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 and looked 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 many things. But once you leave, the beautiful side will appear.
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 and computers have something in common, and the more advanced part of the human brain is that it also has its own Adaptable software.
"The team will have some activities next, but I have talked with your instructor, Professor Tian, ​​so you don't need to participate. In addition, we have created a group and we have not included you. Don't have any other ideas. The main thing is that you leave It's so close. It's very convenient to notify you.
Zhou Liang was talking next to 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 knows that winning a gold medal is very important to him. Doesn't make much sense.
But Professor Schultz had won a gold medal that year, and Professor Pan across from him had also won a gold medal. If he didn't win one, he always felt like he was sorry for 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 so close, so we don’t include him in the group? It’s just because he’s afraid that he’ll cause trouble again and hit a few friends who are competing together. Of course, this can’t be blamed on Zhou Liang for thinking too much, it’s mainly because of his small size. The psychological quality of my partners is so poor.
Faced with a small setback, he is not calm at all. Playing a game can make his mentality collapse once. It will probably be difficult for him to be the leader or coach of the team. Eliminate him as a guy who may bring instability. Outside, it 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's for everyone's benefit this time." .”
Professor Zhou showed a smile on his face and said with emotion: "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 and have collaborated with Huaqing several times. There are a series of related lectures and seminars held today, and many experts are specially invited from abroad, which is enviable.
Qiao Yu finally retracted his gaze from the window, turned to look at Professor Zhou next to 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, his mentor and Grandpa Shi still loved him. Although they didn't tell him explicitly, they had 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 held as easily as a tutor who could not handle the task? After all, inviting relevant professors and scholars from abroad requires money, let alone inviting people to eat and stay, which is all money. .In addition, you have to keep up with 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 would be useless. In short, at this moment, Qiao Yu really understood how important having a good tutor is to his studies. How helpful it is.
Lao Xue, sincerely do not deceive him!
On the other side of the ocean, in Madison, the state 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 had ended, and his tutor Dennis was 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 chatting with Mr. Yuan that day, Pan Jingyuan has been feeling a little uneasy. This is a very strange 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 questions Qiao Yu asked that day did make 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 it will take several more 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. However, this obviously took time, and in fact Pan Jingyuan had already started to do 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 when Mr. Yuan forwarded the questions raised by Qiao Yu. He wanted to talk to his tutor about Qiao Yu's thoughts, 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 is not sure what Dennis's attitude will be when he hears such remarks, and whether it will have the opposite effect. .
The relationship between students and tutors is never necessarily a good one. Because some conflicts turn into enemies, whether in China or abroad, it is 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, and has invited many foreign professors. There is a high probability that the news will 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 objections to this decision. Of course he 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 very big, at least compared to the size of the country, it is very unreasonable. But there is no way, the academic world is often like the Olympics. If you want to speak and be listened to, it ultimately depends on your strength.
Why is it generally recognized that English journals are more authoritative? Because a series of tools used in mathematical research are basically summarized by Westerners. The main theorems encountered in college classes are basically named after Westerners.
Abel's theorem in algebra, Gauss' theorem, Fermat's theorem in number theory, Euler's theorem, Biggras' theorem in geometry, Heron's formula, De Morgan's law in analytic geometry, L'Hourbid's law in calculus...
In addition to Markov's random process, Yebes' theorem for calculating probability...
The efforts of our predecessors have allowed the modern Western world to firmly grasp the right to speak in academic circles. Even if you don’t know English, especially English for mathematics majors, you cannot 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, in the future, there will be a mathematician in Huaxia whose achievements are comparable to those of Newton and Euler. Even if he speaks in a low voice, he can Deafening.
There has never been a pure land in the real world, or places like the Peach Blossom Spring only exist in people's imaginations. People's intelligence and social nature have long been determined. Anyone who has achieved success will definitely stick together and raise the entry threshold for related fields.
School valves have 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, elite governance, through the most basic education, directly physically separates the elites from the children of ordinary people, and achieves the strategic goal of starting children in the third, sixth, and ninth grades.
Pan Jingyuan felt that Qiao Yu had hope of becoming such a scholar. But the current situation made him feel confused.
But 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 had already thought of a way 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 made a joke: "What's wrong? Pan, can't this be the case today?" Does it get you excited? Don’t worry, there will be more important meetings in the future.”
Pan Jingyuan shook his head, then smiled and said: "No, Dennis, actually I benefited a lot from this meeting. I just want to tell you something... By the way, do you still remember what you planned to let me review before? A paper?"
Dennis replied: "Of course, that paper left a deep impression on me. I also exchanged opinions with Schulz specifically about this paper. In fact, he also spoke highly of this paper.
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 publishing a paper of this level requires 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 wants me to urge you to speed up the review. It's that he has recently become interested in the geometric Langlands conjecture, and is targeting our The work raises some questions.
Phew...I have actually been thinking about how to systematically answer his questions for the past two days, so that I can give him a very definite answer so that the child will not waste his efforts in this regard."
"Oh?" Dennis was obviously interested and said, "I heard that the author of that paper, Qiao Yu, was still very young. This is what Schulz told me. Obviously he knew something that I didn't know.
Information, so can you tell me how old that 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
Did you understand our paper and ask 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 exchanges on academic aspects. He is a young man who is very easy to learn and studies well."
Things are really fast.
After about a week or so, I already felt that many of the questions he raised 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, wanting to say something, but no sound came out. Finally he asked with a surprised expression: "Well, you have made me more and more interested in this matter. Tell me, what did he propose?"
Are the questions difficult for you to answer?"
Finally waiting for this sentence, Pan Jingyuan took out a printed copy from the information he carried with him and handed it to Dennis. This was specially prepared by him.
In fact, the report that Yuan Zhengxin forwarded to him was translated into English, and some content was added in the middle. The main reason was that 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 printed copy, and instead of moving forward, he stood there and read it.
After all, Qiao Yu's question had no specific examples, 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 printed document.
After returning the printed copy to Pan Jingyuan, Dennis slowly said: "If these are really the questions that a sixteen-year-old child raised after reading the paper after reading the paper, then I can only say that he is extremely talented."
Pan Jingyuan nodded and replied: "In fact, he is indeed gifted. In fact, it can be seen from his paper. It is said that since he decided to become independent, he used the theory of near-complete space to analyze the problem of the upper bound of the rational point of the curve.
It only took about twenty days to write that paper.
What’s even more surprising is that he only came into contact with Professor Schulz’s mathematical ideas and a series of tools for only a month. It is said that he studied Schulz’s paper because of the recommendation of another teacher.
"
Dennis nodded. If the genius Pan Jingyuan mentioned changed his question, he might be interested in talking more about Qiao Yu with Pan Jingyuan. But the question was exactly about their subject.
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 give. This is indeed a difficult question to refute, but it is not based on the proof itself. Rigor.
The interaction of multiple papers does increase the complexity of verification. It is very important to explain that during the entire proof process, the systematic analysis tools we used can ensure that the designed geometric objects, algebraic structures and related properties maintain strict consistency. Complex and massive work.
But to be honest, I can probably understand your feelings. The questions he raised made me feel a little nervous. But you see, he has not been able to find a counterexample. This at least shows that our argument is rigorous, at least relatively Rigorous, counterexamples are not that easy to find.”
Pan Jingyuan nodded with a wry smile, and then asked softly: "What if he finds it? For example, at a certain time 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 will mean that our work will continue.
Otherwise? At least I won't give up on this proposition. It's just to solve the special case proposed by the other party. I believe it will never 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 have held a series of seminars specifically on the geometric Langlands conjecture. After I return to China in two days, I will also attend this meeting. I guess Qiao Yu will also talk about it at the meeting. raised the question. 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 can communicate directly, which might be very interesting. However, considering that I am still reviewing his paper, this time point is not suitable. Well, let’s wait until the final review opinion on his paper comes out.
But if you have any fresh ideas at this meeting, you can send me an email at any time. Of course, if Qiao Yu really does what he thinks and finds a counterexample, you can call me directly. Although I think this possibility is unlikely. .By the way, of course I’m not just talking about the seminar period.”
Pan Jingyuan nodded and agreed.
"Do you know why I want to add the last sentence? Because guys like Schulz often have terrible mathematical intuitions. Especially when they have not studied mathematics in depth. How can I put it, young people always He is 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, jokingly:
"Okay, let's go eat now. Don't look sad. I think you should be happy that another mathematical genius has appeared in China. Even if you feel uncomfortable, I think it should be Schultz because of his unique genius. The position is being challenged."
Hearing these words, Pan Jingyuan also laughed, and then there was a hint of bitterness in his heart.
Yes, his tutor is a rich second generation, and he doesn’t need to live on the salary of a professor. He studies mathematics purely out of interest, so he takes fame and fortune less seriously 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 their efforts may not be worth their few months of research.
The existence of such people may even lead 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 100,000 whys... What a fool!
..
Huaxia, Beijing, Yanbei University.
As soon as Qiao Yu walked into the Mathematics Research Center, he met old Xue hurriedly walking out. "Teacher Xue."
"Hey, you're back?"
"Yeah, just arrived." As he said that, Qiao Yu raised his hand and showed Xue Song the lightweight suitcase that Qiao Xi specially bought for him online - from Golden Eagle, a brand! Anyway, Qiao Yu thought it was 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, there’s a new box.” Instead, he directly asked, “How is it? Have you made any breakthrough with that idea?”
Hey, I don’t know how to be a tutor, I don’t have a student mentality 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 fruitful." 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 is not very good at speaking, you won't feel that those casual words about Versailles are so hurtful. "By the way, is Director Tian in the office?" Qiao Yu took the initiative to ask again. sentence.
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 and thank Director Tian. I just learned on the high-speed rail that Director Tian has organized a series of seminars in cooperation with Huaqing in order to help me solve my questions."
Hearing Qiao Yu mention this matter, 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 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 the two parties to support this, from the cooperation in organizing this series of seminars, we can see that this trend has already occurred. At least the two sides are no longer in a state of never communicating with each other.
Of course, if you really want to talk about it, the conflict between Yuan Zhengxin and Tian Yanzhen did not affect the training of students too much. As Xue Song learned after coming to Yanbei, there are many students in the Mathematics Department of Huaqing. A professor with whom Tian Yanzhen has a good relationship.
Occasionally, Mr. Yuan's students would come to Yanbei to give lectures in seminars, and even young professors from the mathematics centers on both sides would collaborate and publish articles. Not everyone would care about such disputes.
But if the estrangement disappears, the communication between the two parties will naturally be better.
After all, the big guys on both sides have a lot of resources. These resources are not necessarily funds, but also a lot 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 geometric analysis level that the two are best at in the future. And for the Chinese mathematics community as a whole, it can also be regarded as a breakthrough. A shot in the arm.
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 openly hinder him. ?
After all, what both parties are fighting for is the right to speak... Thinking about it this way, Xue Song felt envious again.
"Well, I should go 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 and picked up his brand new suitcase. He walked excitedly towards the research center.
Xue Song stopped and looked at Qiao Yu's back, sighing in his heart that it's 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, what is he going to do? Coming?
...
"Director Tian, ​​I'm back!" "Oh, I just arrived."
"Yes, Director Tian, ​​I am here specifically to thank you. You are definitely the best and most perfect mentor in the world, bar none."
Tian Yanzhen put down the pen in his hand and raised his head to look at this sixteen-year-old kid who was becoming more and more outrageous and even ran to his office without knocking on the door... Well, even though it was a rainbow fart, he still decided to accept it. .
But looking at Qiao Yu's singing, Tian Yanzhen couldn't help but give him a lesson: "It's useless to just talk. I can only help you so much. 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. It’s still the same sentence. To learn from other people’s experiences, 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? And to tell you the truth, I have read all five papers during the training period, including most of the citations. literature. I am now very familiar with this proposition.
Tian Yanzhen nodded and said, "That's okay. You're here just in time, and I have something to ask you. Didn't you say you were interested in prime number research last time? I also helped you choose a prime number model. proposition, and I plan to ask you to attend several conferences on prime number research. Why are you suddenly interested in the geometric Langlands conjecture again?"
If you don’t discipline the students who come to your door, it will be useless.
Although he flattered him as soon as he walked in, Tian Yanzhen still disapproved of this kind of behavior. No matter how Qiao Yu answered, he planned to have a good talk with the little guy, Let him realize the seriousness of academic research.
If you don’t work on the topic you have planned, and someone else publishes an important result, you will rush to find fault with it. It’s just that you are young, and you can pretend to be ignorant. But if you develop this habit of being careless, you will be a good person in the mathematics community in the future. Public enemy.
After all, people will grow up, but habits may remain.
Although this time he decided to help the emperor, 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 knew that during the research process, I searched A few things lead to this conclusion.
Then I found that the geometric Langlands conjecture was helpful for me to study the random prime number model, so I started to study this series of papers with a learning attitude. Then I felt that the papers might have some imperfections.
Tian Yanzhen frowned, and 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, then 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 the flaws..." Well, in fact, he also has this ability, but his summary is not as good as Yu Wei's. In place.
To be honest, Qiao Yu didn't want to deceive Tian Yanzhen. But he had no choice, and he didn't want anyone to know that he had a living father abroad. Yes, even if his living father licked his face in the future to acknowledge his marriage, he I will never admit it.
So Qiao Yu answered calmly: "Because I wanted to find a new way. Initially, I wanted to analyze prime numbers through modular forms. Then I found that the geometric Langlands conjecture can also provide a geometric perspective for understanding modular forms, so I wondered if I could do it through research. Use the geometric properties of modular forms to understand the distribution of prime numbers.
Then I searched for the content of the geometric Langlands conjecture, and I happened to search for that paper. After reading it, I discovered that in the limit of large numbers, the geometric structure and representation theory tools they introduced 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 it, I felt that something was not right. It was quite complicated anyway, you know? Do you understand?"
Tian Yanzhen stared at Qiao Yu for a long time. He really felt that this little guy didn't seem to be 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 study of the entire Langlands conjecture system, including of course the geometric Langlands conjecture, is intended to provide a series of theoretical tools for mathematical research.
It can be seen from Qiao Yu's last paper that this kid has a very broad thinking model and is very good at using tools constructed by others to solve the problems he encounters. He can even create more useful tools in the process. tools.
Okay, this seems to be untrainable.
After all, according to this kid, he had actually been working on the propositions he had 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 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 Tian Yanzhen feels that this kind of turning method should not be criticized, but should be supported.
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, and has super 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, used in the most popular deep learning and machine learning, the characteristics of random primes can not only be used to optimize algorithms, model parameter selection and feature selection, but also play a role in random weight initialization and generation of adversarial networks.
So the criticisms that I had prepared were 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 be held at the Huaqing Mathematics Research Center next Monday, so hurry up." "Okay, don't worry." With that, Qiao Yu walked out of the office with high spirits.
.
Tian Yanzhen smiled, then picked up the pen again, and was about to continue writing comments, when he suddenly felt something was wrong...
When the kid was assigned the topic of random prime number distribution, Qiao Yu was still reluctant. He just wanted to have a good rest during the training, and even begged him to make a mess in order to avoid the weekly reading and research and development reports.
Such tasks.
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 you are attracted by high-quality papers? As a math genius, this is normal...
After telling the lie, Qiao Yu returned to the room. He did not rest. Instead, he followed Tian Yanzhen's instructions and checked the official website for the list of experts who would attend the seminar, and then continued to read the paper.
After all, fooling the instructor is a technical job.
And in many cases, whether it's really a fool's errand depends on the results.
For example, although he gave a reason that sounded ridiculous, if he could really use these ideas to make a model, it would not be a fool, but that is what he really thought at the time.
The same goes for bragging.
If you say 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 after he 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 were really not many people who could throw money at him, but he often used money to throw money at others.
So as long as you are good enough, no matter how you talk nonsense, others will believe it.
In fact, mathematics is 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 hard...
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, with his ray of grief, he had almost no contact with anyone else.
Oh, by the way, in fact, Senior Brother Chen came to see him once.
He really let him find out some secrets that were spread privately among the overseas students. However, after Qiao Yu heard about it, he forgot about it. After thanking Senior Brother Chen, he told him not to ask anymore. After all, Chen Zhuoyang has been very busy recently.
Preparing for 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 let your supervisor be too embarrassed. 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 that Qiao Yu looked back and looked at the problem of solving the geometric Langlands conjecture.
Guessing his understanding of that theory, he has a vague feeling that he has almost touched the key to the problem...
It seems that he already has the prototype of a counterexample in his mind... There is a feeling that it is ready to come out. In the words of many people who laugh at themselves, it is as if they have grown a brain again, so that they always feel itchy in their brains. This situation continues until Hua Hua
The series of seminars on Qing Dynasty's geometric Langlands conjecture officially opened.
The lecturer on the first day was Professor Everton from Princeton. Qiao Yu once again enjoyed the special arrangement and sat in the front row.
Yuan Zhengxin also directly arranged Pan Jingyuan next to Qiao Yu to facilitate communication between the two at any time.
Although the two have communicated frequently on WeChat and have 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?" The young man shook his head and replied 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 enthusiastically, "Professor Pan, do you want to hear me explain my thoughts 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 is not a lecture at Yanbei University. You have to pay attention to the face of Yanbei University, and it is estimated that grandpa will come over when you meet. You have to look good to the adults. Not to mention that there are many foreign friends in the front row of this seminar.
Qiao Yu knew very well how restrained he was on such occasions, and how unrestrained he could be in the offices of his mentor and grandpa Shi. It was a very simple truth, but unfortunately many people didn't understand it.
Sure enough, as he expected, Mr. Yuan walked into the venue with a foreign professor. He saw Qiao Yu sitting upright. Grandpa Shi smiled at him, his eyes full of doting.
Qiao Yu listened very carefully to the whole lecture. Probably because many academic things are more interesting to talk about when sitting on the stage like this, 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 focus on two points.
The first is how to combine symmetry and geometric structure in representation theory to obtain 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 narrated from simple to profound, 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, and the long-lost inspiration was on the verge of bursting out.
Crazy temptation...
Chapter completed!