Top academic

Chapter 122 The Name of Genius
At least what Tian Yan said was right. No matter how everyone felt about his results, Qiao Yu, a sixteen-year-old boy, had become the star of this seminar.

Even at the lecture the next morning, some professors, such as Professor Everton, felt very sorry for his absence.

When he attended Professor Phyllis's lecture in the afternoon, he was surrounded, physically surrounded, and many people wanted to discuss with him the ideas he had expressed yesterday.

Before the lecture began, Professor Phyllis even invited him to stand on the podium and took a photo with him. This caused Professor Everton's dissatisfaction for a while, until he also stood on the podium and took a photo with Qiao Yu, and then the lecture officially began.

Qiao Yu also listened more carefully.

In fact, he had to be serious, because the professor on the stage would look at him from time to time. Well, this was something Director Tian had specifically emphasized, the so-called most basic respect.

It is very easy to offend a mathematician. The most embarrassing way is to tell him that the theorem he proved is meaningless. The second most embarrassing way is to show disdain for his lecture. But the latter means the same thing as the former.

As fellow mathematical researchers, if we believe that each other's work is meaningful, we will not take each other's lectures lightly.

Even though Qiao Yu is not considered a mathematician yet and does not understand the unspoken rules in the mathematics circle, he understands men's inexplicable competitive spirit.

Although these are all professors from well-known universities and research institutes, didn’t you see that Professor Everton just insisted on taking a group photo before letting Professor Phyllis’ lecture officially begin because there was no group photo taken on the first day of his lecture?

So if he listened carefully to Professor Everton's lecture on the first day and gained a lot from it, but today he did not listen carefully to Professor Phyllis' lecture, he offended him unknowingly.

Qiao Yu doesn't mind offending people.

But considering that Professor Phyllis had shown goodwill to him before the lecture, and that he was the kind of big shot who might become an ally in the world academic community in the future, it would be a shame to offend him. This was the simplest calculation problem, and it did not require complex mathematical knowledge. Anyone who had learned addition and subtraction in the first grade of elementary school could do it.

And that saying is deeply rooted in people's minds: it is always better to have many friends.

The same is true in the world of mathematics. Combining what Qiao Yu knew about the experiences of Director Tian and his master, when the person on the other side raises his head and looks around and finds that he cannot find a single friend in the whole world, then he has already won.

Moreover, Qiao Yu found that being young was the most perfect amulet, and it was easy for him to be liked by these uncles and grandpas.

As soon as the lecture ended, he was surrounded, and some people even asked him for his WhatsApp and email accounts.

He had never heard of the former software, but he signed up for a QQ mailbox for the latter, which was the free version.

This was obviously the first time that Professor Everton encountered an email address containing ten digits only, and he proofread it several times.

As a result, Yuan Zhengxin gave Qiao Yu a lecture and asked him to go back to Tian Yanzhen to ask for a proper unit email address. He also stopped the professors who asked Qiao Yu for email addresses and told them to communicate when they left.

So Qiao Yu gave the most sufficient excuse - he had to rush back to write his thesis, and hurriedly "escaped" from Huaqing University back to the Mathematical Research Center of Yanbei University.

He couldn't be fooled by the sugar-coated bullets. His most important task now was to give a complete proof, spread it as quickly as possible, and have it accepted by the mainstream mathematics community.

Although he had an idea, it still took time to ensure the rigor of the proof process. But it didn't take much time. Qiao Yu stayed up until two in the morning last night and got up at seven in the morning. Before attending the lecture, he had already completed the most difficult part.

I can go back now and eat something. I should be able to finish everything by evening and then send it to my tutor and Mr. Yuan.

All he had to do next was to see how his two mentors arranged it.

……

"In a classical geometric setting, ambiguity theorems rely on an equivalence between certain local and global geometric objects. For example, local homological algebraic objects can be made global via higher-order category theoretic axioms.

However, after research, it was found that a type of singular point with a conjugate ridge structure will produce abnormal behavior through high-order categories in a nonlinear geometric background. This paper temporarily named this type of singular point as Qiao point and denoted by P.

Assume that the category C we use is some kind of deformation category, where objects are modules with certain geometric behavior. For an algebraic variety X, the objects in the category C can be represented as a set of p-adic sheaths F.

Near the Joe point, the behavior of the local module M is affected by the ridge structure, which causes it to no longer be a conventional object in higher-order category theory, but requires the addition of some complex deformation parameters to describe it: Floc=Defjoe(M).
Here Def is a functor in the deformation category, which describes how the module M1 at the singular point P1 affects other singular points in the entire geometric space through deformation. The specific proof process is as follows:…”

At 9:30 in the evening, Pan Jingyuan was invited to Qiuzhai's small conference room by Yuan Zhengxin through a phone call. At this time, he was not the only one in the conference room. Most of the professors invited to attend the meeting had already arrived, and there was this article on the table.

It is not a standard paper, but the proof is concise and clear.

Pan Jingyuan could tell at a glance that this was probably the work of that sixteen-year-old boy, which was consistent with his stereotype of Qiao Yu.

Yesterday, he publicly proposed a counterexample that might invalidate their proof, and today he gave the complete proof and even attended an academic lecture in between. If he was a little older, his efficiency probably wouldn't be so high.

However, at this time, Pan Jingyuan's mentality was completely relaxed.

People are like this. When they feel that something bad is about to happen, the waiting process is actually the most tormenting. After the result comes out, even if it is not a good result, the mentality can often be quickly adjusted to the right place.

Just like what his mentor Professor Dennis said, since the problem has been pointed out, all he has to do is think about how to solve it. It is very difficult, but it will never be more difficult than starting from scratch.

Anyway, even if those five papers are eventually published, his next work will be to continue thinking about and studying the problem of local geometric Langlands. Now he just has to extend this process a bit.

The proof process given by Qiao Yu is actually not long, and including some cited literature it is only three pages.

Silently reading the proof, he recalled the time when he first entered this field under the guidance of Dennis many years ago. At that time, he knew almost nothing about geometric representation theory, and most of the basic knowledge was learned under the guidance of Dennis.

It’s been more than six years in a flash, almost seven years…

After sighing in his heart, Pan Jingyuan looked up and looked around the conference room. He did not find any loopholes. Some of the professors who had previously thought that Qiao Yu's ideas were a bit whimsical were still frowning in thought, while others had already started whispering to the people around them.

Pan Jingyuan thought about it, and simply stood up. Under the gazes of several people, he walked to Yuan Zhengxin's side and asked, "Mr. Yuan, I want to send a copy of the proof process to Professor Dennis."

In fact, there is no need to ask. Even if he sent it, it’s no big deal.

The reason I specifically ask this question is mainly because there is a Qiao point in it, which is a type of singular point discovered by Qiao Yu. Although it is not a great achievement in mathematics, it is also a new result.

Even out of basic courtesy you have to ask.

"Of course." Yuan Zhengxin smiled and nodded.

The meeting records are all original videotaped and professors from world-renowned universities participated, so there is no possibility that Qiao Yu’s ideas were plagiarized by anyone.

"Thank you." Pan Jingyuan nodded, then returned to his seat, took out his mobile phone, opened the commonly used scanning software, entered Qiao Yu's proof process into the mobile phone, and then sent it directly to Dennis's email.

After doing all this, Pan Jingyuan began to think about what he would say during the discussion later.

As one of the seven-member team studying the geometric Langlands conjecture, Pan Jingyuan knew that everyone would be looking forward to him sharing his ideas later.

Even if he doesn't want to speak, he can't avoid it, so it's better to be generous.

There was no way. After a careful inspection, he couldn't find any faults...

……

Across the ocean, Berkeley.

Professor Univess Frank is receiving Professor Sam, one of the initiators of the research team, in his office.

Apart from the slight unhappiness caused by something he had learned before, Frank was actually in a good mood during this period.

If nothing unexpected happens, their paper will be published soon. The publicity from several major partners and a series of lectures during this period have greatly shortened the review process.

Most of the main reviewers have given their approval.

It is basically impossible to conduct double-blind review for such results.

As early as thirteen years ago, Professor Dennis, one of the main leaders of the team, published a paper: "Singular Support of Cohesive Layers and Geometrized Langlands Conjecture".

The entire mathematical community around the world knows what they are researching, and there are only a few experts who are qualified and capable of reviewing papers of this level, so it cannot be hidden at all.

Five years ago, Dennis proposed a series of ideas, such as "white noise".

In the classic field of signal processing, sound waves can be constructed from sine waves, and their frequency corresponds to the pitch of the sound. If you have studied Fourier transform, you will know that this information can be used to write the sound as a combination of sine waves:

That is, just start with a sine wave with an amplitude of 1, then multiply that sine wave by the appropriate loudness factor, and then add those sine waves together. The sum of all the different sine waves with an amplitude of 1 is "white noise."

In the geometric Langlands program, the characteristic layer acts like a sine wave. Dennis identified something called the Poincare layer, which acts like "white noise." However, Dennis was not sure whether every characteristic layer could be represented in the Poincare layer.

He and Sam also joined the team at this time.

They worked together to prove that each feature layer could contribute to "white noise" in some way, and sent the results to Dennis. After gaining recognition, they joined Dennis's team and became another important member of the team.

Three years have passed, and the time has finally come to bear fruit, and Frank is naturally in a good mood.

He has his own goals and plans, and now every step is moving steadily towards his desired goal.

His next topic has been chosen, which is the connection between a type of number theory problem and Riemann surface objects. It can basically be understood as an application of the geometric Langlands conjecture.

This time he will form his own team and he will serve as the main leader to tackle this difficult problem.

In fact, research on this proposition has already begun, which is the guarantee for him to win the Fields Medal.

Although Frank has won the Ostrosky Award and the Clay Research Award, these awards are still not convincing enough. As an ambitious person, Frank has many ideas.

The Chinese mathematics community is in a period of transition.

The older generation of mathematicians are almost in their seventies or eighties, the former young generation mostly teaches abroad, and among the new generation of mathematicians, no one has yet had the hope of winning the Fields Medal.

He seems to be the most promising one at the moment.

The current world pattern is very clear. Although China and the United States have their own problems, looking around the world, they have become the two most competitive forces.

With awards and honors, and the support of many Chinese mathematicians, he may even be able to hold up the banner of the Chinese mathematics community in the future.

To be honest, he thinks everything here is good, but being an academician is actually meaningless. If China can develop better in the future, he really doesn't mind returning to China like Mr. Yuan, building a new mathematics research center named after him, and becoming one of the leading figures in the Chinese mathematics community.

China still admires capable scholars, especially those who have won awards and have great abilities.

As long as he can reach this point before the age of fifty, he will be able to achieve fame and fortune in this life. His name will be recorded in the history books of the world's most populous modern country, and this life will be worth it.

By the time……

In short, just thinking about it can make people feel happy.

……

"Sam, Professor Lola sent me an email and said that our theory has good internal consistency and it is hard to believe that we are wrong," Frank said with a smile.

This was the last reviewer to speak out, which also means that the academic community has almost no objections to their proof process.

Now all that’s left is to go through the process with the journal’s editorial department.

It is only a matter of time before I receive a reply confirming publication, but I don’t know how long it will take for typesetting.

However, Fran thought such a significant achievement was worthy of a special issue.

Even Acta Mathematica, one of the four top mathematics journals in the world.

The simultaneous publication of the five papers in the special issue is worthy of the value of this research topic spanning more than 30 years.

"I received the news too. I have to say, we got a good result. I plan to take a break for a while, what about you?" Sam Lars nodded and replied.

He was also invited to Berkeley this time and gave a joint lecture with Frank.

They conveyed some of their thoughts and mathematical ideas in proving this problem and answered some questions.

This kind of academic exchange is very necessary. In an open academic world, important results need to be widely disseminated to transform them into mathematical tools.

Frank immediately said sincerely: "Of course I still want to invite you to join my research group. I really like what you said yesterday: we need to transfer these ideas to a different environment where we didn't expect to use them! This is exactly what I hope to do next.

There is no equivalent to the ideas of CFT in the number theory and function field setting, but CFT allows us to build special layers of features in the geometric setting. So Sam, join me and let's make it permeable through all the barriers between disciplines, which is a great thing! "

Sam Lars smiled and was about to decline Frank's invitation when his cell phone rang.

Sam Lars shrugged at Frank, took out his cell phone and took a look. He was about to stand up and go to a quiet place to answer the call, but he gave up the idea and said to Frank, "It's Dennis' call."

Then he directly clicked on the answer button.

"Hi Dennis, how are you doing? ... Oh? Not so good? Let me guess... No, that's impossible, you have to be kidding, right?..."

Frank watched the expression on Sam's face change from relaxed to gradually solemn, and his heart couldn't help but hang in the air.

When a professor says directly on the phone that he is not feeling well recently and it can affect the mood of his collaborators, it is probably not good news.

Sam Lars seemed to realize that Frank next to him should also know the content of their conversation, so he simply interrupted him and said, "Wait, Dennis, Frank is right next to me. I will turn on the speakerphone. I think he should know this too."

After saying that, Sam Lars moved the phone away from his ear and turned on the speakerphone, and Dennis's voice began to echo in the office.

"...Okay, here's what happened. To put it simply, I just received some information from Pan, from China. This information constructed a counterexample, which directly led to the partial failure of the Ambidexterity Theorem.

I just looked at this counterexample and couldn't find any flaws. So I feel the need to inform you that we may have to withdraw some papers first. Especially the proof of the fourth Ambidexterity Theorem.

Anyway, the publication of the paper may be delayed, at least until this problem is solved. God, this is really a weird miracle. Of course, I am not unable to accept that the paper may have loopholes, really...

I simply cannot accept that this loophole was discovered by a 16-year-old kid, and he is in Huaxia. Oh, damn... Frank, you should know that I have no opinion on Huaxia, or any prejudice against the development of Chinese mathematics.

Pan is my student, he is also Chinese, and I am very satisfied with him. I say this simply because there are not many people in China who study this problem, so this kid mainly relies on self-study. But what if he is a student of Schultz?

This is really depressing. My 16 years of hard work could be easily discovered by a self-taught child. I believe you can understand how I feel at this moment. It seems that this problem is very simple, but I am too incompetent, so I find it so difficult..."

Dennis was still chattering on and on. Chattering is a way to vent emotions, and it's a very civilized way.

At least he didn't say anything bad.

But Dennis obviously didn't notice that his negative emotions were spreading to the outside world along with his mumbling.

The two collaborators listened to his ramblings, which meant that these negative emotions doubled during the transfer process.

Happiness can be transmitted, but it is difficult to double it, but it is easy to double this kind of negative emotion.

At this moment, Sam Lars and Frank looked at each other in surprise. Just a second ago, they were still talking about the news that the paper had received praise from all the reviewers, and were discussing about continuing with new projects after the official publication. Then suddenly, the main collaborator told them that someone had found a flaw in the paper?
A 16-year-old boy? And he was self-taught?
It is indeed hard to accept so many BUFFs stacked together.

Of course, for Frank, there is something even more unbearable.

So he couldn't stand it anymore and interrupted Dennis's seemingly endless chatter: "Excuse me, Professor Dennis, I want to interrupt you for a moment. I want to know if this sixteen-year-old boy you mentioned is the author of the paper you asked me to review before?"

"Yes, Frank, that's him, the Chinese Joe. He is undoubtedly a genius! Because you can't imagine why a sixteen-year-old kid was still studying the problem of the upper bound of rational points on a curve.

But a month later, he suddenly came to his reviewer and said, "Hey, Dennis, have you finished reviewing my paper? Oh, no final opinion yet? But it doesn't matter, I have reviewed your paper and found a big problem!"

Oh, this is such a bad experience. You know what? I suspect he is taking revenge on me for not taking the time to review his paper carefully. Maybe I should review his paper efficiently, so that he might let me off!
But you know what I'm going to do? I'm going to call Lott Dugan and tell him, damn, that paper passed! Don't ever let me review this kid's paper again! I've decided to surrender!"

Apparently, by the end of his complaints, Dennis was in a much better mood, and he was even in the mood to start making fun of himself.

It's just that all the accumulated negative emotions have piled up on the other side of the phone.

"Okay, I've sent the counterexample that Qiao constructed in China to your email. I also need to notify the rest of the team. By the way, tonight at 8 o'clock, of course I mean the time in the West 5th District, after all, it's Pan's time. If you are in California...

Damn it, when can we use the same time zone as China? Forget it, remember to open your email and look at the counterexamples that Joe found. I hope everyone can give some constructive suggestions at the meeting tonight! "

After saying that, Dennis hung up the phone.

Sam was stunned for a moment, then looked up at Frank who was obviously distracted, sighed in his heart, and then said: "Okay, Frank, I know what this topic means to you. But any emotion is useless at this time.

I think what we need to do now is borrow your printer and run that damn counterexample Dennis sent us. Let's see if there really is no loophole, don't you think?"

Frank came back to his senses and said, "Yes, wait a moment."

Having said that, he immediately went to his computer and logged into his mailbox. Sure enough, the first unread email was sent by Dennis ten minutes ago.

After downloading the attachment, Frank directly printed two copies, without binding them, and gave one to each person, and sat there to study them.

At this time, the two of them still had a glimmer of hope in their hearts. What if Pan Jingyuan and Dennis had made a mistake?
He is just a 16-year-old boy. Can the counterexamples he cited really have universal significance? Can the proof process really be flawless?
If they can find the problem, then perhaps nothing will happen. Of course, this may require starting a debate in the academic community, but it is better than making major revisions to the paper.

You know, that’s a huge project!

Although they have found more than one path in this direction, if there are counterexamples, whether it is to revise the paper or try a different approach, it will take time, and a lot of time.

But time is the most precious thing for everyone, especially for Frank.

At the age of 34, he still had six years to go before he turned 40, but there were only two World Congresses of Mathematicians during that period. He was only the main researcher of this topic, but not the leader. If he wasted most of his time on this topic, his achievements would definitely not convince the public.

The most regrettable thing is that the proposition he chose next was closely related to the current proposition, which meant that he could not even skip the proof of the geometric Langlands conjecture and start his own proposition research.

In other words, if what Qiao Yu gave is irrefutable, it is definitely a sad story for Frank.

So Frank read it very carefully, even more carefully than he read Qiao Yu's paper.

He did not miss any details of the proof, but even so, after an hour, he finally gave up.

Although this is not a paper, there is no doubt that this guy's proof process is exactly in accordance with the paper that needs to be published. The wording is as rigorous as that of a paper, and it is even impossible to find a flaw in the wording.

In other words, it is irrefutable.

Frank raised his head and looked at Sam across from him, and Sam was looking at him.

After a long silence, Sam asked first: "How did you come up with the idea of ​​inducing non-trivial effects at the homology level? Is it really like Dennis said, that Joe was specifically looking for loopholes in the paper? Just because the paper he was given was not reviewed quickly enough? Look, he even created a high-dimensional singularity for this purpose!"

Frank didn't say anything, but he always felt something was wrong.

He couldn't even be sure whether Qiao Yu knew of his existence. Everything was too coincidental. First, a paper by Qiao Yu was delivered to him, and then the kid found a loophole in the work he had contributed to.

If everything is a coincidence, it would be too much of a coincidence.

"Okay, the most important theorem is indeed partially invalid. This situation is not something we have considered. What do you think?" Sam asked after a moment.

Frank shook his head and said, "I don't know. I feel a little confused."

Sam nodded in understanding, then stood up and said, "Well, maybe we should calm down and think about it carefully. Frank, you don't have to be too depressed. This is indeed a problem, and what we need to do now is to solve this problem.

I think the problem of distortion when the higher-order derived functor is globalized is solvable. This is a fixable problem. In theory, it is enough to make the exported object at P1 correctly map to P2. If everything goes well, maybe we can solve this problem this year. "

Well, Sam Lars wasn't too confident when he said this.

But what else could he say?

As one of the most important contributors to the project, his mood was not much better at the moment.

damn it……

What is this?
……

After watching Sam Lars leave the office, Frank sat at his desk and thought for a moment, then opened his mailbox again and edited an email to Pan Jingyuan, mainly asking about some information about Qiao Yu.

This is a normal reaction.

After reading Qiao Yu's paper before, I didn't ask any special questions. But now, his paper, as one of the main authors, has been picked out by a young genius from China, and if he doesn't ask any questions, it will seem that there are problems.

However, this letter was a bit difficult to write and I kept deleting and revising it.

Mainly, while getting to know Qiao Yu, he also hopes to find out whether Qiao Yu knows of his existence without leaving any trace. This is what happens when you have something on your mind, you are always afraid that others will judge something different from your words.

Just like that, Frank took a full hour to edit a letter of only a few hundred words, and then he clicked send.

It was probably already late at night in China at this time. After editing the email, Frank felt extremely confused... What the hell was going on?

……

Just when Frank was feeling confused, Qiao Yu's name had already spread throughout the entire circle of people studying the Langlands Program.

This is thanks to Dennis.

The Harvard professor not only called his collaborators on the project, but also called the reviewers of the paper and famous scholars who had commented on the paper to inform them of the matter.

I also did not forget to send Qiao Yu's counterexample to these academic leaders via email.

This naturally includes Peter Schulz and Alexander Beilinson, one of the founders of the geometric Langlands program.

The former has praised this latest achievement as the culmination of thirty years of hard work, while the latter believes that this proof is extremely beautiful and the best of its kind.

Oh, and there’s also Professor Phil Rolla, currently at the Clay Mathematics Institute, who just recently published his review.

Dennis even thought that it would have been better if Laura had made this comment two days later, so that both of them would have been less embarrassed.

After all, they had just praised their theory for its excellent internal consistency, which made it hard to believe that it was wrong, but then someone else proved that there were loopholes in the proof of the most important theorem, and both sides were embarrassed.

Especially when the person on the other side is a sixteen-year-old boy, this age is enough to make the big guys who have been famous for many years feel ashamed.

After Dennis made a round of phone calls, he soon received a call back from Schultz.

Dennis could hear that this recognized genius in Western mathematics even had a hint of excitement in his tone.

"Ha, Dennis, I've read the counterexample Joe gave, and I have to say, it's brilliant. Well, I guess you won't be too upset by that, right?"

"Of course, I have accepted this fact."

"Then why not invite him to the algebraic geometry conference next month? I think we should send him an invitation letter and he can give a thirty-minute talk. I'm sure many people will be interested in his ideas."

"It is up to you to make that recommendation to the organizing committee, Professor Schultz."

"Of course. In fact, I have already suggested it. Professor Gray from the organizing committee said that he would seriously consider my proposal. He called you because I am also very interested in his idea. But I think I should take your idea into consideration. I don't know if you can accept this... You know, after all, we are friends."

This made Dennis speechless...

So this is how geniuses take their friends' ideas into consideration and just do it first and talk about it later?

"There's nothing unacceptable, Schultz. Like I said just now, this is the fact. I just want to solve this problem quickly."

"Right! So I think you need to communicate with him. People who raise questions are often better at solving them. But you also know that he doesn't have any outstanding achievements yet. You are also one of the reviewers of that paper. Please pass his review as soon as possible so that his paper can be published in the May issue of Ann.Math."

"Cough cough..."

"In fact, I have just called Lott Dugan. The paper has also been reviewed."

"Smart idea. Okay, I'm hanging up then."

"Wait, Schultz, do you think there will be an era of talent explosion next?"

There was no reply from the other end for a long time. After a while, a voice came: "I hope so, but who knows? Goodbye."

Hearing the busy tone on the phone, Dennis didn't feel that uncomfortable. He even felt that Schultz was considering his face.

At the age of 16, I was able to publish a paper in Ann.Math and was invited to attend the World Congress of Algebraic Geometry to give a 30-minute presentation. This conference is not open to just anyone, after all, it is one of the satellite conferences of the World Congress of Mathematicians.

Most of the people who get the invitation letter and are invited to give a report at the conference are truly top mathematicians, researchers and scholars. After all, algebraic geometry is one of the most cutting-edge and popular research directions in mathematics.

It seemed psychologically easier to accept having problems in my paper pointed out by such a child.

The world of mathematics welcomes geniuses, especially those who work in theory, who need geniuses even more!
……

Huaxia, Yanbei University, International Center for Mathematical Research.

Qiao Yu lay quietly on the bed, not yet asleep.

He was very sure that there was no problem with his proof process.

Qiao Yu was very confident about this point, and it was just a very brief proof process.

From Qiao Yu's perspective, it is difficult to find inspiration for mathematical problems, but once the inspiration comes, it is actually very simple to prove them.

Moreover, he used widely used tools, which means that if anyone said that his proof process was unreasonable, a large number of mathematical papers might have to be removed from journals.

Of course, he doesn't know now that his proof process and ideas have been recognized by many bigwigs around the world.

Even after it was passed to that man, he tried very hard to find something unreasonable in it but failed. But Qiao Yu was very clear about one thing, that after his proof was spread, it would definitely give someone a little shock.

So Qiao Yu was actually very calm at this time. He couldn't sleep not because he was excited, but mainly because he was still thinking about how to make up for this loophole. That is, how to solve the applicability of the local-global consistency problem of the geometric Langlands conjecture on Qiao points.

If the scope is expanded, even complex singular points can be used to replace Joe points.

The other party should have two choices: either to redeer this part of the paper or to directly patch it.

After thinking about it from another perspective, Qiao Yu felt that the latter option would be much simpler, such as adding a coherent layer to the new category...

However, after this question went through Qiao Yu's mind for a while, he began to think about a more critical question.

In this game of intellectual confrontation, he temporarily won one round, but it seemed that he was still a long way from realizing his dream.

That’s right, it’s the dream of buying a residential community and renovating it after making a lot of money.

After two months of training at Yanbei University, he was no longer the young man who was ignorant of the ways of the world and had no idea of ​​the rules that governed society.

According to his observation, mathematicians with a certain status would not be short of money. For example, neither Tian Yanzhen nor his master's grandfather Yuan Zhengxin were short of money.

But to say that both of them are very rich, that is not necessarily the case.

At least the assets are definitely not enough to afford to acquire a community and then rebuild it.

The two bigwigs don't seem to be that interested in money. Relatively speaking, they value their status in the academic world more.

This made Qiao Yu a little worried.

From the books they prepared for him and their daily teachings, it can be seen that the two bosses want him to develop in the field of pure mathematics in the future. Originally, this was not a big problem for Qiao Yu.

But after staying in Yanbei University for so long, reading some books, attending some classes, and communicating more with the school professors on weekdays, he discovered the most serious problem. Not to mention whether he can solve the series of difficult problems such as the mystery of prime numbers, even if he really researched it, how to monetize it is also a problem.

If something is accidentally leaked, it will cause all of humanity to completely lose confidence in the modern financial system. It will be very difficult to make money with it. And it may cause a big mess...

Of course, this doesn’t mean that Qiao Yu is short of money.

In fact, he had already discovered that with his current status, he would never be short of money in his life. After all, he could live a relatively wealthy life. The only thing he was afraid of was that his life would pass by in a muddle...

He was afraid that when he grew up, he would become like Brother Chen, no longer thinking about changing anything, but content to be a world-famous mathematician, thinking only about making waves in the academic circle every day, and completely giving up the idea of ​​becoming a legitimate billionaire.

He couldn't put his grandfather's statue at the entrance of a mathematics center - it wouldn't be right.

Yes, when many mathematics giants around the world began to pay attention to Qiao Yu, the rising star of mathematics, the problems he was thinking about while lying in bed had already transitioned from simple mathematics to the level of having to stay true to his original intention.

The difference is that Qiao Yu's appetite has grown, and the small fights in the past can no longer satisfy him. After all, he is now truly living a carefree life, and can allow Qiao Xi to live a good life.

His grandfather has already hinted to him that after graduation he should go directly to Huaqing to inherit his mathematics research center. He doesn't even need to think about finding a house to settle down in Beijing, because the old man has almost explicitly stated that he can use the policy of introducing special talents, so he doesn't need to worry about housing or his children's future education.

Qiao Yu felt that the old man was trying to shake his resolve. After all, he would be able to live near Huaqing in the future, and with that meal card that he could almost never finish, after being blown up by the cannonball made of sugar coating and sugar core, he was afraid that he would have no motivation to strive to become a rich man in the future.

This is absolutely not possible, so Qiao Yu feels that it is time to put on the agenda how to plan for making money in the future.

　The 37th day of the -word check-in is completed!
　　I strongly recommend the new book by Hulucunren, a big name in industrial literature of this era: "In 1978, I Was Admitted to Harbin Institute of Technology". It is a fine work of art and trustworthy!

(End of this chapter)