Chapter 119 The silent dedication of the mentors
The first phase of IMO training is over. Although Qiao Yu planned to take a rest, he still honestly wrote a paper about his experience in reading the paper and sent it to Director Tian and Huaqing. Mr. Yuan. This time it was really not to let the two mentors know how hard they worked, but it was for a purpose.
Because he has been studying the geometric Langlands conjecture paper during the entire training period.
Director Tian didn’t know if he would find someone to check on his experience, but Qiao Yu believed that Mr. Yuan would casually forward it to Professor Pan.
In this way, if he has any understanding problems, Professor Pan can point them out to him.
The main reason why he didn't send it directly to Professor Pan himself was because Qiao Yu felt embarrassed.
Do not do to others what you do not want others to do to you.
If someone thinks of a question every day, just send it to him directly... And he can summarize several questions every day, and this lasts for nearly half a month. Qiao Yu feels that he has blocked this person directly. .
Although Professor Pan did not block him, he had clearly felt that the Huaqing Professor's messages were getting slower and slower.
Anyway, he was the quickest to reply to messages in the first two days after I added him. Almost every time I had a question, he would reply immediately. After that, the reply to messages became slower and slower.
During the training camp, there was even a situation where it took Professor Pan a full day and a half to reply to a question he sent the day before...
Qiao Yu did not consider whether the questions he asked were getting more and more tricky. , Professor Pan also needs to discuss it with someone before he dares to give a reply. Moreover, Professor Pan did not tell him that he was not in Huaqing at all now, but was going abroad for a meeting.
Qiao Yu was just sensitive and felt that Professor Pan might have changed and started to annoy him a little. It was difficult to ask this question directly, so he could only make a roundabout way.
There is nothing to talk about in the next week. I will continue to read books and papers.
It was just that Qiao Yu was supposed to read the paper on prime numbers before, but instead read the more than 800-page paper on the geometric Langlands conjecture.
Learning while reading will undoubtedly slow down the speed of reading papers.
In the eyes of a normal professor, the books I read this week are starting to look unsystematic.
But this is what Qiao Yu is best at, finding books to read on demand.
There are quite a lot of books to read about the Langlands Program of Geometry. Qiao Yu felt tired before because he had no direction, but now that he has a goal to strive for, this kind of task does not feel so tiring anymore. .
Moreover, the training time schedule is not too tight. The collective life also ensures that Qiao Yu can go to bed on time at 11 o'clock every day and get up on time at 6:30 in the morning. The sleep he lost some time ago was fully made up during the training period. .
By the way, there is one more thing worth mentioning.
Yu Yongjun also pulled Gong Jiatao into his friend group.
No way, the two of them have been getting along best these past few days. However, as the group leader, when Qiao Yu saw these two people in the same group, he decided to talk less in the group from now on.
After all, it is easy to hide when you are exposed, but it is difficult to prevent when you are undercover.
Yu Yongjun is a standard bright and coquettish character with extremely strong brain jumping ability, but he only talks about all kinds of shameless coquettish operations but does not do them.
Gong Jiatao is naturally a secret coward. He looks like a dog to ordinary people, but he is very liberal in playing various tricks. Whether it is successful or not, he will do it first.
As for Yu Wei...
Qiao Yu originally thought that he was the only kind and good person in the group, but he was a bit withdrawn. But now it seems that this guy can lie without blushing or heartbeat, and he looks very sinister.
This time made Qiao Yu suspect that the reason why these people wanted to compete instead of taking the college entrance examination normally was probably because if they took the college entrance examination, everyone would find that based on their ideological and political level, they should be arrested immediately and then Shoot him immediately...
Of course, the feeling is mutual.
What Qiao Yu didn't know was that when Yu Yongjun and Gong Jiatao often chatted in private, they actually had similar views... For example, non-human beings like Qiao Yu should not participate in math competitions with them, and their destination should be sent to some high-end creature. The laboratory conducts live biopsy research directly.
The friendship formed during the competition is so pure and beautiful.
Of course, this does not mean that the two sides will really be on the same page.
In fact, everyone is learning from each other all the time. It was as if Qiao Yu felt that he should learn from the shamelessness of Yu Yongjun and Gong Jiatao, while Gong Jiatao and Yu Yongjun had agreed that after returning to school this time, they must find some classmates and play games with them while solving problems.
They even tried it secretly in private. If they replaced the Olympiad questions with ordinary practice questions like high school, they could still handle it.
Of course, the rules of the competition need to be slightly changed, and you can't play against guys who are very good at the game.
But these don’t seem to be problems. For ordinary students in the high school they live in, to keep up with most of their classmates, they already have to do their best, and there is not much left to focus on games.
After all, those who are really qualified to waste some time on games during their studies these days have to be primary school students...
But their reasons are also very good. Only with self-esteem at your feet can you regain your confidence and achieve good results in international competitions.
From this point of view, among the four friends, Yu Wei is probably the only one who can write the word "good" in one stroke.
But Qiao Yu didn't care.
The only thing that makes him sad is that recently, even Director Tian and Grandpa Shi across from him have been slower and slower in replying to his messages.
Well, at the beginning of the semester, the bosses are all very busy, Qiao Yu comforted himself like this.
But there are still some gains. For example, Professor Pan, who was getting slower and slower in replying to messages, suddenly one day sent an address directly to Qiao Yu and gave him an account password. After logging in, Qiao Yu discovered that the latest videos inside were all about various seminars held recently on the geometric Langlands conjecture.
Although the lectures were still given by the two main leaders, Dennis and Sam, they also included everyone in the entire team, including Professor Pan. The focus of the demonstrations in the several lectures was also different.
Qiao Yu also keenly noticed that the man appeared in the third most scenes...
There is no doubt that for Qiao Yu, the discussions in these seminars were very useful, and they indeed solved his unsolved problems. Fewer questions.
For example, if you have a high-level understanding of the overall proof idea of the paper, then when you read through the details of the paper, you will be able to solve many problems that you did not understand before.
The most important thing is that this made him more and more sure that his intuition might be right.
Local-global phenomena in algebraic geometry or category theory need to be frequently used to locate the interaction with the global when extending the consistent equivalence results to the general case. Then if some minor errors occur during local calls, it will inevitably cause global errors.
This may even lead to the key theorem proved by the authors - the applicability of Ambidexterity may be limited in some specific cases
To know the last paper, it is to use this conclusion to generalize the conjecture to general situation, if the applicability of the most critical Ambidexterity theorem is limited in the situation discussed in the paper, then this proof of the geometric Langlands conjecture can only be declared a failure.
But it is still not easy for Qiao Yu to prove this.
Because the paper itself relies on specific axioms and assumptions, the results in higher-order category theory are correct in a specific context, but if the axioms or category structure change, the applicability of the theorems may also be affected.
Even in the geometric Langlands Programme, some complex homological algebraic problems treated by this theorem have been successfully solved.
In words that ordinary people can understand, this paper is the result of an environment constructed by mathematicians themselves, relying on specific theoretical background and assumptions. To prove that there is a problem, Qiao Yu may need to find a way to prove that the entire framework constructed has logical loopholes.
You must know that in modern mathematics, the self-consistency of the axiomatic system and the category theory framework is highly rigorous. Any effort to question or attempt to uncover logical holes must be based on more rigorous reasoning and innovative perspectives, making the task of questioning this construct extremely difficult.
But when you want to prove an error in mathematics, there is also a trickiest way, which is to construct a counterexample.
Counterexamples are a very powerful tool in mathematics, which can directly show that a certain theorem or inference does not hold under specific conditions. Theoretically, as long as he can carefully design an algebraic geometry situation under the logical framework established by the other party, and prevent local objects from meeting the requirements of the Ambidexterity theorem globally, he can achieve this goal.
If we can go one step further and use this counterexample to discuss the reasons for the axiom mismatch, for example, through the technical assumptions in the backtracking proof, we can deduce the loopholes in this paper and give a preliminary solution, then He may become a star in mathematics again...
Of course, this is still not a simple matter.
In fact, it is much more difficult than any problem Qiao Yu has encountered so far.
Anyway, the week after the training camp passed so uneventfully. He thought about it while reading books and papers, and even thought about it while taking a shower and sleeping, but he still failed to construct a suitable counterexample. .
However, while sitting on the high-speed train from the capital back to Star City, Qiao Yu still shared his work experience this week with Director Tian and Grandpa Shi across from him as usual.
“Dear Master Tian/Grandpa Master: My main job this week is still to read in depth about the proof of the geometric Langlands conjecture. The main gain this week is that I have a clear understanding of one of the key conclusions, namely the Ambidexterity theorem. , I have some thoughts and I would like to report to you
The Ambidexterity Theorem plays a very important role in this series of papers, especially in generalizing the conjecture from specific situations to a more general algebraic geometry background.
But as I further looked at the structure of the theorem and its application in the proof of the geometric Langlands conjecture, I began to have some doubts about its applicability, especially when dealing with situations involving singular points or complex geometry.
According to my superficial understanding, this theorem relies on a certain equivalence of local and global objects, especially in the framework of homologous algebra and category theory. It requires that locally defined geometric objects can be globally defined. Be consistent.
This kind of local-global equivalence seems reasonable in the context of smooth geometry. The paper also discusses some special cases, but when I think about some more complex cases, such as algebraic varieties containing non-identical Are there possible limitations to the general case of singular points?
Specifically, I suspect that local structure near some specific singular points may cause certain properties in homology algebra, such as local flatness or projectiveness, to not be correctly globalized.
That is, if the Ambidexterity theorem must rely on this good behavior of local geometric structures, is there any limit on the applicability of the theorem to algebraic varieties where such specific singular points exist?
I have not found a specific counterexample yet, but in next week’s training event I plan to think deeply from the following two aspects: 1. Whether there are extraordinary singular points that will affect the properties of local homology algebra Impact, causing the local-global equivalence of the theorem to be violated.
2. The proof of the Ambidexterity theorem involves certain axiomatic structures in higher-order category theory. I would like to further explore how these category theory axioms behave in the case of exotic geometries. Are there some implicit assumptions that cannot hold in more complex geometric backgrounds?
Although my ideas may certainly seem naive to you, I think they have some value for exploration. The proof of the geometric Langlands conjecture is very complex, and the Ambidexterity theorem is a key conclusion. Any potential applicability issues may affect the validity of the proof.
So I hope to start with the local geometric structure at the singular point to further verify the limitations and potential problems of the theorem. If you have a better idea, please tell me quickly, your dearest Student/grandson, for the first time this week, I felt the distress of hair loss. ”
This experience was sent by Qiao Yu to his mentor and grandpa Shi while he was sitting on the high-speed train. The person sitting next to him was Professor Zhou Liang, the leader of this IMO team.
But in fact, he had already edited this content last night and saved it in his mobile phone. What he just did was copy and paste and add the names of the people, and then slightly change the self-identification at the end, and then click Just click the send button.
The main reason for doing this is to avoid being asked by the mentor or grandpa to give him a lecture again, saying that he does not know how high the sky is and how high it is. After only reading the paper for a few days, you want to find loopholes in it - this is very possible.
The old man is more accepting that he discovered loopholes in the process of learning, and his thinking was obviously based on the idea of finding fault with other people's papers.
But there is no way, an honest and step-by-step report cannot reflect the seriousness of this problem. He is in great need of help from the two big guys now. It is best to mobilize many brains to start from this direction and give him some constructive ideas to inspire him.
Naturally, he must tell his thoughts truthfully.
To put it bluntly, I want to make full use of the resources around me, but I don’t want to bear the responsibilities caused by it.
After all, he was led astray by two guys, Yu Yongjun and Gong Jiatao.
......
Yanbei University, Tian Yanzhen really didn’t expect that Qiao Yu would suddenly send such a report today.
Because he had to participate in the training camp, Tian Yanzhen had actually agreed that Qiao Yu could take a break this week. Who would have thought that not only did Qiao Yu not take a break, he also showed him how scary it is to be serious!
In fact, the proof of the geometric Langlands conjecture did not trigger much discussion outside the mathematical community.
Because the Langlands Program is too far away for ordinary people, it is not even as close to it as the Riemann Hypothesis and the N-S equation.
This does not mean that the Langlands Program is necessarily more difficult than solving these world-class conjectures. The main thing is that the threshold for anything involving the unity of basic theory is extremely high.
For example, the main problem that needs to be solved in the Langlands Program is to establish a bridge between the Galois representation and the automorphic form on the algebraic number field. You can know this thing just by looking at the definition without spending several years on algebra. In geometry, number theory, and representation theory, I can't understand the question stems at all.
Really, if you don’t believe it, you can go to various major mathematics colleges for interviews. Just a self-defeating form can make countless college students and graduate students struggling to learn, and they still half understand it, and some even know nothing about it.
If it is the self-defense expression involved in the Langlands Program... then it is really even more embarrassing. After all, automorphic forms are just abstractions, while automorphic representations are higher-level abstractions that describe how the algebraic group acts on a specific Hilbert space or Banach space. The elements in these spaces may be analytic functions or some special structures.
The Langlands Program of Geometry studies the correspondence between local systems on algebraic curves and the geometrization of automorphic forms. It simply replaces the number theoretical objects involved in the classic Langlands program with algebraic geometric objects.
The main research is to geometricize abstract number theory problems so that they can be processed in the algebraic geometry framework. This is arguably not about solving specific problems, but rather providing a valuable tool for mathematicians to solve more specific problems, with such a wide range of potential applications.
This field also mainly attracts mathematicians who wish to open new paths in number theory and algebraic geometry.
One can even understand the Langlands Program of Geometry as an important mathematical tool like calculus. Like the Langlands Program, calculus was not born to directly solve a specific problem, but to build a set of tools for dealing with continuous changes and limit problems.
So the Langlands Program of Geometry may completely change the way future mathematicians deal with certain problems, just as calculus changed the way mathematicians of this era deal with changes. It is natural to be interested in this area. are also mathematicians.
Because once someone succeeds, it means that everyone will have a new framework that can be used directly when studying number theory problems in the future. Treat classical number theory problems through a new dimension.
Even one day in the future, it will become a compulsory course in college mathematics just like calculus.
Tian Yanzhen has actually been concerned about the development of the proof of the geometric Langlands conjecture. And we are also very optimistic about the results obtained by this research team.
But who would have thought that Qiao Yu would suddenly give him a big one.
My students suspect that there are loopholes in the results that were finally released after more than fifteen years of research? !
What should I say...
It would be easy to say if there is a loophole in this, but if it is just a conjecture, it would really offend people.
Of course, considering that Qiao Yu is only sixteen years old, probably no one will really care about him. But it was precisely because Qiao Yu was only sixteen years old that Tian Yanzhen felt a little nervous when he saw this weekly report posted by Qiao Yu.
Still a bit too much.
You have only read the paper for a few days and you have so many ideas? !
I don’t care whether the idea is right or wrong, but at least it shows that when Qiao Yu read the paper, he was really deconstructing the most basic things in the paper.
In the field of mathematics, this is really strong.
In other words, being able to quickly grasp the core of a paper and deconstruct its basic content is definitely an ability that many mathematicians seek.
Deep understanding, quick learning ability, and strong mathematical intuition are all indispensable.
If coupled with the fact that this kid is so bold, Tian Yanzhen only feels like him even more.
Really, he felt that it would be impossible for him to have another student like this in a short time.
Unless the world is crazy...
Or maybe a new era of technological explosion is about to begin, just like after quantum physics was proposed, a bunch of talented people came one after another to build on this foundation. , paving a broad road, using quantum mechanics to explain how electrons travel through pn junctions and how to control current in field-effect transistors, laying a theoretical foundation for the development of the semiconductor industry.
This will pave the way for human society to officially enter a new electronic information era. Children of the new era have begun to be unable to understand something like the telegraph that has been buried in the dust of history. In fact, it was only a few decades before telegraph technology was officially eliminated.
Typewriters, fax machines, and even early dial-up Internet access are gradually being forgotten. In probably a few years, these products that once represented advanced productivity will become memories in history books.
As soon as this idea emerged in his mind, Tian Yanzhen suddenly felt excited.
What a coincidence... Qiao Yu turned out to be his student, it was like a dream.
After thinking for a long time, Tian Yanzhen took out his mobile phone. There was a phone number in the address book. Although he had spoken to the owner of this number once before, Tian Yanzhen always felt that there was a high probability that he would not take the initiative to call this number.
But at this moment, the emotions I once had faded away, really faded away.
With such a student, Tian Yanzhen feels that he can face everything in the past calmly.
No matter what, when Qiao Yu is introduced in the history of mathematics in the future, there will definitely be a sentence of "studied from the famous Chinese mathematician Tian Yanzhen". This is actually enough. At his age, it is almost impossible to achieve anything in mathematics.
But his students have unlimited possibilities, so why are they still struggling so much?
Men, it’s okay to be more open-minded.
Sometimes people are like this, one thought can make the world wide.
So when he pressed the dial button, Tian Yan was really calm and calm.
The phone rang for more than ten seconds before being answered. This probably meant that the old man opposite had gone through some mental processes, but it didn't matter.
“Hello, Mr. Yuan, hello.”
"I don't want to take it, I don't want to take it. What advice does Professor Tian have?"
Hey, the old man is still a little narrow-minded.
Tian Yanzhen said warmly: "Mr. Yuan, there is no need to be angry. You should also think that I am making this call because of that child Qiao Yu. I think he also sent you a copy of his study summary report this week. Right?"
The person on the other side became quiet, and after a while he said, "Yes, I got it. , I forwarded a copy to Professor Pan.”
Tian Yanzhen said the purpose of the call: “That’s what I thought. We also have scholars in the Mathematics Research Center who focus on research in this field, such as. Professor Tan Zhiqing has been working on the subject of P-Langlands Program for these years
In particular, there have been many breakthroughs in the direction of local analytical representation and L-invariant theory. Why not wait for Qiao Yu to come back from Star City, and we will cooperate to hold a series of exchange meetings on the Geometric Langlands Programme. What do you think? "
The person on the other side pondered for a moment and then asked: "Where will it be held? "
Asking this, the old man opposite was obviously moved.
Tian Yanzhen said grandly: "Why don't we do it in Huaqing? It's so close anyway, let's do it for him. After doing so much, it was appropriate to let that kid take a few more steps. "
"The time will be after Qingming Festival, and Professor Pan from the research team will not be able to come back until then. ”
Tian Yanzhen asked: "No problem. You can arrange the specific time. Let me clear the air first and see which other professors can be invited to participate. By the way, Professor Pan, can you invite Professor Dennis?"
"It's probably difficult. Dennis and Sam probably won't treat Joe I don't like Yu's idea, but you can ask Professor Everton from Princeton if he has time. He has profound knowledge in both geometric representation theory and p-adicHodge theory. Let him help make a judgment. Very helpful to Qiao Yu. "
" Invite in your name? "
"Professor Everton, I will invite you. By the way, you and Professor Felice are from the same Abel Prize. The judges should be familiar with it. He has been experimenting with the geometric Langlands conjecture. It would be more helpful if we could invite him to come."
"Okay, I'll send him an email right away. If he doesn't have anything special to do in the near future, he should be able to come. But you have to. Set the time first.”
"Wait a minute...well, April 5th to April 8th, just two days on the weekend."
"Okay. I will contact you as soon as I receive the news. "
"Okay."
"Old Yuan, I'll hang up first."
"Dududu..."
Tian Yanzhen smiled to himself. The old man still had a resolute and resolute temper, so he hung up the phone easily.
But it doesn’t matter, at least now everyone has the same goal.
After hanging up the phone, Tian Yanzhen opened WeChat. He originally planned to send a message to Qiao Yu, but after thinking about it, he decided to forget it.
We will wait until this series of meetings are prepared.
And there is Qiao Yu's grandpa opposite... They have already decided to do it in Huaqing, so let's just let the other side sell it. There is no need to fight about this kind of thing. With Qiao Yu's intelligence, he naturally has a strong mind.
...
After taking the high-speed train for six hours, classmate Qiao Yu finally returned home.
Only reporting for training on the second day, Qiao Yu came with the team leader just to go home a day earlier.
It was naturally impossible for Zhou Liang to disagree with such a small request. For safety reasons, he even arranged for someone to deliver Qiao Yu to the gate of the community before leaving. Although this seems completely unnecessary to Qiao Yu...
Star City is his territory. He has followed his grandfather to visit the entire Star City since he was a child. He is definitely more familiar than Professor Zhou, a foreigner, and even a black taxi can't cheat his money.
"Open the door quickly, the community is here to send warmth!" Standing at the door, Qiao Yu knocked on the door and shouted in a low voice.
The sound of footsteps soon came, but before the door was opened, a woman's voice was heard inside: "I'm back when I'm back. What kind of community provides warmth? Why are you still so childish after you've gone to college?" He doesn’t look grown up at all.”
After finishing his words, the door was fully opened. When their eyes met, Qiao Yu felt full of emotions. Frustrated, he asked unhappily: "No, how did you know that I was back?"
"Oh... Teacher Lan, you called me early in the morning and said you would be back today. What did you do just now?" The newly appointed Principal He called again to ask if you were here. How could I not know that you were back? "
Okay, the case has been solved.
However, the coordination between the two parties was very good. He just set out from the capital in the morning, and his high school alma mater received the news. Is this because he was afraid that he would run away on the high-speed train?
Originally, I wanted to give Qiao Xi a surprise, but they found out in the morning.
"Wait...how did you become Principal He? Where did Lao Zhang go?"
"What about Lao Zhang and Xiao Zhang? Principal Zhang was transferred to the director of the District Education Bureau. Are you hungry? Do you want me to eat some noodles? It’s better not to eat yet. Principal He just said that Director Zhang is going to invite us to have a meal together in the evening. I can’t refuse.”
Well, being unable to refuse means that Qiao Xi has already declined in every possible way, but No match for Principal He's eloquent tongue.
Qiao Yu nodded. He hadn't seen him for two or three months, but Principal Zhang had been promoted. This was something he didn't expect. And it was indeed necessary to eat this meal, not to congratulate Principal Zhang on his promotion, but mainly because he was still thinking about Qiao Xi borrowing the school laboratory.
If you choose physics and chemistry, the college entrance examination requires biology, chemistry and physics experiments.
Not only because these three courses cover the most majors, but also because Qiao Yu knows Qiao Xi’s strengths. Social science candidates have to rely on two more difficult courses, physics and chemistry, to improve their scores. Pure science subjects are more competitive.
But the college entrance examination also requires experiments, and they must be included in the total score.
"You can eat as long as you want, but mom, I really miss you when I go to Yanbei this time. You have to work hard and get admitted to a university in the capital." Qiao Yu said seriously, and then went to the He took a step forward and hugged Qiao Xi gently.
"Is there a possibility that you think I am because you are only sixteen? If you wait until you are twenty, I am afraid you will be far away from me." Qiao Xi said something habitually, but she still raised her eyebrows He started to rub Qiao Yu's head with his hand.
"Of course it's not possible. We have agreed to depend on each other for the rest of our lives. Let me tell you, going to the capital this time is very interesting. I will tell you in detail about me and my mentor, Lao Xue, and It’s about Grandpa Shi.”
“Well, I won’t write papers today, thank you. I’ll take half a day off!”
“You don’t have to be so polite. As long as you agree to wait until you finish the college entrance examination, I will go to whichever school you go to and be your teacher.”
"Qiao Yu, are you trying to find some way to get Yanbei University to recruit me?"
"Haha, you also admit that I am a treasure. Yanbei University will definitely be reluctant to let me go, right? I have told you a long time ago that I am just a piece of gold, and you still laughed at me at that time!"
" Haha..."
...
In the living room, Qiao Yu babbled to Qiao Xi about what he had seen during his trip to the capital, such as how he got in touch with Mr. Yuan Zhengxin, and how much the old man cared about him. Any student card for entering and exiting Huaqing could get him After living a prosperous life for four years in college, he almost lost the motivation to make money.
Of course, he also vividly described to Qiao Xi how beautiful the scenery of Yanbei University and Huaqing University was, and how loving the classmates were.
He also proudly told Qiao Xi that he had even been able to help his senior brother solve a huge problem...
Actually, he talked about a lot, mainly focusing on two things, introducing how pleasant and beautiful college life is, And how highly regarded he is now. As for the man, neither of them mentioned it.
Just as Qiao Xi said, no matter what his goal is at this time, there is no need to mention that man to spoil the fun, which will change the taste of this warm moment.
Mother and son reunited after a short separation, and it was enough to be happy.
But most of the time, Qiao Yu talks incessantly, while Qiao Xi listens quietly.
After all, her life at home is very simple. There is really nothing to say. She just answers questions every day and watches TV when she is tired. Even after Qiao Yu left, she didn't even bother to cook. When she was hungry, she would order takeout or a bowl of instant noodles.
Life is simple.
Just when Qiao Yu felt that he had said everything he needed to say and could not think of anything else to say, Director Zhang, Principal He and Lan Jie came to the door together. When there was a knock on the door, Qiao Yu subconsciously looked at the time displayed on the old wall clock on the wall. It was half past five, which was almost time for dinner.
......
After a few words of greeting, it was time to eat. When going to the restaurant, Lan Jie walked beside Qiao Yu and asked about the recent situation.
Qiao Yu also answered all questions about Teacher Lan who helped him get on the right track.
Then we had a meal together.
While eating, Zhang Tiejun specifically mentioned the contracts he had signed with Qiao Yu before. Principal He naturally promised to fulfill them. Qiao Yu also casually mentioned that Qiao Xi had borrowed the school laboratory. matter.
Principal He naturally patted his chest and agreed.
Qiao Xi was even invited to attend classes with her first year of high school students, but Qiao Xi naturally declined politely.
Going to college is quite interesting, but taking classes with high school students, to be honest, even Qiao Yu thinks it's too cruel for an adult.
The host and guest enjoy a meal. By the way, the time for Qiao Yu to come to Xingtie No. 1 Middle School to give a speech was determined, and it was scheduled for the afternoon of the last exam.
The main reason is that after the training camp, Qiao Yu will return to the capital with Team Leader Zhou the next day, and he cannot stay in Star City for long. Just take half a day off during the training camp. Anyway, this matter has been agreed with Professor Zhou a long time ago.
Although all the things that should be discussed were discussed at the dinner, Zhang Tiejun still pulled Qiao Yu to talk to him again after the meal before letting Qiao Yu go home.
No matter what, returning to Star City still made Qiao Yu feel the enthusiasm of his alma mater for him, which was good.
And Qiao Yu also heard a lot of good news about Xingtie No. 1 Middle School from Zhang Tiejun.
For example, Lao Zhang is trying to find ways to promote the construction of the city's first-class key high school in Xingtie No. 1 Middle School. In vernacular, if successful, Star City will no longer have a pattern of four major and five small ones in the future, but will be changed to four The big six is now small.
And this idea has received a lot of support. After all, the district where Xingtie No. 1 Middle School is located is recognized as an educationally weak district. From junior high school to high school, there is nothing particularly good. Especially high school.
Let's put it this way, Star City now has six districts. Except for the district that was divided into county districts in the past two years, only Rongcheng District, where Tieyi Middle School is located, does not have a key high school. Yes, none of the four legendary big and five small schools are located in Rongcheng District.
It is directly ridiculed by people as an educational resource depression.
Zhang Tiejun's rise to power this time actually has something to do with this. The city leaders still hope that Zhang Tiejun can build a key middle school in Rongcheng District, and Tieyi Middle School just caught up with this opportunity.
If done properly and with some policy support, it is really possible to get to the top.
Of course Qiao Yu just listens, at least for now he can't make much contribution to his alma mater. However, Zhang Tiejun said something very pertinent before leaving. As long as Qiao Yu continues to work hard and study hard, the higher he goes in the future, Tie Yizhong will naturally get better and better.
There are many things in history that change a school's local status because of a celebrity.
Qiao Yu naturally agreed to this.
Don’t worry if you have a lot of debt.
He has promised Qiao Xi that he will be a man standing on the top of the mountain in the future. Work hard to learn this kind of thing. He has to do it even if Lao Zhang doesn’t say anything. He doesn’t need to do anything extra to let those Those who have helped them will get what they want, and no one will refuse.
That night, Meimei slept in her room, and chatted with Qiao Xi again the next morning until ten o'clock in the morning. Qiao Yu took a taxi and came to the headquarters of the High School Affiliated to the Normal University, which hosted the second training camp this year. .
There is actually not much to say about the second training camp. Qiao Yu's feeling is actually similar to the first time, except that there are fewer people studying together and there are more questions that need to be practiced. But for him, the topics were just something he could brush up on occasionally when he needed to rest his brain. He was still thinking hard about the paper on the geometric Langlands conjecture.
Director Tian and his grandpa did not even pay attention to him...
Tian Yanzhen probably didn't expect that he thought Yuan Zhengxin would definitely send a message to Qiao Yu, but Yuan Zhengxin thought the same way. After all, Tian Yanzhen agreed to hold this meeting in Huaqing, which was considered a concession.
Qiao Yu felt slightly sad. Neither his mentor nor his grandpa cared about his hair.
But having said that, he actually didn’t lose much hair...it was just an exaggeration to attract the attention of his mentor and grandpa Shi.
But it’s a pity...
As for the exam, there is nothing to say.
During weekday self-study, he still had to deal with complicated papers on the Langlands Conjecture in geometry, but as long as he took the exam and solved those simple questions, he could free up his brain and rest.
Really, since he started to come into contact with abstract mathematical knowledge and mastered it, when he looked at these so-called Olympiad questions, he suddenly felt very simple. Basically it doesn't take much thinking to make.
He didn't know how to explain this situation. After all, according to the understanding of many mathematics professors, there is a big difference between doing mathematical research and doing high school mathematics problems. So the only attraction of this training camp for Qiao Yu was probably the closing ceremony.
Because I can directly determine who can be his teammate this year and go to compete in the 66th IMO together.
But to be honest, there is no big surprise, because the four friends are all there. The most amazing thing is probably the fat guy Yu Yongjun, who always stumbles...but always manages to pass through dangers.
The other two are from Jiangcheng, the capital of Xingbei Province next to Xiaozhou and Xingnan. This makes the six members of this year's IMO evenly distributed, coming from Jingcheng, Linhai, Shuangqing, Xingcheng, Jiangcheng, and Xiaozhou, six people and six cities.
It fits Qiao Yu’s aesthetic very well.
Thanks to book friend 20230114003824260 and the little things in the night notes for the reward and encouragement!
Completed the 34th day of the 10,000-word punch-in!
PS: I recommend this book to everyone, Daguo Electronics: The Rise from the Explosion of Pagers, the author of Industrial Flow.
(End of this chapter)