Chapter 122 The Name of Genius
At least one thing Tian Yanzhen said is right. Regardless of everyone's attitude towards his results, Qiao Yu, a sixteen-year-old child, has become the star of this seminar. figure.
Even in the lecture the next morning, some professors felt very sorry for his absence, such as Professor Everton.
When he attended Professor Felice's lecture in the afternoon, he was surrounded in a physical sense. Many people wanted to discuss with him the ideas he expressed yesterday.
Before the lecture began, Professor Felice even invited him to stand on the podium and take a photo with him. This caused Professor Everton's dissatisfaction. It was not until he stood on the podium and took a photo with Qiao Yu that the lecture officially began.
Qiao Yu also listened more seriously.
In fact, it’s okay if he is not serious. The professor’s eyes on the stage fall on him from time to time. Well, this is what Director Tian specifically emphasized, the so-called most basic respect.
It is actually very simple to offend a mathematician. The most embarrassing way is probably to say to his face that the theorem he proved is meaningless. The second most embarrassing way is probably to dismiss his lectures. But in fact the latter means the same as the former.
We are both mathematics researchers, and if we think each other’s work is meaningful, we will not fail to take each other’s lectures seriously.
Even though Qiao Yu is not yet a mathematician and does not understand the unspoken rules in the mathematical circle, he understands the inexplicable competitiveness of men.
Although these are all great professors from well-known universities and research institutes, I didn’t see Professor Everton just now because he didn’t take a group photo on the first day of his lecture. In the end, he had to take a group photo before he let Professor Felice. Has the lecture officially started?
So if he listened carefully to Professor Everton’s lecture on the first day and gained a lot, but today he didn’t listen carefully to Professor Phyllis’s lecture, he unknowingly offended others. .
Qiao Yu doesn't mind offending people.
But considering that Professor Phyllis showed goodwill to him before the lecture began, he is the kind of big boss who may become an ally of the world's academic community in the future, and it is not worthwhile to offend him. This is the simplest calculation problem and does not require complex mathematical knowledge. You can do it if you have learned addition and subtraction in the first grade of elementary school.
And that sentence is deeply rooted in the hearts of the people, it is always better to have more friends.
The same is true in the world of mathematics. Based on what Qiao Yu knows about the experiences of Director Tian and Grandpa Shi, when the person opposite raises his head and looks around and realizes that he can't find a single friend in the whole world, then he has already won.
And Qiao Yu found that being young is the perfect talisman, and it is really easy to attract the likes of these uncles.
As soon as the lecture here ended, he was surrounded, and some even asked him for his WhatsApp and email accounts.
He had never heard of the former software, and he signed up for a QQ mailbox for the latter, which is the free version.
It was obviously the first time Professor Everton encountered this kind of ten-digit mailbox, and he proofread it several times.
As a result, Yuan Zhengxin taught Qiao Yu a lesson and asked him to go back to Tian Yanzhen to ask for a serious workplace email address. He also stopped the professors who asked Qiao Yu for their email addresses so that they could communicate with each other after they left.
So Qiao Yu gave the most sufficient reason - to rush back to write a thesis, so he hurriedly "escaped" from Huaqing University back to the Mathematical Research Center of Yanbei University.
He can’t really be blown away by sugar-coated bullets. His most important task now is to give the complete proof. Then it is disseminated as quickly as possible and accepted by the mainstream mathematics community.
Although we already have ideas, it still takes 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. He had already completed the most difficult part before coming to the lecture.
Go back now and eat something. You should be able to finish it all in the evening, and then send it to the instructor and Mr. Yuan.
What he has to do next is to see how his two mentors arrange it.
…
“In the classical geometric context, the Ambidexterity theorem relies on some kind of equivalence between local and global geometric objects. For example, local homological algebraic objects can be represented by high Globalization of the axioms of order category theory
However, after research, it was found that a type of singular points with conjugate ridge structures exist on non-lines. In the context of sexual geometry, abnormal behavior will occur through higher-order categories. This article temporarily names such singular points as Qiao points, and represents them as P
Suppose the category C we use is some kind of deformation category, in which objects. is a module with specific geometric behavior. For an algebraic variety X, the objects in category C can be represented as a set of p-adic layers F.
Near the Joe point, the behavior of the local module M is affected by the ridge structure, causing its performance in higher-order category theory to no longer be a conventional object, but needs to be described by adding some complex deformation parameters: Floc=Defjoe (M).
Here Def is the functor of 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:..."
When Pan Jingyuan was invited to Qiuzhai's small conference room by a phone call from Yuan Zhengxin at 9:30 in the night, he was not the only one in the conference room at this time. He was invited this time Most of the professors who came to participate have already arrived, and what is on the table is It is such an article.
It is not a standard paper, but the proof process is simple and clear.
Pan Jingyuan can tell at a glance that this is probably written by that sixteen-year-old child. It fits his stereotype of Qiao Yu
From yesterday's counterexample that might invalidate their proof process to the public, today they gave a complete proof process, and even attended an academic lecture in the middle. If you are older, your efficiency may not be so high.
However, Pan Jingyuan's mentality was completely relaxed at this time.
People are like this. When you have a premonition that something bad is about to happen, the waiting process is actually the most painful. After the result is obtained, even if it is not a good result, the mentality can often be adjusted quickly.
Just like his mentor Professor Dennis said, since a problem has been raised, it is nothing more than thinking about how to solve the problem. It’s very difficult, but it’s never any more difficult than starting from scratch.
Anyway, even if those five papers are finally published, his next work will continue to think about and study the Langlands problem of local geometry. Now he just has to prolong the process.
The proof process given by Qiao Yu is actually not long, and it only lasts for three pages including some cited documents.
Reading the proof process silently reminded him of the time when he first entered this field under the leadership of Dennis many years ago. At that time, he knew almost nothing about geometric representation theory, and learned most of the basic knowledge under the guidance of Dennis.
It has been more than six years in a flash, almost seven years...
After sighing in his heart, Pan Jingyuan raised his head and looked around the conference room. He did not find any loopholes. Among the professors who had previously thought Qiao Yu's idea was a bit whimsical, some were still frowning in thought, while others had already started whispering to the people around them.
Pan Jingyuan thought for a while, then simply stood up, walked up to Yuan Zhengxin under the gaze of several people, and asked: "Mr. Yuan, I would like to send a copy of the proof process to Professor Dennis."< br>
In fact, there is no need to ask, even if he sends it, it won't matter.
The main reason why I ask specifically is because there are Qiao points in it, which are a type of singular points discovered by Qiao Yu. Although it is not a great achievement on a mathematical level, it is still a new result.
Even if it is the most basic courtesy, you must ask.
"Of course." Yuan Zhengxin smiled and nodded.
The meeting minutes include original videos, and professors from world-renowned universities participated. There is no possibility that Qiao Yu’s ideas will be plagiarized by anyone.
"Thank you." Pan Jingyuan nodded, then returned to his seat, took out his mobile phone and opened the commonly used scanning software, entered Qiao Yu's certification process into his mobile phone, and then sent it directly to Dennis' mailbox.
After doing this, Pan Jingyuan began to think about what he would say during the discussion.
As one of the seven-member team members who researched the geometric Langlands conjecture, Pan Jingyuan knew that everyone would be looking forward to him sharing his thoughts later.
Even if he doesn’t want to speak, he can’t avoid it, so he might as well be more generous.
No way, after looking at it carefully, he couldn't find anything wrong...
……
Across the ocean, Berkeley.
Professor Univers Frank is receiving one of the initiators of the research team, Professor Sam, in his office.
Except for the slight discomfort caused by knowing something before, Frank was actually in a good mood during this period.
If nothing else happens, their paper will be published soon. During this period, publicity by several major partners and a series of lectures were held, which greatly shortened the review process.
Most of the main reviewers have given agreed review opinions.
It is basically impossible to conduct a double-blind review of this kind of results.
As early as thirteen years ago, Professor Dennis, one of the main leaders of the team, had published a paper: "Singular Support and Geometrical Langlands Conjecture of Coacervates".
The mathematics community all over the world knows what they are studying. There are only a few experts with the qualifications and ability to review papers of this level, and they cannot hide it at all.
Five years ago Dennis proposed a series of ideas, such as "white noise".
Classically in the field of signal processing, sound waves can be constructed from sine waves, whose frequencies correspond to the pitches in the sound. Those who have studied Fourier transform will know that this information can be used to write sound as a combination of sine waves:
That is, just start with a sine wave with an amplitude of 1, and then multiply the sine wave by the appropriate loudness factor , and then add these sine waves together. The sum of all different sine waves with an amplitude of 1 is "white noise".
Geometric Langlands Programme, the function of the feature layer is similar to a sine wave. Dennis identified something called the Poincare layer, which acts like "white noise." It’s just that Dennis doesn’t know whether every feature layer can be represented in the Poincaré layer.
He and Sam also joined the team at this time.
They collaborated to prove that each feature layer contributes to "white noise" in some way, and sent the results to Dennis. After gaining recognition, he joined Dennis' team and became an important other pole of the team.
Three years later, when it finally came time to bear fruit, Frank was naturally in a happy mood.
He has his own goals and plans, and every step now is making steady progress towards his desired goal.
His next topic has also been selected, which is the connection between a type of number theory problems 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 be the main leader to overcome this problem.
In fact, research on this proposition has already begun. This is his guarantee for winning the Fields Medal.
Although Frank has received the Ostrowski Award and the Clay Research Award, these awards are still not convincing enough. As an ambitious man, Frank had many ideas.
The Chinese mathematics community is in a period of drought.
The older generation of mathematicians are almost 70 or 80 years old. Most of the younger generation have taught abroad. Currently, no one of the newly grown generation of mathematicians has any hope of winning the Fields Medal.
Currently it seems that he is the most promising one.
The world structure is now very clear. Although China and the United States have their own problems, looking at the world, they have become the two most competitive forces.
With awards and honors around him, and with the support of many Chinese mathematicians, he can even hold up the banner of the Chinese mathematics community in the future.
To be honest, he thinks everything is good here, but being an academician is actually not interesting. 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 leaders in the Chinese mathematics community.
China still admires capable scholars, especially those with awards and 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. The modern country with the most population in the world will leave his name in the history books. This life is worth it.
When the time comes...
Anyway, just thinking about it can make you feel good.
......
"Sam, Professor Rolla sent me an email. He said that the internal consistency of our theory is very good, making it difficult for people to believe that we are wrong." Frank Said with a smile.
This is the last reviewer to speak out, which also means that the academic community has almost no objections to their proof process.
Now it’s up to the journal editorial department to go through the process.
It's only a matter of time before I receive a reply that's confirmed for publication, but I don't know how long it will take for typesetting.
However, such a significant result Fran believes it deserves a special issue.
Even "ActaMathematica", one of the four top mathematics journals in the world.
Only when five papers are published in the special issue at the same time can it be worthy of the value of this research topic that spans more than 30 years.
"I also received the news. I have to say that we achieved a good result. I plan to take a rest for a while, what about you?" Sam Lars nodded and replied.
He was also invited to the Berkeley campus this time and gave a joint lecture with Frank.
Conveyed some of their thoughts and mathematical ideas on proving this problem, and answered some questions.
This type of academic exchange is very necessary. In an open academic world, important results are transformed into mathematical tools and they need to be widely disseminated.
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 place that was not originally thought of. to be able to use them in different contexts! This is exactly what I hope to do next
Sam Lars smiled and was declining Frank's invitation when his cell phone suddenly rang.
Shrugging at Frank, Sam Lars took out his cell phone and looked at it. Sam Lars, who was planning to stand up and go to a quiet place to answer the phone, gave up the idea and said to Frank: "Dennis's phone number."
Then he clicked on the answer button.
"Hi Dennis, how are you doing?... Oh? Not so good? Let me guess... No, that's impossible, you must be joking, right?..."< br>
Frank watched the expression on Sam's face change from relaxed and carefree to gradually serious, and his heart couldn't help but feel suspended in his chest.
When a professor directly says on the phone that he is not doing well recently, and it can affect the mood of his collaborators, that is probably not good news.
Sam Lars seemed to realize that Frank next to him should also know the content of the two people's chat, and simply interrupted the other person: "Wait, Dennis, Frank is next to me, I will open the free Mention, I think he should know this too."
After saying that, Sam Lars moved the phone away from his ear and clicked on the speakerphone, and Dennis's voice began to echo in the office.
“…Okay, that’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 it is necessary to inform you that we may have to withdraw part of the paper first, especially the proof of the fourth Ambidexterity theorem. br>
In short, the publication of the paper may be delayed, at least until this problem is resolved. God, this is a weird miracle. Of course, it's not that I can't accept that the paper may have loopholes, really...
I simply can't accept that this loophole was discovered by a sixteen-year-old child, and he was still in China. Oh, damn... Frank, you should know that I don't have any opinions against China or any bias against the development of mathematics in China.
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 studying this issue, so this child mainly relies on self-study. What if he is a student of Schulz?
This is really shocking. After sixteen years of hard work, a self-taught child can easily see the loopholes in the proof process. I believe you can experience my feeling at this time, as if This question is originally very simple, but I am too incompetent, so I find it so difficult..."
Dennis is still chattering, nagging is a way to vent emotions, and this method is very Civilization.
At least he didn't say anything bad.
But obviously Dennis did not notice that his negative emotions were spreading to the outside world along with his nagging.
The two collaborators listened to his ramblings, which meant that these negative emotions doubled during the transfer process.
Happiness can be transmitted, but doubling it is difficult, but doubling this negative emotion is very simple.
At this time, Sam Lars and Frank were looking at each other. A second ago, the two of them were talking about the news that the paper had been praised by all the reviewers, and discussing starting a new topic after it was officially released. Suddenly the main collaborator told them that there were flaws in the paper?
Or a sixteen-year-old boy? Are you self-taught?
So many BUFFs stacked together are really hard to accept.
Of course, for Frank, there are even more intolerable points.
So he couldn't bear it anymore and directly interrupted Dennis's seemingly endless chatter: "I'm sorry, Professor Dennis, interrupt you. I want to know if the sixteen-year-old boy you are talking about is the one you mentioned before. The author of the paper I was asked to review? ”
"Yes, Frank, that's him, that Chinese Joe. There is no doubt that he is a genius! Because you can't imagine why a sixteen-year-old kid was still studying the problem of the upper bound of the rational point of the curve.
But after a month, suddenly Ran came to his reviewer and said, Hi, Dennis, have you finished reviewing my paper? Oh, no final opinion yet? But it doesn’t matter, I have finished reviewing your paper and found a big problem! >
Oh, this is such a bad experience. ? I suspect that he is retaliating against me for not taking the time to review his paper carefully. Maybe I should review his paper efficiently, so that he might let me go!
But you know what I am going to do! I'm going to call Lot Dugan later. , and then told him, damn, that paper passed! Never let me review this kid’s paper again!”
Obviously, Dennis was in a good mood at the end of the complaint. Many times, he was even in the mood to laugh at himself.
It’s just that the accumulated negative emotions have all piled up on the other side of the phone.
"Okay, I have sent the counterexample of the Qiao organization in China to your mailbox. I also want to inform the rest of the team, by the way, at eight o'clock tonight, of course I am referring to West Five District’s time, after all, it’s Pan’s time, if you are in California...
Damn it, when will we be able to use the same time zone as China? Forget it, remember to open your email first and take a look at the counterexamples that Qiao found. I hope everyone can give some constructive opinions in the evening meeting. !”
After that, Dennis hung up the phone directly.
Sam stayed 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 subject means to you. But at this time, any emotions It's no use.
I guess what we need to do now is borrow your printer and study that damn counterexample Dennis sent us. Let’s see if there are really no loopholes, what do you think? "
Frank came back to his senses and said, "Yes, wait a moment." ”
As he said that, he immediately came to his computer and logged into his mailbox. Sure enough, the first unread email was sent by Dennis ten minutes ago.
Download the attachment, and then Frank directly I printed two copies, and there was no need to bind them. I just sat there and studied them.
At this time, the two of them still had a sense of luck, what if Pan Jingyuan and Dennis had made a mistake. ?
He is just a sixteen-year-old boy. Do the counterexamples he cited really have universal significance? Can the proof process really be flawless?
If they can find the problem, then maybe nothing will happen. Of course, this may require starting a debate in the academic community, but it is better than a large-scale revision of the paper.
You must know that it is a huge project!
Although they have found more than one path in this direction, if there is a counterexample, whether it is to revise the paper or try another way, it will take time, and it will still be a lot of time.
Time is the most precious thing for everyone, especially for Frank.
Thirty-four years old, although there are still six years left before the age of forty, the World Congress of Mathematicians has only been held twice during this period. He is only the main participant in the research on this proposition, not the leader. If he wastes most of his time on this proposition, his achievements will definitely not convince the public.
The most regrettable thing is that the proposition he chooses next is closely related to the current proposition. This means that he cannot even skip the proof of the geometric Langlands conjecture and start his own proposition research.
In other words, if what Qiao Yu gives is irrefutable, it will definitely be a sad story for Frank.
So Frank read it very seriously, even more seriously than when he read Qiao Yu's paper.
He did not let go of every detail of the proof process, but even so, he finally gave up after an hour.
Although this is not a paper, there is no doubt that this guy's proof process was completely based on the paper that needs to be published. The wording is as rigorous as the paper, and he cannot even find a flaw in the wording.
In other words, it is impossible to argue with.
Frank raised his head and looked at Sam opposite, who was also looking at him.
After a long silence, Sam first asked: "How did you come up with the idea of inducing non-trivial effects at the homology level? Is it really like Dennis said that this Joe is specifically looking for loopholes in the paper? Just because The paper given to him is not reviewed as soon as possible? Look, he also created a high-dimensional singularity for this!"
Frank didn't say anything, feeling that something was strange.
Now he couldn't even be sure whether Qiao Yu knew about his existence. Everything was too coincidental. First, a paper by Qiao Yu was delivered to him, and then the kid found out the loopholes in the results he had made as a major contributor.
If everything was a coincidence, it would be too much of a coincidence.
"Well, the most important theorem is indeed partially invalid. This situation is something we did not consider. What do you think?" After a moment, Sam asked.
Frank shook his head and said: "I don't know, I feel a little confused."
Sam nodded understandingly, then stood up and said: "Okay, maybe we You should calm down and think about it carefully. Frank, you don't have to be too depressed. This is indeed a problem. What we need to do now is to solve it.
I think the problem of distortion when high-order derived functors are globalized can be solved. This is a fixable problem. In theory, it is enough to make the exported object at P1 map correctly to P2. If all goes well, maybe we can solve this problem this year. ”
Well, when he said this, Sam Lars was actually not too confident.
But what else could he say?
As the most important subject One of the important contributors, his mood is not much better at this time
Damn...
What is this?
......
Watching Sam Lars leave the office, Frank sat at his desk and thought for a moment, opened his mailbox again, and then edited an email to Pan Jingyuan, mainly He was asking about some information about Qiao Yu.
This is a normal reaction.
After reading Qiao Yu’s paper before, I just didn’t ask anything about it. Now, as one of the main authors, his paper has also been picked out by young geniuses in China. If I didn’t ask a word, it would seem wrong. question.
However, it was a bit difficult to write this letter, and I was constantly deleting it.
Mainly because while getting to know Qiao Yu, he also hoped to find out whether Qiao Yu knew about his existence without leaving any trace. It's like this when you have something on your mind. You're always afraid that others will taste something different from your words.
Just like that, it took Frank an entire hour to edit a letter of only a few hundred words, and then clicked send.
It was probably late at night in China at this time. After editing the email, Frank felt extremely confused... What the hell is going on?
……
Just when Frank felt confused, Qiao Yu's name had spread throughout the circle of people studying the Langlands program.
This is all thanks to Dennis.
The Harvard professor not only called the collaborators on the project, but also called the reviewers of the paper and the famous experts who evaluated the paper to inform them. This matter.
I also never forgot to send Qiao Yu’s counterexamples to these academic leaders via email.
Of course this also includes Peter Schulz, and Alexander Bellinson, 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 very beautiful and the best of its kind.
By the way, there is also Professor Phil Rolla, who currently works at the Clay Mathematics Institute, who just recently made a comment.
Dennis even felt that it would have been better if Laura had made this comment two days later, so that both of them would be less embarrassed.
After all, I just praised the internal consistency of their theory so well that it was hard to believe that it was wrong. But then it was proven that the most important theorem proving process had loopholes. Both sides faced it. There is no light on it.
Especially when the opposite person is still a sixteen-year-old boy, this age is enough to make a big boss who has been famous for many years feel ashamed.
After Dennis made a series of calls, he soon received a call back from Schultz.
Dennis could hear that this recognized genius in the Western mathematics community was even a little excited in his tone.
“Ha, Dennis, I’ve finished reading the counterexample Joe gave, and I have to say, it’s so exciting. Well, if I say this, you shouldn’t be too frustrated, right?”
"Of course, I have accepted this fact."
"Then why not invite him to the algebraic geometry conference next month? I think I should send him an invitation letter and he can Give a thirty-minute speech and I believe many people will be interested in his ideas.”
"Then it's up to you to make a suggestion to the organizing committee, Professor Schultz."
"Of course, in fact, I have already suggested it. Professor Gray of the organizing committee said that he would seriously consider my proposal before I called you because I was also interested in his idea but I wanted to. I should take care of your thoughts, I don’t know if you can accept this... You understand, after all, we are friends."
This made Dennis speechless...
So genius is. You care about your friends’ thoughts so much, do it first and then talk about it?
"There is nothing unacceptable, Schulz. As I just said, this is the fact. I just want to solve this problem quickly now."
"That's right! So I think you need to communicate with him. People who ask questions are often better at solving them. But you also know that he doesn't have any impressive results yet. You are also one of the reviewers of that paper. As soon as possible If it passes his review, his paper will be published in the May issue of Ann.Math."
"Ahem... "
"In fact, I just called Lot Dugan and the paper has been approved."
"Smart idea, then I'll hang up. ”
“Wait a minute, Schulz, do you think there will be an era of genius outburst?”
There was no reply for a long time, and a voice came after a while: "I hope so, but who knows? Goodbye."
Listening to the busy signal on the phone, Dennis didn't feel too uncomfortable, and even felt comfortable. Ertz is taking care of his face.
At the age of sixteen, he was able to publish a paper in Ann.Math and was invited to attend the World Congress on Algebraic Geometry to give a thirty-minute report. This conference is not something that cats and dogs can attend. After all, it is one of the satellite conferences of the World Congress of Mathematicians.
Most of the people who can get the invitation letter and be invited to give reports at the conference are truly top mathematicians, researchers and scholars. After all, algebraic geometry is the most cutting-edge and one of the most popular mathematical research directions.
It seems psychologically easier to accept the problems in the paper being picked out by such children.
The world of mathematics welcomes geniuses, especially those who engage in theory, and they need geniuses even more!
……
Huaxia, Yanbei University, International Mathematics Research Center.
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 in this point, and it was just a very brief proof process.
From Qiao Yu's point of view, it is difficult to find inspiration for mathematical problems, but once the inspiration comes, it is actually very simple to prove.
And he used widely used tools, which means that if anyone says that his proof process is unreasonable, a large number of mathematics papers may have to be removed from the journals.
Of course he doesn’t know now that his proof process and ideas have been recognized by many big names around the world.
It has even been passed to the man, and he tried very hard to find something unreasonable in it but failed. But Qiao Yu knows one thing very well. After his proof spreads, it will definitely give someone a little shock.
So at this time, Qiao Yu was actually very calm inside. 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 local-global consistency problem of the geometric Langlands conjecture on the Joe point.
If the scope is expanded, complex singular points can even be used instead of Joe points.
There should be two options on the other side, either to redo the derivation of this part of the paper, or to directly patch it.
After thinking from his perspective, Qiao Yu felt that it would be much simpler to choose the latter, such as adding a homology layer to a new category...
But this problem only exists in Qiao Yu's mind. After going around in a circle, he began to think about a more critical question.
In this game of peak intelligence duel, he temporarily won one game, but it seemed that he was still far away from realizing his dream.
That’s right, it’s that dream of buying a community and then renovating it after making a lot of money.
After two months of training at Yanbei University, he is no longer the young man who was inexperienced in the world and completely ignorant of the rules of social operation.
After his observation, there is a high probability that mathematicians with a certain status will not be short of money. For example, neither Tian Yanzhen nor his senior master Yuan Zhengxin is short of money.
But it is not necessarily true that both of them are rich.
At the very least, it is absolutely impossible for the assets to afford to acquire a community and then rebuild it.
The two big guys don’t seem to have that much interest in money. Relatively speaking, they value their status in academia more.
This made Qiao Yu a little worried.
It can be seen from the books they prepared for him and the daily teachings they gave him that both of them wanted 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 at Yanbei University for so long, reading some books, attending some classes, and communicating a lot with school professors on weekdays, he discovered the most serious problem. Let’s not talk about him yet. Whether the mystery of prime numbers can be solved is a series of difficult problems. Even if it is really researched, how to realize it is still a problem.
If something is accidentally leaked, it will make all mankind lose confidence in the modern financial system. It is very difficult to make money from this thing. And it may lead to a big trap...
Of course, this does not mean that Qiao Yu is short of money.
In fact, he has discovered that with his current status alone, he will never be short of money in this life. After all, he can now live a relatively wealthy life. The only thing he is afraid of now is that his life has passed in such chaos...
He is afraid that when he grows up, he will start to be like Senior Brother Chen, no longer thinking about changing anything, but settling for the status quo. A world-famous mathematician only thinks about making waves in the academic circle every day, and has completely given up on becoming a serious billionaire.
He can't put his grandfather's statue at the entrance of a mathematics center - it's not justified.
Yes, when many mathematics tycoons around the world began to pay attention to Qiao Yu, a rising star in mathematics, the issues he was thinking about while lying in bed had transitioned from pure mathematics to the level where he must not forget his original intention.
The difference is that Qiao Yu's appetite has become bigger now, and the small fights in the past can no longer satisfy him. After all, he really has a worry-free life now and can make Qiao Xi live a good life.
Grandpa Shi has already hinted that after graduation, he will directly go to Huaqing to inherit his mathematics research center. He does not even need to consider the issue of settling in the capital, because the old man's land is almost expressly available to introduce special There is no need to worry about talent policies, housing, and children's future education.
Qiao Yu felt that this was the old man trying to shake his mind. After all, he would be able to live near Huaqing in the future, plus the meal card that was almost endless, after being blown up by a cannonball composed of sugar coating and sugar hearts. , he is afraid that he will not have the motivation to strive to become rich in the future.
This is absolutely not possible, so Qiao Yu feels that how to plan for making money in the future should also be put on the agenda.
The 10,000-word punch-in was completed on the 37th day!
I highly recommend the new book written by Hulucunren, a master of industrial literature in this era: "In 1978, I was admitted to Harbin Institute of Technology", a high-quality author and trustworthy!
(End of this chapter)