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Chapter 119 The Silent Dedication of the Mentors
After the first phase of IMO training, although Qiao Yu planned to take a rest, he still wrote a review of the paper and sent it to Director Tian and Professor Yuan of Huaqing. This time, it was not to let the two mentors know how hard he worked, but for a purpose.

Because during the entire training period he had been studying the paper on the geometric Langlands conjecture.

Director Tian didn't know whether he would ask someone to look at his experience, but Qiao Yu believed that Mr. Yuan would definitely forward it to Professor Pan.

In this way, if he has any misunderstandings, Professor Pan can point them out to him.

The main reason why he didn't send it directly to Professor Pan was because Qiao Yu himself felt embarrassed.

Do unto others, do not impose on others.

If someone thinks of a problem every day, just send it to him... and he can summarize several problems every day, and this has lasted for nearly half a month. Qiao Yu feels that he has blocked this guy directly.

Although Professor Pan did not block him, he could clearly feel that the Huaqing professor was responding to messages more and more slowly.

Anyway, he was the fastest in replying to messages in the first two days after I added him. Whenever there was a question, he would reply immediately. After that, his reply speed became slower and slower.

During the training camp, there was even a situation where Professor Pan didn’t reply to a question he had sent the day before for a full day and a half…

Qiao Yu did not consider whether the questions he asked were becoming more and more tricky, and Professor Pan also needed to discuss with others before he dared to reply. Moreover, Professor Pan did not tell him that he was not at Huaqing at all, but was attending a meeting abroad.

Qiao Yu just sensitively felt that Professor Pan might have changed and was beginning to be annoyed with him. However, it was not easy to ask this question directly, so he could only think of it in a roundabout way.

There is not much to say about the following week. I continued to read books and papers.

It was just that instead of reading the paper on prime numbers, Qiao Yu changed it to reading the 800-plus page paper on the geometric Langlands conjecture.

Learning while reading will undoubtedly slow down the speed of reading the paper.

The books I read this week are starting to seem unsystematic to a normal professor.

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 Geometric Langlands Program. Qiao Yu felt tired before because he had no direction, but now that he has a goal to strive for, this task doesn’t feel that tiring anymore.

Moreover, the training schedule was not very tight, and the collective life also ensured that Qiao Yu could 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 had lost in the previous period was made up during the training period.

By the way, there is one more thing worth mentioning.

Yu Yongjun also added Gong Jiatao to the friend group.

There was no way, these two people were the ones who got along the best these 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 in the future.

After all, it is easy to avoid obvious flirting, but difficult to guard against hidden meanness.

Yu Yongjun is a typical show-off type of person. His brain is very quick to think, but he only talks and does not do any shameless things.

Gong Jiatao is naturally a despicable person. He looks like a decent person in normal times, but he is very open when it comes to using various tricks. He will do it first and see whether it will succeed or not.

As for Yu Wei...

Qiao Yu originally thought that he was the only kindhearted person in the group, but he was a little withdrawn. But now it seems that this guy can lie without blushing or beating his heart, and he seems to be very sinister.

This made Qiao Yu suspect that the reason these people wanted to participate in the competition instead of taking the college entrance examination was probably because if they took the college entrance examination, everyone would find out that they had a certain level of ideological and political awareness, and they should be arrested and executed immediately...

Of course, the feeling is mutual.

What Qiao Yu didn't know was that Yu Yongjun and Gong Jiatao often had similar views when they chatted privately... For example, non-humans like Qiao Yu should not participate in math competitions with them, and their fate should be to be sent to a high-end biological laboratory for direct live biopsy research.

The friendships formed during the competition are so pure and beautiful.

Of course, this does not mean that the two sides will really be at loggerheads.

In fact, everyone has been learning from each other. Just like Qiao Yu thought that he should learn from Yu Yongjun and Gong Jiatao's thick skin, while Gong Jiatao and Yu Yongjun 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 and found that if they replaced the Olympiad questions with ordinary high school exercises, they were still able to handle it.

Of course, the competition rules need to be slightly changed, and you can't play against those who are very good at the game.

But these don't seem to be a problem. For ordinary students in their high school, just to keep up with the pace of most of their classmates, they have to do their best and don't have much spare energy to spend on games.

After all, the only students who are really qualified to waste time on games during their studies these days are elementary school students...

But the two have very good reasons. Only by regaining the self-esteem that has been trampled underfoot by others can they regain 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 "kindness" in one stroke.

But Qiao Yu didn't care.

The only thing that made him sigh was that recently Director Tian and his senior master across the street had been getting slower and slower in replying to his messages.

Well, it’s the beginning of the semester and the big guys are all very busy, Qiao Yu comforted himself in this way.

But there were still gains. For example, Professor Pan, who was increasingly slow in replying to messages, suddenly popped up one day and sent Qiao Yu an address and an account and password. After logging in, Qiao Yu found that the latest videos were all about various recent conferences on the geometric Langlands conjecture.

Although the lectures were still given by the two main leaders, Dennis and Sam, everyone in the entire team was also included, including Professor Pan, and the focus of the arguments in the several reports was also different.

Qiao Yu also keenly noticed that the man was the third most frequently seen person...

There is no doubt that the discussions at these conferences were very useful to Qiao Yu and indeed answered many of his questions.

For example, if you have a high-level understanding of the overall proof ideas of the paper, when you read through the details of the paper, many problems that you couldn't figure out before can be easily solved.

Most importantly, it made him more certain that his intuition might be correct.

When extending the uniform equivalence results to the general case, it is necessary to frequently use local-global phenomena from algebraic geometry or category theory to locate the interaction with the global. Then if there are some minor errors in the local calls, they will inevitably cause global errors.

This could even lead to the key theorem that the authors prove: Ambidexterity may be limited in certain circumstances.

It should be noted that the last paper used this conclusion to generalize the conjecture to general cases. If the applicability of the most critical Ambidexterity theorem is limited in the case discussed in the paper, then the proof of the geometric Langlands conjecture can only be declared a failure.

But it is still not an easy task for Qiao Yu to prove this point.

Because the paper itself relies on specific axioms and settings, results in higher-order category theory are correct in a specific context, but the applicability of the theorems may be affected if the axioms or category structure change.

Even in the geometric Langlands program, some complex homological algebraic problems treated using this theorem have been successfully solved.

In other words, this paper is the result of mathematicians' self-constructed environment, which relies on specific theoretical background and assumptions. In order to prove that there is a problem, Qiao Yu may need to find a way to prove that the entire constructed framework has logical loopholes.

It is important to know that in modern mathematics, the self-consistency of axiomatic systems and category theory frameworks is highly rigorous. Any work that questions or attempts to discover logical loopholes must be based on more rigorous reasoning and innovative perspectives, which makes the task of questioning such constructions extremely difficult.

But when you want to prove something wrong in mathematics, there is also a most clever way, which is to construct a counterexample.

Counterexamples are very powerful tools in mathematics, which can directly show that a theorem or inference does not hold under certain conditions. In theory, as long as he can carefully design an algebraic geometry situation under the logical framework built by the other party, and make it impossible for local objects to globally meet the requirements of the Ambidexterity Theorem, he can achieve this goal.

If he could go one step further and use this counterexample to discuss the reasons why the axioms do not match, such as by backtracking the technical assumptions in the proof, he could deduce the loopholes in the paper and give a preliminary solution, then he would probably become a star in the mathematics world again...

Of course, this is still not an easy task.

In fact, it was much more difficult than any problem Qiao Yu had encountered so far.

Anyway, a week after the training camp ended passed uneventfully. He thought about it while reading books, papers, and even when taking a shower and sleeping, but he still could not construct a suitable counterexample.

However, while sitting on the high-speed train from Beijing to Star City, Qiao Yu, as usual, shared his work experience of this week with Director Tian and the master sitting opposite him.

“Dear Professor Tian: My main task 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 some thoughts on one of the key conclusions, namely the Ambidexterity Theorem, and I would like to report it 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 examined the structure of the theorem and its application to the proof of the geometric Langlands conjecture, I began to have some doubts about its applicability, especially when dealing with situations involving singularities or complex geometries.

From my limited understanding, the theorem relies on some kind of equivalence of local and global objects, especially in the framework of homological algebra and category theory, which requires that locally defined geometric objects be globally consistent.

This kind of local-global equivalence seems reasonable in the context of smooth geometry, and the paper discusses some special cases, but when I think about more complicated situations, such as algebraic varieties with unusual singularities, are there possible limitations?
Specifically, I suspect that the local structure near certain particular singularities may cause certain properties in homology algebra, e.g., local flatness or projectivity, to not generalize correctly globally.

That is, if the ambiguity theorem must rely on this kind of well-behaved local geometry, then is the applicability of the theorem restricted to algebraic varieties with these particular kinds of singularities?

I have not found a specific counterexample yet, but in next week's training I plan to think deeply about the following two aspects: 1. Whether there are unusual singular points that will affect the local homological algebraic properties and cause the local-global equivalence of the theorem to be destroyed.

2. The proof of the Ambidexterity Theorem involves some axiomatic structures in higher-order category theory. I would like to further explore how these category theory axioms perform in the context of exotic geometry. Are there any implicit assumptions that do not hold in more complex geometric contexts?

Although my ideas may seem naive to you, I think they have some exploration value. The proof of the geometric Langlands conjecture is very complicated, and the Ambidexterity theorem is a key conclusion. Any potential applicability issues may have an impact on the validity of the proof.

So I hope to start from 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 as soon as possible. Your dearest student/grandson, this week I felt for the first time the distress of hair loss. "

Qiao Yu sent this reflections to his supervisor and master's teacher while sitting on the high-speed train. Sitting next to him was Professor Zhou Liang, the leader of this IMO team.

But in fact, he had already edited all this content last night and saved it on his mobile phone. All he did just now was to copy and paste, add the person's name, slightly change the self-introduction at the end, and then click the send button.

This is mainly to avoid being called by the tutor or the master's teacher to scold him again, saying that he doesn't know the height of the world. It is very possible to find loopholes in the paper after reading it for a few days.

The old man could more accept that he found loopholes during the learning process, and it was obvious that his thinking was intended to find faults in other people's papers.

But there was no way, simply reporting according to the procedure could not reflect the seriousness of the problem. He was in great need of help from the two bosses, and it would be best if they could mobilize many brains to start from this direction and give him some constructive ideas to inspire him.

Naturally, he had to speak his mind truthfully.

To put it bluntly, it means that you want to make full use of the resources around you, but you don't want to bear the responsibilities that come with it.

In the end, he was led astray by Yu Yongjun and Gong Jiatao.

……

Yanbei University, Tian Yanzhen really didn't expect that Qiao Yu would suddenly send such a report today.

Because of 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, but he also showed him how terrible I was when I got serious!
In fact, the proof of the geometric Langlands conjecture did not cause much discussion outside the mathematical community.

Because the Langlands Program is too far away for ordinary people, and its appeal is not even as good as the Riemann hypothesis and the NS equation.

It’s not that the Langlands Program is necessarily more difficult than solving these world-class conjectures. It’s mainly because the threshold for anything involving the unification of basic theories is extremely high.

For example, the main problem that the Langlands program needs to solve is to build a bridge between Galois representations and automorphic forms on algebraic number fields. Just by looking at the definition, you can tell that if you don't spend a few years studying algebraic geometry, number theory, and representation theory, you won't be able to understand the question at all.

Really, if you don't believe it, you can go and interview various major mathematics schools. Just the automorphic form alone can make countless college students and graduate students exhausted, and they still only partially understand it, and some are even worse, they know nothing at all.

If it is the automorphic representation involved in the Langlands program... then it is even more ridiculous. After all, automorphic forms are just abstractions, while automorphic representations are higher-level abstractions that describe how algebraic groups act on specific Hilbert spaces or Banach spaces, where the elements may be analytic functions or some special structures.

The geometric Langlands program studies the correspondence between local systems and automorphic forms on algebraic curves. It simply replaces the number theory objects involved in the classical Langlands program with algebraic geometry objects.

The main research is to geometrize abstract number theory problems so that they can be processed in the framework of algebraic geometry. This can be said to be not to solve specific problems, but to provide valuable tools for mathematicians to solve more specific problems, which has such a wide range of application potential.

The field also primarily attracts mathematicians who wish to blaze new trails in number theory and algebraic geometry.

We can even think of the geometric Langlands program as an important mathematical tool similar to calculus. Like the Langlands program, the birth of calculus was not to directly solve a specific problem, but to build a set of tools to deal with continuous changes and limit problems.

Therefore, the geometric Langlands program may completely change the way mathematicians in the future deal with certain problems, just as calculus changed the way mathematicians of this era deal with changes. Naturally, mathematicians are also interested in this area.

Because if someone succeeds, it means that when people study number theory problems in the future, they will have a new framework that can be used directly, and they can deal with classical number theory problems from a new dimension.

One day in the future, it may even become a required college mathematics course just like calculus.

Tian Yanzhen has actually always been concerned about the development of the proof of the geometric Langlands conjecture, and is also very optimistic about the results obtained by the research team this time.

But who would have thought that Qiao Yu would suddenly give him a big one.

My own students suspected that the results that others had researched for more than 15 years and finally published had loopholes? !

What should I say...

It would be fine if there really was a loophole, but if it was just imagination, it could be quite offensive.

Of course, considering that Qiao Yu is only sixteen years old, probably no one would really care about him. But it was also because of Qiao Yu's age that Tian Yan's heart began to beat when she saw the weekly report sent by Qiao Yu.

It's still a bit too much.

You only read the paper for a few days, and you have so many ideas? !

Regardless of whether the idea is right or wrong, it at least shows that when Qiao Yu read the paper, he was really deconstructing the most basic things in the paper.

In the area 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 a skill that many mathematicians desire.

Deep comprehension, rapid learning, and strong mathematical intuition are all essential.

If you add in the fact that this kid is really daring, Tian Yan really likes him even more.

Really, he felt that it would be impossible to find another student like this in the short term even if he looked for a way.

Unless the world is crazy...

Or perhaps a new round of technological explosion is about to begin, just like after quantum physics was proposed, a bunch of great people came one after another to pave a smooth road on this basis, explaining through quantum mechanics how electrons pass through pn junctions and how to control current in field effect transistors, laying a theoretical foundation for the development of the semiconductor industry.

This paved the way for human society to officially enter a new electronic information age. Children in the new era have begun to be unable to understand the telegraph, which has been buried in the dust of history. It has only been a few decades since the telegraph technology was officially eliminated.

Typewriters, fax machines, and even early dial-up Internet access are gradually being forgotten. In a few years, these products that once represented advanced productivity will become memories in history books.

Once this idea popped up in his mind, Tian Yanzhen suddenly felt excited.

What a coincidence...Qiao Yu is actually his student. It feels 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 he would not actively call this number again.

But at this moment, those emotions have faded, really faded.

With such a student, Tian Yan really felt that he could face everything that had happened in the past with ease.

In any case, when people in the history of mathematics introduce Qiao Yu in the future, there will definitely be a sentence that says "he studied under the famous Chinese mathematician Tian Yanzhen", which is actually enough. At his age, it is almost impossible for people to achieve anything in mathematics.

But his students have unlimited possibilities, so why bother so much?
As a man, it’s okay to be more open-minded.

Sometimes people are just like this, a thought can make the world wider.

So when pressing the dial button, Tian Yan was very calm and composed.

The phone rang for more than ten seconds before it was connected, which probably meant that the old man on the other end had gone through some mental processes, but it didn't matter.

"Hello, Mr. Yuan, how are you?"

"I don't deserve it, I don't deserve it, what advice do you have, Professor Tian?"

Alas, the old man is still a little narrow-minded.

Tian Yanzhen said gently, "Mr. Yuan, there's no need to fight. You should also be able to guess that I'm calling because of Qiao Yu. I guess he also sent you a copy of his study summary report this week, right?"

The other party fell silent for a long while before he responded, "Yes, I got it. I forwarded a copy to Professor Pan."

Tian Yanzhen said the purpose of this call: "I think so. We also have scholars in our mathematics research center who focus on research in this field, such as Professor Tan Zhiqing, who has been working on the P-advanced Langlands program in recent years.

In particular, there have been many breakthroughs in local analytical representation and L-invariant theory. How about we cooperate to hold a series of communication meetings on the geometric Langlands program after Qiao Yu returns from Star City? What do you think? "

The other party hesitated for a moment and then asked, "Where will it be held?"

After asking this, it was obvious that the old man opposite was also interested.

Tian Yanzhen said generously: "Why not hold it in Huaqing? It's so close anyway. We have done so much for him, so it's only right that the boy should walk a few more steps."

"Then the time will be set after Qingming Festival. Professor Pan from the research team will be able to come back by then."

Tian Yanzhen asked, "No problem. You can arrange the specific time. I'll let you know which professors can be invited to attend. By the way, can Professor Pan invite Professor Dennis?"

"It's probably difficult. Dennis and Sam probably won't be happy with Qiao Yu's idea. But we can ask Professor Everton of Princeton if he has time. He has profound attainments in both geometric representation theory and p-adic Hodge theory. It should be of great help to Qiao Yu if he can help make a judgment."

"So is it an invitation in your name?"

"Let me invite Professor Everton. By the way, you and Professor Phyllis are both judges of the same Abel Prize, so you should be familiar with each other. He has been working on the verification of the geometric Langlands conjecture, so it would be of greater help if we could invite him."

"Okay, I'll send him an email right away. If he doesn't have anything special to do recently, he should be able to attend. But you have to confirm the time first."

"Wait a minute... um, April 4th to April 5th, that's just the weekend."

"Okay. I'll contact you anytime I get the news."

"it is good."

"Mr. Yuan, I'm hanging up first."

"Beep beep..."

Tian Yanzhen smiled self-deprecatingly. The old man was still a decisive person and hung up the phone very decisively.

But it doesn’t matter, at least now everyone has the same goal.

After hanging up the phone, Tian Yanzhen opened WeChat and planned to reply to Qiao Yu, but after thinking about it, she decided to give up.

Let’s wait until this series of meetings are prepared.

Besides, there is Qiao Yu's master across the street... They have already decided to hold it in Huaqing, so why not just let them sell it? There is no need to argue about this kind of thing. With Qiao Yu's intelligence, he naturally has a scale in his mind.

……

After taking the high-speed train for six hours, Qiao Yu, who had a scale in his heart, finally returned home.

Qiao Yu reported for the training camp on the second day and followed the team leader just to go home one day earlier.

Zhou Liang naturally agreed to this small request, and even arranged for someone to take Qiao Yu to the gate of the community for safety reasons before leaving. Although this seemed completely unnecessary to Qiao Yu...

Xingcheng was his territory. He had been touring the entire city with his grandfather since he was a child. He was definitely much more familiar with Xingcheng than Professor Zhou, a foreigner. He was so familiar with Xingcheng that even black taxi drivers couldn't cheat him out of his money.

"Open the door quickly, the community is here to bring warmth!" Standing at the door, Qiao Yu knocked on the door and shouted in a holding voice.

Soon, footsteps were heard. Before the door was even opened, a woman's voice was heard from inside: "You're back, so what? What community warmth? You're already in college, so why are you still so childish? You don't seem to have grown up at all."

As soon as he finished speaking, the door was completely opened. When their eyes met, Qiao Yu felt a sense of frustration and asked unhappily, "No, how did you know I was back?"

"Heh... Teacher Lan, you called me early in the morning to tell me that you would be back today. Just now, the newly appointed Principal He called again to ask if you had arrived. How could I not know that you were back?"

Okay, crime solved.

But the two sides coordinated so well that his high school alma mater received the news when he just left Beijing in the morning. Are they afraid that he would run away on the high-speed train?
I originally wanted to give Qiao Xi a surprise, but she found out in the morning.

"Wait... why did it become Principal He? Where is Lao Zhang?"

"What's Old Zhang and Little Zhang? Principal Zhang has been transferred to the District Education Bureau as director. Are you hungry? Do you want me to make you a bowl of noodles? But I suggest you don't eat yet. Principal He just said that Director Zhang will invite us to dinner tonight, and we can't refuse."

Well, the fact that he couldn’t refuse meant that Qiao Xi had already tried every way to refuse, but was no match for the eloquence of Principal He.

Qiao Yu nodded. He hadn't seen Principal Zhang for only two or three months, but he hadn't expected that he would get a promotion. And he really needed to go to this meal. It wasn't to congratulate Principal Zhang on his promotion, but mainly because he was thinking about Qiao Xi borrowing the school laboratory.

If you choose physics, chemistry and biology, you will be required to take biology, chemistry and physics experiments in the college entrance examination.

Not only because these three courses cover the most majors, but also because Qiao Yu knows Qiao Xi's strengths. Social candidates have to rely on the two more difficult courses of physics and chemistry to increase their scores, and pure science options are more competitive.

But the college entrance examination also includes experiments, and they must be included in the total score.

"Eat if you want, but mom, I really missed you when I went to Yanbei this time. You must work hard and get admitted to a university in Beijing." Qiao Yu said seriously, then took a step forward and hugged Qiao Xi gently.

"Is there a possibility that you miss me because you are only sixteen years old? If you wait until you are twenty years old, I am afraid you will want to stay away from me." Qiao Xi said habitually, but still raised his hand and rubbed Qiao Yu's head.

"Of course not. We agreed to stay together for the rest of our lives. Let me tell you, this trip to the capital is going to be very interesting. I will tell you in detail about my experience with my mentor, Lao Xue, and my master."

"Well, then I won't do the test paper today. Thank you for giving me 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 the school you attend to be your teacher. How about that?"

"Qiao Yu, are you trying to find a way to get Yanbei University to recruit me?"

"Haha, you also admit that I'm a treasure. Yanbei University will definitely not want to let me go, right? I've said it before, I'm just a piece of gold, and you pooh-poohed me at that time!"

"Ha ha……"

……

In the living room, Qiao Yu chattered to Qiao Xi about his experiences during his trip to Beijing, such as how he got in touch with old man Yuan Zhengxin, and how much the old man loved him. He said that a student card that allowed him to enter and leave Huaqing could allow him to live a rich life for four years in college, which almost made him lose the motivation to make money.

Of course, he also gave Qiao Xi a vivid description of how beautiful the scenery of Yanbei University and Huaqing University is, and how loving the classmates are.

He even proudly told Qiao Xi that he had even helped his senior brother solve a huge problem...

In fact, they talked a lot, mainly about two things: how comfortable and wonderful college life was, and how much he was valued now. As for the man, neither of them mentioned it.

Just as Qiao Xi said, no matter what his goal was at this moment, there was no need to mention that man to spoil the fun and ruin this warm moment.

It is enough for the mother and son to be happy after a short separation.

But most of the time, it was Qiao Yu who talked incessantly and Qiao Xi listened quietly.

After all, her life at home was very simple, there was really nothing much to say, every day she just did some exercises, and watched TV when she was tired. Even after Qiao Yu left, she was too lazy to cook, and 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 couldn't 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 glanced at the time shown on the old wall clock. It was half past five, almost time for dinner.

……

After a few pleasantries, they started to eat. On the way to the restaurant, Langjie walked beside Qiao Yu and asked him about his recent situation.

Qiao Yu answered every question he asked to Teacher Lan, who put him on the right track.

Then we had a meal together.

During the meal, Zhang Tiejun specifically mentioned to Principal He the contracts that had been signed with Qiao Yu before. Principal He naturally promised repeatedly that he would fulfill them. Qiao Yu also mentioned the matter of Qiao Xi borrowing the school laboratory.

Principal He naturally agreed with a pat on his chest.

He even invited Qiao Xi to attend classes with the first-year high school students, but Qiao Xi naturally declined.

Going to college is quite interesting, but to be honest, even Qiao Yu feels that attending classes with high school students is too cruel for an adult.

The dinner was a great success. Qiao Yu was also scheduled to give a speech at Xingtie No. 1 Middle School in the afternoon of the last exam.

The main reason was that after the training camp, Qiao Yu would return to Beijing with Team Leader Zhou the next day, and he couldn't stay in Xingcheng for long. He might as well take half a day off during the training camp. Anyway, this matter had already been discussed with Professor Zhou.

Although everything that needed to be discussed had been discussed at the dinner, Zhang Tiejun still pulled Qiao Yu aside to talk to him for a while after the meal before letting him go home.

No matter what, returning to Star City still made Qiao Yu feel the enthusiasm of his alma mater, which was good.

Moreover, 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 promote the construction of Xingtie No. 1 Middle School into a first-class key high school in the city. In plain words, if successful, Xingcheng will no longer have a structure of four large schools and five small schools, but will have four large schools and six small schools.

This idea has received a lot of support. After all, the area where Xingtie No. 1 Middle School is located is a recognized educationally weak area. From junior high school to high school, there is no particularly good one, especially high school.

Let's put it this way, Xingcheng now has six districts. Except for the district that was reorganized from a county in the past two years, only Rongcheng District, where Tieyi Middle School is located, does not have a key high school. Yes, the legendary four big and five small schools are not in Rongcheng District.

It is directly ridiculed by people as a low point of educational resources.

Zhang Tiejun's promotion this time was actually related to this. The city leaders still hoped that Zhang Tiejun could also build a key middle school in Rongcheng District, and Tieyi Middle School just happened to catch this opportunity.

If handled properly, with some policy support, it is really possible to get promoted.

Of course, Qiao Yu was just listening, at least for now he couldn't make much contribution to his alma mater. But Zhang Tiejun said something very pertinent before he left, that as long as Qiao Yu continued to work hard and study hard, he would go further and further, and Tieyi Middle School would naturally get better and better.

There are many cases in history where a school's local status was changed because of a celebrity.

Qiao Yu naturally agreed to this.

Don't worry about having too much debt.

He has already promised Qiao Xi that he will be a man standing on the top of the mountain in the future. As for studying hard, he would have done it even if Lao Zhang didn't say it. He doesn't need to do anything extra, and he can also make those who have helped him get what they want. No one will refuse.

That night, Meimei slept well in her room. The next morning, she chatted with Qiao Xi until ten o'clock in the morning. Then Qiao Yu took a taxi to the main campus of the Normal University Affiliated High School, which hosted the second training camp this year.

There was nothing much to say about the second training session. Qiao Yu felt that it was similar to the first time, except that there were fewer people studying together and there were more questions to practice. However, for him, the questions were just for occasional rest. He was still thinking hard about the paper on the geometric Langlands conjecture.

Director Tian and his master ignored him...

Tian Yanzhen probably didn't expect that he thought Yuan Zhengxin would definitely send a message to Qiao Yu, but Yuan Zhengxin thought so too. After all, Tian Yanzhen agreed to hold this meeting in Huaqing, which was also a concession.

Qiao Yu felt a little sad. Neither his tutor nor his master's grandfather cared about his hair.

But then again, he didn't actually lose much hair... He was just exaggerating to get the attention of his mentor and master's master.

But it's a pity...

As for the exams, there is even less to say.

During his self-study on weekdays, he still had to face the tedious paper on the geometric Langlands conjecture, which was a headache, but during the exam, as long as he finished the simple questions, he could empty his mind and rest.

Really, ever since he started to learn those abstract mathematical knowledge and mastered them, he suddenly found these so-called Olympiad questions very simple. Basically, he could solve them without much thinking.

He didn't know how to explain this situation. After all, according to the understanding of many mathematics professors, doing mathematical research is very different from doing high school math problems. So the only attraction of this training camp for Qiao Yu was probably the closing ceremony.

Because it can directly determine who will be his teammate this year and compete together in the 66th IMO.

But to be honest, there weren't any big surprises, because all four friends were there. The most amazing thing was probably the fat guy Yu Yongjun, who was stumbling all the time... but always managed to get through it.

The other two are from Xiaozhou and Jiangcheng, the capital of Xingbei Province next to Xingnan. This makes the six members of this year's IMO evenly distributed, from Beijing, Linhai, Shuangqing, Xingcheng, Jiangcheng, Xiaozhou, six people, six cities.

It is in line with Qiao Yu's aesthetic.

　Thanks to book friends 20230114003824260 and Yejixiaoshi for their rewards and encouragement!

　　The 34th day of the -word check-in is completed!
　　PS: I would like to recommend this book to everyone, Great Power Electronics: The Rise from the Explosion of Pagers, written by an industrial writer.

　　
　
(End of this chapter)