University. He is Qiao Yu’s senior uncle by seniority. In fact, Qiao Yu has already been online for a long time. I investigated the reasons and process of the conflict between my teacher and my grandfather.

The details on the Internet are not very detailed, but the process is still there. For Qiao Yu, the biggest gain is probably that he discovered that his grandfather, who was usually kind to him, was actually quite fierce when he was young, with a particularly hot temper. However, regarding the things mentioned on the Internet, Qiao Yu felt that it was just a battle of spirits, so he also showed great respect for his uncle.

As Xue Song said, the grudges of the previous generation are not his fault.

Of course, if anyone on both sides sees him uncomfortable, then I'm sorry. Qiao Yu thinks that if he loses his temper, he can actually be quite fierce. Well, he must be as fierce as Grandpa Shi when he was young, and he must learn all the skills.

Fortunately, both Professor Zhang and Professor Guo were quite friendly to him, but at present, Professor Guo mostly did it for Mr. Yuan's sake, and that kind of friendly politeness was often accompanied by a touch of alienation and disdain. Qiao Yu could feel it, but didn't care.

People are not renminbi, and it is impossible to be liked by everyone. It was said in the ethics and rule of law class that the key point is to grasp the main contradiction. The attitude of a senior uncle is irrelevant. On the contrary, Professor Zhang, who was quite strict with him that day, was still quite strict. , but I told him a lot of things, all of which were practical.

His words were full of protection. Before leaving, he also suggested to Qiao Yu that if he was willing, he could go to the Institute for Advanced Study in Princeton as an exchange doctor in a few years to study for one or two years and get in touch with some more advanced foreign students. Mathematical thinking, broaden horizons.

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

In fact, Qiao Yu has always felt that paper communication is more efficient, because high-end papers really don't have so much nonsense, and all the proof processes are clear at a glance. It is enough for him to understand the mathematical ideas of the author of the paper. In short, Qiao Yu feels that his work at Yanbei University Life was still very comfortable.

Most of the time every day is spent reading books and papers, and occasionally going out to attend a few classes. Moreover, this kind of peaceful life is very rewarding.

In terms of learning, Qiao Yu's progress in just two weeks can be said to be very amazing. Yes, it must be described as amazing. After all, it can satisfy both academicians at the same time, and there is a bit of surprise in the joy, which is enough to explain Qiao Yu's learning. How capable he is. Even the two bosses support him to take more classes at the Institute of Physics.

In addition, Qiao Yu discovered through observation that Teacher Lan really did not lie 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 have caught up with Qiao Yu's aesthetics.

I have nothing to do but go to the nearby Weiming Lake for a walk. You can always see a lot of eye-catching seniors.

It seems that there is a reason why many math people around me, including Teacher Lan, Lao Xue, Senior Brother Chen, etc., are still single at a very young age.

I didn’t have much contact with female classmates, and all of them had to focus on those boring numbers when they were young. It’s strange to have a girlfriend.

The only thing that worries Qiao Yu is probably scientific research. His research on the proposition he proposed before seems to have entered a dead end. What he thought he could show off in front of his mentor and grandpa now seems like

It was like a piece of chicken rib, which made him feel that it was tasteless and a pity to throw away.

But overall, life is quite peaceful and fulfilling. This peaceful and fulfilling life is suddenly disrupted by a group of friends.

Because Qiao Yu has been too lazy to talk in the friend group for a long time, this group of three people has gradually become deserted, and no one has made any comments for a long time. After all, everyone is actually quite busy.

But on Tuesday of the third week of February, that guy Yu Yongjun suddenly started to go crazy in the group @Qiao Yu.

"@蛷 Linfeng Damn it, Damn it, Damn it, the first phase of special training this year is really at Yanbei University! Boss, you are invincible!" "Please, Boss, come out and say something. Let me pay my respects."

Show me your heroic appearance."

"Don't abandon me, boss. You have forgotten that I helped you carry a gun back then, and I also helped you fight against that idiot Yu Wei. Seriously, come out and say whatever you want. Without your instructions,

I can't even breathe!" I have to admit, the little fat guy started running really fast. Within a few minutes, he posted dozens of messages in the group, half of which were @ 青宇.

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

Unable to bear the disturbance, Qiao Yu finally picked up her phone, quickly scrolled through Yu Yongjun's crazy words, and then sent an angry expression to the group. "Boss, you are finally out!"

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

"No, boss, you can't just focus on studying and forget that you still have a life! And we! You immerse yourself in the ocean of knowledge every day and arm your mind with culture. After a long time, in addition to that little knowledge, you also have

What's left?" We haven't seen each other for several months, and this fat man is still the same as before... shameless and irritable.

But don't say it yet, don't say it yet, it will really work...

Qiao Yu obviously felt that these days were very fulfilling, but when the fat man said these words, he suddenly felt that his life was a little bit empty. Yes!

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

Yes! Now he spends most of his time studying on his own, and even the joy of hitting his classmates has been temporarily deprived of him.

The most annoying thing is that when you look around you, there are no enemies for the time being, but only friends.

His fellow seniors all took special care of him when they met him. As for his peers..., there seemed to be no peers around him. So he felt unhappy all of a sudden, and the next moment Qiao Yu also started to use his hand speed very quickly.

.

"Don't worry, I'm studying a very important mathematical problem. Do you know Schulz's theory of quasi-complete spaces and the problem of upper bound estimation of rational points on curves? Oh, you definitely don't understand, but it doesn't matter. You just need to know how to put these

The combination of the two will be my recent research topic.

By the time everyone goes to participate in IMO, I will probably be able to conquer this topic. Then you will know that I have not only gained knowledge, but also gained the admiration of the mathematics community and rewards from teachers.

By the way, I may also gain tons of envy, jealousy, and hatred... Well, thinking about it this way, I am actually a little jealous of you two. You live a more fulfilling life than I do, and you don't have to experience the coldness of high places.

Loneliness, but maybe this is the fate of genius."

Yu Yongjun: "!!!" Chan Zhimixue: "???"

Yes, Yu Yongjun sent nearly a hundred messages in the group, but failed to blow up Yu Wei. Qiao Yu directly blew up Yu Wei with just one message. It can be seen that this guy has been peeking at the screen and just refused to come out.

His voice was still as arrogant as usual.

Qiao Yu suddenly felt a little sorry for Yu Wei, because he suddenly thought of Senior Brother Chen. In the field of mathematics, if you are not talented enough, it seems that the longer you persist, the greater the blow you will suffer.

"Huh? Yu Wei, you are here again. I thought you had given up on mathematics. Although discussing IQ is a serious topic, have you ever thought about the possibility that even CMOs cannot get full marks in the exam, so they may not be suitable for studying mathematics?

? (serious face)" Before Yu Wei could reply, Yu Yongjun jumped out first: "Brother, your attack is a bit broad, and it has also hit your most loyal little brother."

Qiao Yu immediately replied: "It's okay. You can learn calculations and mathematics in the future. I've found out everything for you. This thing is very simple. If you can add, subtract, multiply and divide, you can do this. But Yu Wei is different. He

He must be a man who wants to learn 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 are stupid. In fact, you are quite smart. You are as smart as my brother with a Ph.D. But in this field, smartness is not enough. The requirement for IQ is higher than smartness.

It needs to be higher. For example, your IQ is 160, which is far higher than normal people, but this field requires an IQ of 200, do you understand?"

After posting this, in order to prove his sincerity, Qiao Yu posted another serious expression to the group.

What can I say, after all, he is a brother in the friend group. Qiao Yu really can't stand by and watch a rich second-generation brother choose to jump into the fire pit of mathematics instead of considering going home and inheriting hundreds of millions of assets. But then again

When he came back, he had heard his senior fellow students talk about the lives of many great mathematicians these days. Most of them were really rich second generations, the kind whose families had mines and no shortage of money.

After all, if you get stuck in the research direction of basic mathematics and theoretical mathematics, you may live a lifetime of mediocrity...especially in foreign countries, such as the Earth Science and Technology Center Western University.

A little trivia: Unless you are a particularly well-known scholar at Western University, the salary of professors teaching at Western University is not very high. The median annual income of professors is only more than 80,000 US dollars, and this is pre-tax income.

After personal deductions, after paying taxes in the state of residence, as well as various social security and medical insurance, there is probably only more than 50,000 US dollars left. Calculating the monthly income of less than 5,000 US dollars, it is considered quite poor.

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

Not being famous means that you won't be often invited to give lectures outside, and it will be even harder to get projects.

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?"

"Yes, I have tried to reduce the restrictions or improve the tools, but it doesn't work." "So are the restrictions of these tools completely different?"

"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 similarities, between these conditions." "Huh? Mom , you seem to be right."

"So you can try to study whether there are potential connections between the different parameters. If so, maybe you can unify the multiple parameters? Isn't the math problem about finding possible logical connections between different conditions? Well." Qiao Xi said casually and irresponsibly, she felt that Qiao Yu should understand this better than her.

But the person on the other side didn't say anything for a while...

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

"Mom, did you give way to that man so he could get the first place in the exam?" "Huh?"

"I've been thinking recently about how to optimize those tools and control the parameters. Why didn't I think that since I can't control them, why not unify these parameters? Thank you, Mom, I feel like I have found the direction!" "Isn't it? Are you serious?"

"Of course! God, I have always been jealous of those mathematicians who can create tools at will. What I am doing now is also creating tools, but why did I forget this situation when I was trying to get the best of me? I can create tools without ready-made tools.

What’s the solution?!

Thank you, Mom! By the way, if I really solve this problem because of your tips, this theorem will be called the Qiao Yu-Qiao Xi upper bound theorem from now on! And you will be the second author of this paper!" After that,

, before Qiao Xi could say anything, the other party hung up the phone.

Qiao Xi shook her head inexplicably...
Chapter completed!