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 the capital.
Qiao Yu sat at the window, looking at the scenery outside the window with nostalgia. My hometown is like this. If you stay here for a long time, you will be dissatisfied with it. But once you leave, the bright side emerges.
Distance can always produce some unique filter beauty, just like the beauty software on your mobile phone. This probably shows from the side that the human brain has something in common with computers, and what’s more advanced about the human brain is that it also has adaptive software.
"The team will have some activities next, but I have talked with your tutor, Professor Tian, so you don't need to participate. In addition, we have created a group and we have not included you. You don't have anything else. Idea. The main thing is that you are close, so it is convenient to notify you..."
Zhou Liang was talking beside him, but Qiao Yu just went in and out of one ear and didn't pay much attention. Participating in the IMO competition can probably be understood as an obsession that has a beginning and an end. In fact, Qiao Yu also knew that winning a gold medal didn't mean much to him.
But Professor Schultz won a gold medal that year, and Professor Pan across from him also won a gold medal. If he didn't win either, he always felt like he was regretting his youth.
As for the activities before going to Australia, Qiao Yu had no interest in participating.
It’s nothing more than brushing up on questions.
The most important thing is that he is too lazy to expose Professor Zhou's little thoughts.
Why is he not included in the group because he is so close? It was just that he was afraid that he would cause trouble again and hit some of his friends who were competing together. Of course, this cannot be blamed on Zhou Liang for thinking too much. The main reason is that the psychological quality of his friends is so poor.
Faced with a small setback, it is not calm at all. Playing a game can make your mentality collapse once. No matter who is the team leader or coach, it will probably be 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 arrangements, too. For everyone’s good this time.”
Professor Zhou said with a smile on his face: "Yes, the main reason is that you don't have time. Professor Tian is also worried about you. He knows that you are interested in the geometric Langlands conjecture recently. He has been working with Huaqing for a few days and has a series of related lectures and seminars. , many experts are specially invited from abroad, which is enviable.”
Qiao Yu finally looked away from the window, turned 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.
Sure enough, the mentor and Grandpa Shi still love him. Although they have not told him explicitly, they have been working silently behind the scenes.
Qiao Yu also deeply realized the value of what Lao Xue said to him back then.
Sure enough, if the instructor can handle things, he can do whatever he wants.
How could such a large-scale seminar be possible if we had a tutor who couldn't handle it? After all, it costs money to invite relevant professors and scholars from abroad, not to mention inviting people to eat and stay, which is all money. In addition, you have to match the appearance.
Of course, we have to thank China for its good development over the years, and its external publicity work has also kept up. Otherwise, just talking about money will be useless.
In short, at this moment, Qiao Yu really understood how much having a good tutor would help his studies.
Old Xue, I will not deceive him!
...
Across the ocean, in Madison, the capital of Wisconsin, is the University of Wisconsin-Madison.
Pan Jingyuan was standing outside the conference room, looking at the tutor who was surrounded by many scholars and still discussing some detailed issues.
The lecture just now has ended, and his tutor Dennis is the keynote speaker.
The content of the lecture is naturally about the proof of the geometric Langlands conjecture.
In fact, he could also participate in the discussion, but since talking to Mr. Yuan that day, Pan Jingyuan has been feeling a little uneasy. This is a very weird feeling.
Although he knew that Qiao Yu was just a student who had just come into contact with the Langlands Conjecture of geometry, some of the questions he asked did not need to be taken too seriously. But the question Qiao Yu asked that day really made him feel a little uneasy.
After all, it has been more than ten years since this project was established, and it has been six years since he was invited to participate. He does not want the results of these six years of hard work to become a joke and cost money. A few years to make up for it.
This uneasy feeling even made him re-examine these five papers, trying to make sure that the situation that Qiao Yu judged was impossible. But this obviously takes time. In fact, Pan Jingyuan has already started doing this work.
This is also the reason why he is getting slower and slower in replying to Qiao Yu's messages.
This feeling of uneasiness reached its peak a few days ago after Mr. Yuan forwarded the questions raised by Qiao Yu.
He wanted to discuss Qiao Yu's ideas with his mentor, but he never made up his mind.
After all, he has only been involved for six years and is already very nervous. For a mentor, he has spent fifteen years in it. He wasn't sure what Dennis' attitude would be when he heard such remarks, and whether it would be counterproductive.
The relationship between students and tutors is never necessarily a good one. Because of some conflicts, there are people who turn against each other, whether in China or abroad.
It’s just that in most cases, everyone has a tacit understanding not to expose it.
However, Huaqing is planning to organize a series of seminars on the geometric Langlands conjecture with Yanbei University. They have also invited many foreign professors, and the news will most likely reach the ears of the instructors.
Of course Pan Jingyuan knew who this series of seminars was for.
To be honest, Pan Jingyuan really had no resistance to this decision. Of course he knew what Qiao Yuzhen's growth meant to the Chinese mathematics community.
After so many years, although Huaxia has developed well, its voice in the academic world is not large, at least compared to the size of the country, it is very unreasonable. But there is no way. Academia is often like the Olympics. If you want to speak and be listened to, it ultimately depends on your ability.
Why is it generally recognized that English journals are more authoritative? Because a series of tools currently used in mathematical research are basically summarized by Westerners. The main theorems encountered in college classes are basically named after Westerners.
Abel's theorem and Gauss' theorem in algebra, Fermat's theorem in number theory, Euler's theorem, Biglas' theorem in geometry, Heron's formula, DeMorgan's law in analytic geometry, L'Hôpital's law in calculus...
In addition to Markov's stochastic process and Yebes' theorem for calculating probability...
The efforts of predecessors have given the modern Western world a firm grasp of the academic voice. Even if you don't know English, especially English for mathematics majors, you won't be able to accurately understand the mathematical ideas of those predecessors.
Huaxia is a latecomer, so if it wants to gain more say, someone must be able to take the lead in the world of mathematics in the future.
For example, if there is a mathematician in China whose achievements are comparable to those of Newton and Euler in the future, even if he speaks softly, it will be deafening.
There has never been a pure land in the real world, or places like Peach Blossom Spring only exist in people's imagination. People's intelligence and social nature have long been determined. Anyone who achieves success will definitely stick together and raise the entry threshold for related fields.
Learning valves has always existed. The more developed various operations are, the more common this phenomenon is. The consideration of higher-ranking people is never to ban this kind of thing, but how to use this inevitable phenomenon to promote the development of science.
For example, in elite governance, through the most basic education, the elites are directly physically separated from the children of ordinary people, and the strategic goals of starting from childhood are achieved in the third, sixth and ninth grades.
Pan Jingyuan felt that Qiao Yu had hope of becoming such a scholar.
It’s just that the current situation makes him feel confused.
However, Pan Jingyuan made up his mind today. Instead of waiting for Dennis to hear Qiao Yu's "fallacies" from others, he should take the initiative to report them. And he has already thought of how to deal with it.
Finally, Dennis ended 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 joke: "What's wrong? Pan, Doesn’t today’s occasion excite you? Don’t worry, there will be more important meetings in the future.”
Pan Jingyuan shook his head, then smiled and said: “No, Dennis, actually this meeting. It has benefited me a lot. I just want to tell you something... By the way, you still remember. The paper you were planning to review before?”
Dennis replied: “Of course, that paper left a deep impression on me. I also exchanged ideas with Schulz about this paper. opinion, in fact his evaluation of this paper It's also very high.
But I haven't issued a final review opinion yet. You know, I want to issue a more professional review opinion. The author is still young, and he may not know that it is necessary to publish a paper of this level. Some patience.”
Pan Jingyuan said: "No, you misunderstood. It's 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. It is that he has recently become interested in the geometric Langlands conjecture, and is targeting our The work raised some questions.
Huh... I have been thinking about how to systematically answer his questions for the past two days, so that I can give him a very positive answer. Don't waste your time on this."
"Oh?" Dennis was obviously interested and said, "I heard that the author of that paper is still very young. Schultz told me. Obviously he knew some information that I didn't know, so can you tell me how old Qiao Yu is?"
"Sixteen years old," Pan Jingyuan replied.
"Sixteen years old?" Dennis frowned and looked at Pan Jingyuan again, a little incredulous: "You mean a sixteen-year-old student who not only independently completed a high-quality but also has the A paper of great significance, you also understood our paper and raised some questions that you personally find difficult to answer? ”
"I know this 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 easy to learn and studies well." The speed of things is indeed very fast.
After about a week, I already felt that many of the questions he asked were a bit difficult to deal with. Do you still remember some of the issues we discussed these days? In fact, most of them were questions raised by him."
Dennis opened his mouth and wanted to say something, but made no sound. Finally, he asked with a look of surprise: "Okay, let me answer this question. You are getting more and more interested. Tell me, what question did he ask that made it difficult for you to answer?”
Finally waiting for this sentence, Pan Jingyuan took out a piece of information from the information he carried with him. The printout was handed to Dennis.
This was specially prepared by him.
In fact, he translated the report that Yuan Zhengxin forwarded to him into English, and added some content in the middle, mainly because Qiao Yu had some doubts about the rigor of the paper during his thinking process when the two of them communicated on WeChat.
Dennis glanced at Pan Jingyuan, then took the printout, and instead of moving forward, he stood there and read it.
After all, there were no specific examples of Qiao Yu’s questions, so the article was not long. However, Dennis looked at it very carefully. The two of them stood here for about five minutes before Dennis looked away from the printout. .
After returning the printout to Pan Jingyuan, Dennis slowly said: "If these are really questions raised by a sixteen-year-old child after reading the paper, then I can only say that he is talented. "Extraordinary."
Pan Jingyuan nodded, He replied: "In fact, he is indeed gifted. In fact, you can see it from his paper. It is said that from the time he decided to become independent, he used the theory of near-complete space to analyze the upper bound of the rational point of the curve to conduct research, to write that paper The thesis only took about twenty days
What's even more amazing is that he has only been exposed to Professor Schultz's mathematical ideas and a series of tools for only a month. It is said that he went to study Schulz's thesis because of the recommendation of another teacher. "
Dennis nodded. If the genius in Pan Jingyuan's words changed his question, he might be interested in talking more about Qiao Yu with Pan Jingyuan.
But it was them who questioned it.
Dennis shook his head and said: "The questions he raised are indeed interesting. We all know how important structural consistency is to the conclusions we give. 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 huge task to explain that throughout the entire proof process, the systematic analysis tools we use can ensure that the designed geometric objects, algebraic structures and related properties maintain strict consistency.
But to be honest, I can probably understand how you feel. The questions he asked made me feel a little nervous. But you see, he hasn't been able to find a counterexample. This at least shows that our argument is rigorous, at least relatively rigorous, and counterexamples are not so easy to find. "
Pan Jingyuan nodded with a wry smile, and then asked softly: "What if he finds it? For example, at some point in the future. "
Dennis took a long breath, shrugged and said: "Then we can only re-explore this issue and re-examine the proof process of the paper. That would mean our work has to 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! Are you right, Pan? "
Pan Jingyuan liked Professor Dennis's open-mindedness, which was probably one of the reasons why he chose Dennis as his tutor. So he nodded and said, "I understand, I will continue."
By the way, the two best universities in China 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 questions at the meeting. Is there anything you want me to bring to him? "
Dennis thought for a while and replied: "I originally wanted you to give him my email address so that we could have some direct communication, which might be very interesting. However, considering that I am still reviewing his paper, this time point is not good, so I will wait until the final review opinion of his paper comes out.
But if you have any fresh ideas at this meeting, feel free to send me an email. Of course, if that Qiao Yu really does what he thinks and finds a counterexample, he can call me directly. Although I think this possibility is unlikely. By the way, I’m of course not talking about just during the seminar. "
Pan Jingyuan nodded and agreed.
"Do you know why I want to add the last sentence? Because guys like Schultz often have terrible mathematical intuitions. Especially when they don't have a deep understanding of mathematics. How should I put it? Young people are always good at creating mathematical miracles, which is why I like to teach students. ”
Dennis explained, then raised his hand and patted Pan Jingyuan on the shoulder, joking:
"Okay, let's go to dinner now. Don't look sad. I think you should be grateful for the emergence of another mathematical genius in China. It’s better to be happy. Even if I feel uncomfortable, I think it should be Schultz, because his unique genius status is being challenged.”
Hearing this, Pan Jingyuan also laughed, and then he felt in his heart. There was a hint of bitterness.
Yes, his tutor is a rich second generation, and he does not need to live on the salary of a professor. Studying mathematics is purely out of interest, so he is less concerned about fame and fortune than others.
But to be honest, Pan Jingyuan still hopes to win a grand prize in the international mathematics community.
In a sense, guys like Schultz and Qiao Yu who have their own aura of talent are the public enemies of mathematicians around the world. Half a lifetime of efforts may not be worth their 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 choice. He even knew that the boy was criticizing the paper that he had contributed to, but he still had to find a way to deal with his one hundred thousand whys...
What a mess!
……
Huaxia, Beijing, Yanbei University.
As soon as Qiao Yu walked into the Mathematics Research Center, he met Lao Xue Zheng walking out in a hurry.
“Mr. She showed off to Xue Song the lightweight suitcase that Qiao Xi specially bought for him online - from Golden Eagle, a brand!
Anyway, Qiao Yu thinks this is a good brand, fashionable, lightweight and eye-catching.
But it’s obvious that Lao Xue doesn’t know the goods. He didn’t even say, “Hey, it’s a new box.” Instead, he directly asked, “How is it? Have you made any breakthrough with your idea?”< br>
Hey, I don’t know how to be a tutor. I don’t have the mindset of a student at all.
"Not yet. But I didn't waste the training time. I have read all five papers on the geometric Langlands conjecture, so this training is still very rewarding." Qiao Yuhui reported .
Xue Song thought for a while, and then said: "Well...it's pretty good!"
In fact, as long as you have the expectation that this guy doesn't know how to speak human words, you won't find those casual words of Versailles so hurtful.
"By the way, is Director Tian in the office?" Qiao Yu asked again.
Xue Song nodded and replied: "I just came back. What? Do you have something to do with Director Tian?" Qiao Yu said: "Yes, I plan to go thank Director Tian. I just found out on the high-speed rail In order to help me find a way to solve my doubts, Director Tian also organized a series of seminars with Huaqing.”
Xue Song heard Qiao Yu mention this matter. His expression became weird again.
This reminded him of the email he sent Tian Yanzhen that night.
I never expected that what was just a whim at the time might indirectly lead to the great reconciliation of the two Chinese mathematical schools.
Although there are currently no public statements from both parties to support this, from the cooperation in organizing this series of seminars, we can see that there are already signs of this. At least the two sides are no longer in a state of never communicating with each other.
Of course, if you really want to say it, the conflict between Yuan Zhengxin and Tian Yanzhen has not greatly affected the training of students. As Xue Song learned after coming to Yanbei, there are many professors in the Mathematics Department of Huaqing who have a good relationship with Tian Yanzhen.
Occasionally, Mr. Yuan’s students come to Yanbei to give lectures in seminars, and even young professors from the mathematics centers on both sides collaborate to publish articles. Not everyone cares about the dispute.
But if the barrier is gone, it will be better if the communication between the two parties can go further.
After all, the big guys on both sides have a lot of resources. These resources are not necessarily funds, but also a large number of contacts 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 there may be great breakthroughs in the future at the level of geometric analysis that the two are best at. And it can also be regarded as a boost for the Chinese mathematics community as a whole.
The most important thing is that if Qiao Yu can inherit the academic resources left to him by both parties in the future, then this status... probably no matter how much trouble he makes, at least no one in the country will dare to use it openly against him. Stumbled?
After all, what the two sides are fighting for is the right to speak...
Thinking about it this way, Xue Song felt envious again.
"Well, you should go and say thank you. Just leave your luggage and go as soon as possible. Otherwise, Professor Aida will have to go out again later."
"Okay." Qiao Yu agreed. After making a sound, he picked up his brand new suitcase and walked excitedly towards the research center.
Xue Song stopped and looked at Qiao Yu's back, sighing in his heart that it was so good to be young. It took him a while to come back to his senses... he shook his head and walked towards the outside of the research center. Wait, he What are you going to do?
……
"Director Tian, I'm back!"
"Oh, I just arrived."
"Yes, Director Tian, I'm here specifically to thank you. You are definitely the best person in this world." The best and most perfect mentor, no one else."
Tian Yanzhen put down the pen in his hand and raised his head to look at Shiliu, who was becoming more and more outrageous. He didn't even knock on the door when he came to his office. A year-old kid...
Well, even though it was a rainbow fart, he decided to accept it.
But seeing Qiao Yu's arrogant look, Tian Yanzhen couldn't help but give him a lesson: "It's useless to talk. There's only so much I can help you. How much you can gain ultimately depends on yourself. This time You can check the list of professors participating in the conference on the official website, and that’s the same thing. To learn from other people's experience, you must first have a minimum of respect for other people's research results."
Qiao Yu immediately replied seriously: "Don't worry! Don't you know my attitude towards learning? To tell you the truth, during the training camp, I already wrote those five papers I have read them all, including most of the cited documents. I am very familiar with this proposition."
Tian Yanzhen nodded and said, "That's fine. You're here just in time. I have something to ask you. Didn't you tell me last time? Are you interested in number research? I also helped you choose a proposition to build a prime number model, and I also planned to let you attend several conferences on prime number research. Why are you suddenly interested in the geometric Langlands conjecture? "
Students who come to your door will become useless if you don’t discipline them.
Although he was flattered as soon as he walked in, Tian Yanzhen still disapproved of this kind of approach.
No matter how Qiao Yu answered, he planned to have a good talk with the little guy to make him realize the seriousness of academic research.
If you don’t work on the topic you have planned, then you will go find fault with someone else when they publish an important result. It’s just that you are young, you can just pretend that you are not sensible. But if you develop this habit of being careless, you will become a public enemy of mathematics in the future.
After all, people will grow up, but habits may remain.
Although he decided to help the tyrants this time, he must be severely criticized, at least not in the future.
Who knew that Qiao Yu opened his mouth and replied: "Reporting to Director Tian, it's not that I suddenly became interested in the geometric Langlands conjecture. In fact, I have been studying the topics you assigned me, but who knows During the research, I searched for some things and came across this conclusion.
Then I found that the geometric Langlands conjecture was helpful for me to study the random prime number model, so I started studying this series of papers with a learning attitude. Then I felt that the paper might have some imperfections. "
Tian Yanzhen frowned. This answer seemed to make it impossible to say the training words he had prepared next.
So he subconsciously put down the pen in his hand, and then He leaned back on the chair and said: "Come on, tell me carefully how you found that other people's conclusions are helpful to your topic. Explain the thought process more fully. "
In fact, from the moment Tian Yanzhen asked that question, what Yu Wei said to him flashed through Qiao Yu's mind subconsciously.
"...when telling lies. You must be calm and calm, without any hesitation or letting people see any flaws..." Well, in fact, he also has the ability in this area, but his summary is not as good as Yu Wei's.
To be honest, Qiao Yu didn't want to deceive Tian Yanzhen. But there is no way, and he doesn't want anyone to know that he still has a living father abroad.
Yes, even if his living father in the future licks his face to acknowledge his marriage, he will never admit it.
So Qiao Yu replied calmly: "Because I wanted to find a new way. Initially I wanted to analyze prime numbers through modular form, and then I found that the geometric Langlands conjecture can also provide a geometric perspective for understanding modular form, so I decided I was wondering 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 I happened to find that paper. After reading it, I discovered that the geometric structures and representation theory tools they introduced in Limit of Large Numbers can also be used to study statistical properties.
I also feel that the spectral theory of geometric objects may be related to that of prime numbers. The distribution has similar statistical properties, and then you know, I started to study their paper, but after reading it, it didn’t feel right. It’s quite complicated, can you understand?”
Tian Yanzhen stared at Qiao Yu for a long time. He did feel that this little guy was not lying, but this connection... To be honest, Tian Yanzhen felt that it was a bit far-fetched, but it was not completely impossible.
After all, the research on the entire Langlands conjecture system, including the geometric Langlands conjecture, is to provide a series of theoretical tools for mathematical research.
It can be seen from Qiao Yu's last paper that this guy has indeed a broad thinking model and is very good at using tools constructed by others to solve the problems he encounters. process to create more useful tools.
Well, it seems there is no way to train this.
After all, according to this kid, he has been working on the propositions he assigned, and just wanted to borrow some tools developed by others. However, in the process, he found some loopholes in their tools, so he raised questions. .
This makes sense logically, but it still feels weird.
After all, it is difficult for ordinary people to turn their minds to the direction of the geometric Langlands conjecture when studying the random prime number model. But this kind of abduction... Tian Yanzhen feels that he should not criticize, but should support it.
After all, what if it really works and is very effective?
You must know that if Qiao Yu can really use this method to develop an ideal random prime number model, it will be another major breakthrough for the mathematical community.
For example, it not only complies with the prime number theorem, but also captures the interval between prime numbers, provides error bounds, and is consistent with important functions in number theory. It can even take into account the phenomenon of conjugate primes and prime pairings, which is in line with the super strong Adaptability…
That is of great use. It not only promotes the development of number theory, but also plays an important role in applications.
For example, it is used 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 can also be used in random weight initialization and generative adversarial networks. effect.
So the criticisms I had prepared were forcibly suppressed, and when I spoke again, they became compliments: "You have a good idea. This is what mathematics research is like. You really need to think more broadly."
“Thank you, Director Tian. Director Tian, if there’s nothing else, I’ll leave first.”
“Well, let’s go. Have a good rest today. The seminar will start in China next Monday. Hosted by the Qing Mathematics Research Center, hurry up. ”
"Okay, don't worry." With that said, Qiao Yu walked out of the office proudly.
Tian Yanzhen smiled, then picked up the pen again, and was about to continue writing his opinions, when he suddenly felt something was wrong...
At that time, he assigned this kid the proposition of random prime number distribution. At that time, Qiao Yu was still reluctant and just wanted to have a good rest during the training camp. She even begged him to do a lot of things in order to avoid the weekly tasks of reading books and R&D reports.
But when he was studying the paper on the geometric Langlands conjecture, he didn’t want to rest at all...
This attitude changed a bit quickly, and it was a bit too big, right?
But after a second thought, Tian Yanzhen took the initiative to find a reason for Qiao Yu...
Maybe he was attracted by high-quality papers? As a math genius, this is normal.
......
After telling lies, Qiao Yu returned to the room. Instead of taking a rest, he followed Tian Yanzhen’s instructions and checked the official website for the list of experts who would attend the seminar. Then continue reading the paper.
After all, fooling the instructor is a technical job.
And in many cases, whether it is really a fool depends on the results.
For example, although he gave a reason that sounded ridiculous, if he could really use these ideas to make the model, it would not be a fool, but that is what he really thought at the time. .
The same goes for bragging.
Speaking in public that you want to achieve a goal that others think is impossible. If you don’t achieve it, it’s bragging. If you achieve it, you’re stating the facts, or you’re really awesome.
Before he succeeded, a certain 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 not many people who can throw money at him, but he often throws money at people...
So as long as you are good enough, no matter what nonsense you talk, others will believe it.
Mathematics is actually similar. As long as you are good enough and others can’t find any flaws in the articles you write, then you have to admit that you are right.
Of course, this requires a little effort as a price. Fortunately, this is what Qiao Yu is most interested in, so there is nothing wrong with working harder.
...
In the first few days after returning to Yanbei, Qiao Yu came here while studying hard for his thesis.
Except for calling Qiao Xi on the Qingming Festival, and solemnly entrusting Qiao Xi to go to the cemetery to pay homage to his grandparents, he had almost no contact with anyone else with his ray of grief.
Oh, by the way, in fact, Senior Brother Chen came to see him once.
He actually made him find out some secrets that were spread privately among the overseas students. However, after Qiao Yu heard about it, he put it behind him. After thanking Senior Brother Chen, he told him not to ask anymore.
After all, Chen Zhuoyang has been very busy recently, preparing for his graduation defense. The date has been set.
Although the thesis itself is relatively weak, you still have to ensure that there are no big mistakes during the defense - you can’t embarrass your supervisor too much. So there are actually quite a lot of things to prepare.
Qiao Yu likes this kind of tranquility.
The professors invited this time were all of high standard, and the previous papers were naturally of high standard. After reading through them, he had a much deeper understanding of the entire Langlands conjecture, so much so that Qiao Yu turned around and looked at it. With his previous understanding of the theory that solved the geometric Langlands conjecture, he had a vague feeling that he had almost touched the key to the problem...
He seemed to have the prototype of a counterexample in his mind... He felt ready to make a move. The feeling of coming out.
In the self-deprecating words of many people, it seems that they have grown a brain again, so that they always feel itchy in their brains.
This situation continued until the official opening of the Huaqing seminar series on the geometric Langlands conjecture.
The lecturer on the first day was Professor Everton from Princeton.
Qiao Yu also enjoyed the special arrangement again and sat in the first row.
Yuan Zhengxin also directly arranged Pan Jingyuan next to Qiao Yu to facilitate communication between the two at any time.
Although the two communicated frequently on WeChat and had been close friends for a long time, of course it was mainly Qiao Yu who asked for advice unilaterally, but this was the first time they met in real life.
Especially Pan Jingyuan, although he already knew that Qiao Yu was only sixteen years old, age was just a concept before they met. Seeing that still green face with his own eyes made people feel even more defensive.
It’s easy to wonder why your kid doesn’t just go to high school.
After Qiao Yu greeted Pan Jingyuan honestly, Professor Pan asked: "I read your experience that day, how was it? Did you find any counterexamples?"
Teenager He shook his head and answered honestly: "Not yet, but I feel like I'm almost touching it."
This answer made Professor Pan feel a little more unhappy.
The young man said with great interest: "Professor Pan, do you want to hear me explain my thoughts in detail?"
Pan Jingyuan shook his head and said: "Wait a minute, Ever Professor Dun's lecture is about to begin."
"Oh, okay!" Qiao Yu nodded honestly and corrected his sitting posture to look more formal.
After all, this is not a lecture at Yanbei University. We must pay attention to Yanbei University's face, and it is estimated that grandpa will come over when we meet. I have to show my face to the adults.
Not to mention that there were many foreign friends in the front row of this seminar.
Qiao Yu knew very well how restrained he could be on such occasions, and how unrestrained he could be in the offices of his mentor and grandpa Shi. It’s a very simple truth, but unfortunately many people don’t understand it.
As he expected, Mr. Yuan walked into the venue with a foreign professor. He saw Qiao Yu sitting upright, and the master smiled at him, with eyes full of joy. Pampering...
Qiao Yu listened very carefully to the whole lecture. Probably because many academic things are really more interesting when you sit on the stage and talk about them, or it is easier to get passionate. Anyway, Qiao Yu listened with gusto, which was much more interesting than reading the paper.
Due to limited time, Professor Everton will probably talk about two points.
The first is how to combine symmetry and geometric structure in representation theory to gain an understanding of the conjecture; the second is how p-adicHodge theory provides a new perspective on the geometric Langlands conjecture.
As Professor Everton narrated from shallow to deep, Qiao Yu suddenly felt that the fence that had been blocking his inspiration in his mind was being shaken crazily in an extremely violent way. The long-lost inspiration The edge that is gushing out is testing wildly...
It is as wonderful as a certain mountain that is about to erupt.
The 35th day of the 10,000-word update has been completed!
(End of this chapter)