Top academic

Chapter 120: Inspiration as wonderful as a volcano

After the closing ceremony of the second phase of training, Qiao Yu and Professor Zhou got on the train back to Beijing.

Qiao Yu sat at the window, looking at the scenery outside with nostalgia. Hometown is like this. If you stay here for a long time, there will be many things you are not satisfied with. But once you leave, the beautiful side will appear.

Distance always creates some unique filter beauty, just like the beauty software in mobile phones. This can probably show from the side that the human brain has something in common with computers, and the human brain is more advanced in that it also has adaptive software.

"The team has some activities coming up, but I've talked to your advisor, Professor Tian, ​​so you don't have to participate. Also, we've created a group, but we didn't include you. Don't have any other ideas. The main thing is that you're close, so it's very convenient to get notified..."

Zhou Liang was talking beside him, but Qiao Yu just ignored him. Participating in the IMO competition can be understood as an obsession to have a beginning and an end. In fact, Qiao Yu also knew that winning a gold medal would not mean much to him.

But Professor Schultz won a gold medal back then, and Professor Pan on the opposite side also won a gold medal. He would always feel like he was letting his youth down if he didn't win one.

As for the activities before going to Australia, Qiao Yu had no interest in participating.

It's nothing more than practicing questions.

Most importantly, he was too lazy to expose Professor Zhou's little tricks.

What do you mean they didn't invite him to join the group because they were close to him? They were just afraid that he would cause trouble again and hurt the other players who were participating in the competition. Of course, Zhou Liang couldn't be blamed for thinking too much, it was mainly because the players' psychological quality was too poor.

When faced with a little setback, I don't take it lightly at all. Playing a game can make my mentality collapse. No matter who is the team leader or coach, they will probably find it difficult to cope with it.

Excluding him, who may bring instability, is indeed the simplest way to optimize.

However, the constant nagging still gave Qiao Yu a headache, so he simply responded: "Don't worry, Professor Zhou, you really don't need to explain so much to me. I can understand your arrangement, and it is for everyone's good this time."

Professor Zhou smiled and said with emotion, "Yes, it's mainly because you don't have time. Professor Tian is also worried about you. He knows that you are interested in the geometric Langlands conjecture recently. There will be a series of related lectures and seminars in cooperation with Huaqing in the next few days. Many experts are specially invited from abroad. It's really enviable."

Qiao Yu finally withdrew his gaze from the window, turned his head to look at Professor Zhou beside him, and asked in surprise: "Is there such a thing?"

Zhou Liang also looked at Qiao Yu in surprise and asked, "You don't know?"

Qiao Yu suddenly felt the warmth of spring.

It turned out that his mentor and his master still loved him. Although they didn't tell him directly, they had been working silently behind his back.

Qiao Yu also deeply realized the value of what Lao Xue said to him back then.

As expected, if the tutor is able to take on responsibilities, he can be willful.

If you change a mentor who can't take responsibility, how can such a large-scale seminar be held? After all, you have to pay to invite relevant professors and scholars from abroad, not to mention inviting them to eat and stay, which also costs money. In addition, you have to save face.

Of course, we also have to thank that China has developed quite well in recent years and its external propaganda work has also kept up. Otherwise, it would be useless to just talk about money.

In short, at this moment, Qiao Yu truly understood how much help having a good mentor could provide to his studies.

Old Xue, you never lied to him!
……

On the other side of the ocean, in Madison, the capital of Wisconsin, is the University of Wisconsin-Madison.

Pan Jingyuan was standing outside the conference room, looking at his mentor who was surrounded by many scholars in the conference room and was still discussing some detailed issues.

The lecture just now has ended, and his mentor Dennis was the speaker.

The content of the lecture was naturally about the proof of the geometric Langlands conjecture.

In fact, he could have participated in the discussion, but ever since he talked with Mr. Yuan that day, Pan Jingyuan has been feeling a little uneasy. It's a very strange feeling.

Although he knew that Qiao Yu was just a student who had just come into contact with the geometric Langlands conjecture, and some of the questions he asked did not need to be taken too seriously, the questions Qiao Yu asked that day did make him feel a little uneasy.

After all, it has been more than ten years since the project was launched, and he has been invited to participate in it for six years. He does not want the results of these six years of hard work to become a joke and have to spend several more years to make up for it.

This feeling of uneasiness even made him start to re-examine the five papers, wanting to make sure that the situation that Qiao Yu judged was impossible. However, this obviously takes time, and in fact Pan Jingyuan has already started this work.

This is also the reason why he responded to Qiao Yu's messages slower and slower.

This feeling of uneasiness reached its peak a few days ago after Mr. Yuan forwarded the questions raised by Qiao Yu.

He wanted to talk to his tutor about Qiao Yu's idea, but he hadn't made up his mind.

After all, he was already very nervous after only six years of participation. As for the instructor, he had spent fifteen years in it. He was not sure what Dennis's attitude would be when he heard such remarks, and whether it would have a counter-effect.

The relationship between students and their mentors is never necessarily good. There have been cases of them turning against each other because of some conflicts, whether in China or abroad.

It’s just that in most cases, everyone has a tacit understanding not to expose it.

However, Huaqing University is planning to hold a series of seminars on the Langlands conjecture together with Yanbei University, and has invited many foreign professors. The news will most likely reach the ears of my tutor.

Pan Jingyuan certainly knew who this series of seminars was for.

To be honest, Pan Jingyuan had no objection to this decision. He certainly knew what Qiao Yuzhen's growth meant to the Chinese mathematics community.

Over the years, although China has developed well, its voice in the academic world is not that big, at least it is unreasonable compared to the size of China. But there is no way, the academic world is often like the Olympics, if you want others to listen, you have to look at your strength.

Why do people generally believe that English journals are more authoritative? Because the tools used in mathematical research are basically developed by Westerners. The main theorems that we learn in college classes are basically named after Westerners.

Abel's theorem and Gauss's theorem in algebra, Fermat's theorem and Euler's theorem in number theory, Bigras's theorem and Heron's formula in geometry, De Morgan's laws in analytic geometry, L'Hôpital's rule in calculus...

In addition, Markov's random process, Ye Beis theorem for calculating probability...

The efforts of our predecessors have enabled the Western world to firmly grasp the academic discourse power. Even if you don’t know English, especially mathematical English, you can’t accurately understand the mathematical ideas of those predecessors.

China is a latecomer, so if it wants to gain more voice, there must be someone who can take the lead in the future world mathematics community.

For example, if a mathematician whose achievements are comparable to those of Newton and Euler appears in China in the future, even if he speaks in a low voice, it will be deafening.

There has never been a pure land in the real world, or rather, such a place as the Peach Blossom Spring only exists in people’s imagination. Human wisdom and sociality have long been determined, and those who have achieved success will form groups and raise the entry threshold of related fields.

Academic cliques have always existed, and the more advanced the operation, the more common this phenomenon is. Higher-ups never consider prohibiting such things, but rather how to use this inevitable phenomenon to promote the development of science.

For example, when the country is ruled by elites, the most basic education can be used to physically separate the children of the elites from those of ordinary people, thereby achieving the strategic goal of raising children at the age of three, six, or nine.

Pan Jingyuan felt that Qiao Yu had the potential to become this kind of academic tycoon.

It’s just that the current situation makes him feel conflicted.

But Pan Jingyuan had made up his mind today. Rather than waiting for Dennis to hear Qiao Yu's "absurdities" from others, it would be better for him to report it proactively. And he had already thought of a way to deal with it.

Finally, Dennis finished the discussion with several professors and walked out of the conference room in high spirits. When he saw Pan Jingyuan waiting for him, he couldn't help but make a joke: "What's wrong? Pan, isn't this occasion enough to excite you? Don't worry, there will be more important meetings later."

Pan Jingyuan shook his head, then smiled and said, "No, Dennis, I actually benefited a lot from this conference. I just want to tell you something... By the way, do you remember the paper you wanted me to review?"

Dennis replied: “Of course, I was very impressed by the paper. I even discussed this paper with Schultz, and he actually spoke highly of it.”

But I haven’t made a final review yet. You know, I want to make a more professional review. The author is still young, and he may not know that publishing a paper of this level requires some patience. "

Pan Jingyuan said: "No, you misunderstood. It is not that the author of the paper knows that you are one of the reviewers and hopes that I will urge you to speed up the review. Instead, he has recently become interested in the geometric Langlands conjecture and has raised some questions about our work.

Phew… I have actually been thinking about how to systematically answer his questions these past two days, so that I can give him a very positive answer and prevent the child from wasting his efforts in this regard.”

"Oh?" Dennis was obviously interested and said, "I heard that the author of that paper, Qiao Yu, is very young. This is what Schultz told me. Apparently he knows some information that I don't know, so can you tell me how old Qiao Yu is this year?"

"Sixteen years old." Pan Jingyuan replied.

"Sixteen years old?" Dennis frowned and looked at Pan Jingyuan again with some disbelief: "You mean a sixteen-year-old student not only independently completed a high-quality and significant paper, but also understood our paper and raised some questions that you personally find difficult to answer?"

"I know it sounds unbelievable, but it is true." Pan Jingyuan nodded, and then added: "We have had some academic exchanges. He is a young man who is very studious and learns things very quickly.

After about a week, I felt that many of the questions he asked were difficult to deal with. Do you remember some of the questions we discussed these days? In fact, most of them were questions raised by him. "

Dennis opened his mouth and wanted to say something, but no sound came out. Finally, he asked with a surprised look: "Okay, you have made me more and more interested in this matter. Tell me, what question did he ask that you find difficult to answer?"

Finally, he waited for this sentence and Pan Jingyuan took out a printout from the documents he carried with him and handed it to Dennis.

He prepared this specially.

In fact, he just translated the report that Yuan Zhengxin forwarded to him into English, and added some content in the middle, mainly some doubts about the rigor of the paper that Qiao Yu had in his thinking process during their daily WeChat communication.

Dennis glanced at Pan Jingyuan, then took the printout and did not move forward, but stood there and read it.

After all, there were no specific examples in the questions raised by Qiao Yu, so the article was not long, but Dennis read it very carefully. The two of them stood here for about five minutes before Dennis withdrew his eyes from the printout.

After returning the printout to Pan Jingyuan, Dennis slowly spoke: "If these are really the questions that a sixteen-year-old kid raised after reading the paper and thinking about it, then I can only say that he is gifted."

Pan Jingyuan nodded and replied, "In fact, he is indeed gifted, which can be seen from his paper. It is said that it took only about 20 days from the time he decided to start his own research on the problem of using quasi-complete space theory to analyze the upper bound of rational points on a curve to the time he wrote the paper.

What is even more amazing is that he has only been exposed to Professor Schultz’s mathematical ideas and a series of tools for about a month. It is said that he studied Schultz’s thesis because of the recommendation of another teacher.

Dennis nodded. If the genius that Pan Jingyuan mentioned changed the proposition to question, he might be interested in talking more with Pan Jingyuan about Qiao Yu.

But it is precisely their subject that is being questioned.

Dennis shook his head and said, “The question he raised is indeed very interesting. We all know how important the consistency of the structure is to the conclusions we draw. This is indeed a difficult question to refute, but it is not based on the rigor of the proof itself.

The interaction of multiple papers does increase the complexity of verification. It is a very complex and arduous task to explain that the systematic analysis tools we use throughout the proof process can ensure that the designed geometric objects, algebraic structures, and related properties maintain rigorous consistency.

But to be honest, I can probably understand your feelings. The questions he raised made me feel a little nervous. But you see, he hasn't found a counterexample yet. This at least shows that our argument is rigorous, at least relatively rigorous, and counterexamples are not that easy to find. "

Pan Jingyuan nodded with a wry smile, then asked softly, "What if he finds it? For example, at some point in the future."

Dennis let out a long breath, shrugged and said, "Then we can only re-examine this issue and re-examine the proof process of the paper. That means our work will continue.
What else? At least I won't give up on this proposition. It's nothing more than solving the special case raised by the other party. I believe this will definitely not be more difficult than starting from scratch! Don't you think so, Pan? "

Pan Jingyuan liked Professor Dennis's open-mindedness, which was probably one of the reasons why he chose Dennis as his mentor. So he nodded and said, "I understand. I will continue.

By the way, the two best universities in China have held a series of seminars specifically on the geometric Langlands conjecture. I will also attend this meeting after I return to China in two days. I guess Qiao Yu will also raise his question at the meeting. Do you have anything you want me to say to him? "

Dennis thought for a moment and replied, “I wanted you to give him my email address so that we could have some direct communication, which might be very interesting. But considering that I am still reviewing his paper, this is not a good time. Let’s wait until the final review opinion of his paper comes out before we talk about it.”

But if you have any new ideas during this conference, feel free to email me. Of course, if Qiao Yu really finds a counterexample as he thought, he can call me directly. Although I think this possibility is unlikely. By the way, I am not just talking about the seminar period. "

Pan Jingyuan nodded and agreed.

"Do you know why I added the last sentence? Because guys like Schultz often have a terrifying mathematical intuition. Especially when they haven't done in-depth research on mathematics. How should I put it? Young people are always good at creating mathematical miracles. This is why I like to teach students."

Dennis explained, then raised his hand and patted Pan Jingyuan on the shoulder, jokingly saying:

"Okay, let's go eat now. Don't be so sad. I think you should be happy that China has another math genius. Even if you feel sad, I think it should be for Schultz, because his unique genius status is being challenged."

Hearing this, Pan Jingyuan also laughed, and then a hint of bitterness arose in his heart.

Yes, his mentor is a rich second-generation who doesn’t need to rely on a professor’s salary to live. He studies mathematics purely out of interest, so he cares less about fame and fortune than others.

But to be honest, Pan Jingyuan still dreams of winning a big prize in the international mathematics community.

In a sense, guys like Schultz and Qiao Yu, who are naturally gifted, are the public enemies of mathematicians all over the world. Their half-life efforts may not be as good as their few months of research.

The existence of such people may even cause many people to misunderstand that mathematics is a very simple thing.

But he had no other options. Even though he knew that the guy was picking on the paper he had contributed to, he still had to think of ways to deal with his 100,000 questions...

It's a dog day!

……

Huaxia, Beijing, Yanbei University.

As soon as Qiao Yu walked into the Mathematics Research Center, he ran into Lao Xue who was walking out in a hurry.

"Teacher Xue."

"Hey, you're back?"

"Yes, I just arrived." As he said that, Qiao Yu raised his hand and showed Xue Song the lightweight suitcase that Qiao Xi had bought for him online - it was from Golden Eagle, a brand name!

Anyway, Qiao Yu thinks this is a good brand, fashionable, lightweight and eye-catching.

But it was obvious that Old Xue didn't know what he was talking about. He didn't even say, "Oh, a new box." Instead, he asked directly, "How is it? Have you made any breakthroughs in your idea?"

Alas, I don’t know how to be a mentor. I don’t have the mindset of a student at all.

"Not yet. But I didn't waste the training time. I have already read all five papers on the geometric Langlands conjecture, so this training was still very rewarding." Qiao Yu reported.

Xue Song thought about it, and then uttered: "Hmm... not bad!"

In fact, as long as you anticipate that this guy is not very good at speaking human language, you won’t feel how hurtful those Versailles that come out casually are.

"By the way, is Director Tian in the office?" Qiao Yu asked again.

Xue Song nodded and replied, "I just got back too. What's the matter? Do you have something to talk to Director Tian about?" Qiao Yu said, "Yes, I plan to go and thank Director Tian. I just found out on the high-speed train that Director Tian has cooperated with Huaqing to hold a series of special seminars to help me find a solution to my doubts."

After hearing Qiao Yu mention this, Xue Song's expression became strange again.

This reminded him of the email he sent to Tian Yanzhen that night.

I never expected that what was just a spur-of-the-moment idea at the time could indirectly lead to the century-long reconciliation between the two mathematical schools in China.

Although there have been no public statements from either side to support this point, it can be seen from the cooperation in organizing this series of seminars that such a trend has already emerged. At least the two sides are no longer in a state of estrangement from each other.

Of course, to be honest, the conflict between Yuan Zhengxin and Tian Yanzhen did not affect the training of students too much. Just like what Xue Song learned after coming to Yanbei, there are many professors in the Department of Mathematics of Huaqing who have a good relationship with Tian Yanzhen.

Occasionally, students of Professor Yuan would come to Yanbei to give lectures, and even young professors from the mathematics centers on both sides would collaborate on publishing articles. Not everyone would care about this dispute.

But if the barriers are gone, it would be better if the communication between the two sides could be further improved.

After all, the bigwigs on both sides control a lot of resources. These resources are not necessarily money, but also a lot of connections accumulated over time.

If the two sides can shake hands and make peace, and the research centers on both sides can truly form a synergy, then in the future there may really be a great breakthrough in the geometric analysis that the two are best at. And for the Chinese mathematics community as a whole, it can also be regarded as a shot in the arm.

The most important thing is, if Qiao Yu can inherit the academic resources left to him by both sides in the future, then this status... probably no matter how he makes trouble, at least no one in the country will dare to trip him up openly, right?
After all, what both sides are fighting for is the right to speak...

Thinking about it this way, Xue Song felt envious again.

"Well, we should go and say thank you. Go quickly after you put your luggage down. Otherwise, Professor Tian will have to go out again later."

"Okay." Qiao Yu agreed, picked up his brand new suitcase, and walked excitedly into the research center.

Xue Song stopped and looked at Qiao Yu's back, feeling that it was great to be young. It took him a while to come back to his senses... He shook his head and walked out of the research center. Wait, what was he going to do?

……

"Director Tian, ​​I'm back!"

"Oh, just arrived."

"Yes, Director Tian, ​​I came here specifically to thank you. You are absolutely the best and most perfect mentor in the world, bar none."

Tian Yanzhen put down the pen in his hand and looked up at the sixteen-year-old kid who was becoming more and more outrageous and ran into his office without knocking...

Well, even though it was just flattery, he still decided to accept it.

But seeing Qiao Yu's boastful look, Tian Yanzhen couldn't help but teach him a lesson: "Talking is useless. I can only help you so much. How much you can gain depends on yourself. You can check the list of professors attending the conference on the official website. The same goes for learning from others' experience. First of all, you must have a minimum respect for their research results."

Qiao Yu immediately replied seriously: "Don't worry about that! Don't you know my attitude towards learning? And to be honest, during the training period, I have read all five papers, including most of the references in them. I am now very familiar with this proposition."

Tian Yanzhen nodded and said, "That's fine. You're here just in time, and I have something to ask you. Didn't you say last time that you were interested in prime number research? I helped you choose a proposition for a prime number model, and I also planned to have you attend several conferences on prime number research. Why are you suddenly interested in the geometric Langlands conjecture?"

It would be a waste not to train the students who come to your door.

Although he flattered her as soon as he entered the door, Tian Yanzhen still did not approve of this kind of haphazard approach.

No matter how Qiao Yu answered, he intended to have a good talk with this little guy and make him realize the seriousness of academic research.

You don't work on the topic you have planned, and you find fault with others when they publish important results. It's okay if you are young and can just say you are ignorant. But if you develop this habit, you will definitely become the public enemy of mathematics in the future.

After all, people grow up, but habits may remain.

Although he decided to help the evil this time, he must also be severely criticized, at least it should not happen again.

Who would have thought that Qiao Yu would answer immediately, "Director Tian, ​​it's not that I'm suddenly interested in the geometric Langlands conjecture. In fact, I've been studying the topic you assigned to me. But who would have thought that during the research process, I would search for something and come across this conclusion.

Then I found that the geometric Langlands conjecture was helpful for my study of random prime number models, so I started to study this series of papers with a learning attitude. Then I felt that there might be some imperfections in the papers. "

Tian Yanzhen frowned. This answer seemed to make it impossible for him to say the scolding words he had prepared next.

So he subconsciously put down the pen in his hand, leaned back in his chair, and said, "Come on, tell me in detail how you found that other people's conclusions are helpful to your topic. Describe your thought process in detail."

In fact, from the moment Tian Yanzhen asked that question, Qiao Yu subconsciously flashed through the words Yu Wei said to him.

“…when you tell lies, you must remain calm and frank, without any hesitation or room for people to discover your lies…” Well, actually, he also has this ability, but his summary is not as precise as Yu Wei’s.

To be honest, Qiao Yu didn't want to lie to Tian Yanzhen. But he had no choice. He didn't want anyone to know that he had a living father abroad.

Yes, even if his living father in the future comes to him and claims to be his relative, he will never acknowledge it.

Qiao Yu answered frankly: "Because I want to find a new way. Initially, I wanted to analyze prime numbers through modular forms, and then I found that the geometric Langlands conjecture can also provide a geometric perspective for understanding modular forms. I wondered if I could understand the distribution of prime numbers by studying the geometric properties of modular forms.

Then I searched for the content of the geometric Langlands conjecture, and happened to find that paper. After reading it, I found that the geometric structure and representation theory tools they introduced in the limit of large numbers can also be used to study statistical properties.

I also felt that the spectral theory of those geometric objects might have similar statistical properties to the distribution of prime numbers, and then, you know, I started to study their papers. But after reading them, I felt that it was not right. In short, it was quite complicated. Can you understand it? "

Tian Yanzhen stared at Qiao Yu for a long time and indeed felt that this little guy did not seem to be lying, but this connection... To be honest, Tian Yanzhen felt it was a bit far-fetched, but not completely impossible.

After all, the research on the entire Langlands conjecture system, including the research on geometric Langlands conjecture, is intended to provide a series of theoretical tools for mathematical research.

It can be seen from Qiao Yu’s previous paper that this guy’s thinking mode is indeed very broad. He is very good at using tools constructed by others to solve the problems he encounters, and he can even create more useful tools in the process.

Well, this seems to be unteachable.

After all, according to this guy, he has actually been working on the questions he assigned, and just wanted to borrow some tools developed by others. However, in the process, he found some loopholes in other people's tools, so he raised doubts.

This makes sense logically, but it still feels weird.

After all, when ordinary people study random prime number models, it is difficult for them to turn their thinking to the direction of the geometric Langlands conjecture. But this kind of turning... Tian Yanzhen thinks that it should not be criticized, but should be supported.

After all, what if it really works and is effective?
You know, if Qiao Yu can really use this method to study an ideal random prime number model, it will be a major breakthrough for the mathematics community.

For example, it not only complies with the prime number theorem, but also captures prime number intervals, provides error limits, and is consistent with important functions in number theory. It can even take into account the phenomena of conjugate primes and prime number pairings, and has super strong adaptability...

That is very useful. Not only can it promote the development of number theory, but it can also play an important role in applications.

For example, in the most popular deep learning and machine learning, the characteristics of random prime numbers can not only be used to optimize algorithms, model parameter selection and feature selection, but also play a role in random weight initialization and generative adversarial networks.

So the criticisms that I had prepared were forced to be suppressed, and when I spoke again, it became a compliment: "Your idea is good. This is how mathematical research works. You really need to think more broadly."

"Thank you, Director Tian. Director Tian, ​​if there's nothing else, I'll leave first."

"Well, go ahead. Have a good rest today. The seminar will be held at the Huaqing Mathematics Research Center starting next Monday, so make the most of it."

"Okay, don't worry." With that, Qiao Yu walked out of the office with a proud look on his face.

Tian Yanzhen smiled, then picked up the pen again and was about to continue writing his opinion, when he suddenly felt something was wrong...

When assigning the kid the topic of random prime number distribution, Qiao Yu was still reluctant. He just wanted to have a good rest during the training. He even begged him to do a bunch of random things in order to escape the weekly tasks such as reading books and writing research and development reports.

But he didn't want to rest at all when he was studying the paper on the geometric Langlands conjecture...

This attitude change is a bit fast and a bit big, isn't it?
But then Tian Yanzhen took the initiative to help Qiao Yu find a reason...

Maybe he was attracted by the excellent papers? As a math genius, this is normal.

……

After telling the lie, Qiao Yu returned to the room. Instead of resting, he followed Tian Yanzhen's instructions and looked up the list of experts who would attend the seminar on the official website, and then continued to work on his paper.

After all, fooling the tutor is a technical job.

And many times, whether it is really a trick depends on the results.

For example, although he gave a reason that sounded far-fetched, if he could really use these ideas to make a model, then it would not be fooling around, but rather he really thought so at the time.

The same applies to bragging.

If you say in public that you want to achieve a goal that others think is impossible to achieve, and if you fail to achieve it, then it is bragging; if you achieve it, then it is stating a fact, or it is really awesome.

Before he became successful, a father named Ma once said, "In the future, shopping will be done online, and most goods will be sold online." It sounded unreliable at the time, but he succeeded in the end.

So much so that when he later said in public that he didn't like money and had no interest in money at all, it was difficult for others to refute him.

Because there are really few people who can use money to hit him, but he often uses money to hit others...

So as long as you are awesome enough, no matter what nonsense you say, others will believe it.

Mathematics is actually similar. As long as you are good enough and others can't find any flaws in the article you write, they will have to admit that you are right.

Of course, this requires a little effort as a price to pay, but fortunately this is what Qiao Yu is most interested in, so it is understandable that he should work harder.

……

In the first few days after returning to Yanbei, Qiao Yu spent his time studying his thesis hard.

Apart from a phone call to Qiao Xi on Qingming Festival, in which he solemnly asked Qiao Xi to take his grief with her when she went to the cemetery to pay tribute to her grandparents, he had almost no contact with anyone else.

Oh, by the way, actually Senior Brother Chen came to see him once.

He actually managed to find out some secrets that were passed around among the international students, but after hearing them, Qiao Yu put them out of his mind, thanked Brother Chen, and told him not to ask any more.

After all, Chen Zhuoyang has been quite busy lately, preparing for his graduation defense. The date has already been set.

Although the paper itself is not very good, I have to make sure that there is no big trouble during the defense - I can't embarrass my supervisor. So there are actually quite a lot of things to prepare.

Qiao Yu likes this kind of quietness.

The professors invited this time were all very good, and their previous papers were naturally of high quality. After reading them, he had a much deeper understanding of the entire Langlands conjecture. So much so that when Qiao Yu looked back at his previous understanding of the theory for solving the geometric Langlands conjecture, he felt that he had almost found the key to the problem...

He seemed to have a rough outline of a counterexample in his mind...it seemed to be brewing and about to come out.

As many people self-deprecatingly say, it is as if they have grown a brain again, so that they always feel itchy in their head.

This situation continued until the official opening of the Huaqing series of seminars on the geometric Langlands conjecture.

The keynote speaker on the first day was Professor Everton from Princeton.

Qiao Yu once again enjoyed special arrangements and sat in the first row.

Yuan Zhengxin also arranged Pan Jingyuan to sit next to Qiao Yu so that the two could communicate at any time.

Although the two often communicated on WeChat and could be considered to have known each other for a long time, and of course it was mainly Qiao Yu's unilateral requests for advice, it was the first time they met in real life.

Especially Pan Jingyuan, although he already knew that Qiao Yu was only sixteen years old, but before they met, age was just a concept. Seeing that young face with his own eyes made him feel even more defenseless.

It's easy to wonder why you don't just go to high school and attend classes.

After Qiao Yu greeted Pan Jingyuan honestly, Professor Pan asked, "I read your thoughts that day. What do you think? Did you find any counterexamples?"

The boy shook his head and answered honestly: "Not yet, but I feel like I'm almost there."

This answer made Professor Pan feel even more unhappy.

The young man said excitedly: "Professor Pan, do you want to hear me talk about my ideas in detail?"

Pan Jingyuan shook his head and said, "Wait a minute, Professor Everton's lecture is about to begin."

"Oh, okay!" Qiao Yu nodded honestly and corrected his sitting posture to look more formal.

After all, this wasn't a lecture at Yanbei University, so I had to focus on the reputation of Yanbei University, and Master Shi would probably be here soon. I had to give the adults some face.

Not to mention that there were many foreign friends present in the front row of this seminar.

Qiao Yu knew very well how restrained he was in such occasions, and how unrestrained he could be in the office of his mentor and master. It was a very simple truth, but unfortunately many people did not understand it.

As he expected, Master Yuan walked into the venue with a foreign professor. Seeing Qiao Yu sitting upright, Master Yuan smiled at him with a doting look in his eyes...

Qiao Yu listened very attentively throughout the lecture. Perhaps it is because many things in academia are more interesting when they are presented on stage, or it is easier to be passionate about them. Anyway, Qiao Yu listened with great interest, which was much more interesting than reading papers.

Due to limited time, Professor Everton focused his speech on two points.

The first is how to combine symmetries and geometric structures in representation theory to gain an understanding of the conjecture; the second is how p-adic Hodge theory provides a new perspective for the geometric Langlands conjecture.

As Professor Everton continued to explain the story from the simplest to the most complex, Qiao Yu suddenly felt that the fence that had been blocking his inspiration in his mind was being violently shaken, and the long-lost inspiration was frantically testing the edge of a burst...

As beautiful as a mountain about to erupt.

　The 35th day of the 10,000-word update is complete!

　　
　
(End of this chapter)