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Chapter 104 A sharp eye
There is a joke about a folk scientist in mathematics on the Internet.

It's basically about someone posting something online, saying how he spent decades creating an important mathematical theory, and then simultaneously posting his proof process on the Internet.

As it turned out, a mathematician actually took a serious look at it and told him in the forum that this theorem had actually been proved by a mathematician more than 80 years ago. Anyone who has studied mathematics as a graduate student would know this theorem, and everyone would directly use the conclusion.

Regardless of whether this story is true or not, it at least shows that to study mathematics these days, you first need to have a solid foundation.

This is why Tian Yanzhen and Xue Song discussed and developed a series of systematic courses for Qiao Yu to help him organize his knowledge. But when Tian Yanzhen found out that Qiao Yu had his own ideas and insights after reading Peter Schultz's paper for only one night, he gave up the decision.

The reason is actually very simple.

For example, you will often see people on the Internet claiming to have proved the Goldbach conjecture. It is no exaggeration to say that the Goldbach conjecture is proved hundreds or thousands of times a year by mathematics enthusiasts all over the world.

But the number of math enthusiasts who claim to have proved the Riemann hypothesis will immediately decrease by 90%. As for P=NP?, the turbulence problem involved in the NS equation, and so on, there are even fewer.

This is the threshold of mathematics.

If you can’t even understand the problem itself and can’t describe it accurately, there’s no point in solving it.

As for the things that Peter Schultz studied, there are simply no math enthusiasts on the Internet who would dare to take advantage of him, and even fewer mathematicians would want to take advantage of him.

The threshold is so high that it is difficult to find opportunities to express different opinions or raise debates, because most people find it difficult to even understand the core ideas of their research, let alone make criticisms or suggestions.

In a sense, Peter Schultz's research on mathematics itself challenges many mathematicians' traditional views on such problems. However, we have to admit that his achievements, such as the construction of complete coprojective geometry, do provide new tools and methods for solving previously difficult problems.

But this guy Qiao Yu actually understood Peter Schultz's paper.

To be honest, in the eyes of Tian Yanzhen and Xue Song, this is something that does not make sense mathematically. But it also makes them see the infinite possibilities of Qiao Yu.

At this time, Qiao Yu's performance is probably just one of the infinite possibilities.

In just one night, we found a method that seems to greatly simplify the accurate estimation of the upper bound of rational number points on special curves.

Of course, we can only use the word "seemingly" here, because Qiao Yu directly used the framework set up by Peter Schultz to create five mathematical tools in one go and successfully solved this problem.

But the problem is that although he feels that these newly created mathematical tools must be correct, he is unable to fully prove any of them from a mathematical logic perspective for the time being.

In other words, he was unable to prove any of these mathematical theorems that could potentially solve some of the world's most difficult problems, so it was difficult to say whether these theorems were actually true.

So theoretically speaking, he just proposed five not-so-popular mathematical conjectures.

Regardless of whether it is useful or not, at least three full pages of manuscript paper are filled, which is just right for discussing with everyone during the lecture.

Moreover, with these things, Qiao Yu felt that he was no longer just being polite; this was simply a courtesy, showing the highest Chinese etiquette to the professor who came to give a lecture.

After all, he not only studied the other party's paper, but also found a set of methods that seemed to be able to solve similar problems, which was enough to prove that he had gone through a period of extremely careful thinking.

As long as you don't mind the tiny details that can't be proven for the time being, it's perfect.

And it took him just over an hour to construct the tool.

Qiao Yu finally understood the fun that great mathematicians had in coming up with conjectures whenever they had nothing to do.

It's probably the kind of mentality that I think this mathematical theory is like this, but I can't prove it, and anyone who wants to prove it can try it.

Qiao Yu even fantasized that when he became a world-renowned mathematician like Riemann and Fermat, he would come up with a mathematical conjecture that was so awesome and useful that people would be willing to die for it.

Then he secretly proved it, hid the manuscript, and left it in his will.

Next, he would cooperate with wealthy and well-known mathematical research institutions like the Clay Institute. Both parties would offer a large sum of money as a reward. Whoever could prove his conjecture could take the money immediately!

When he had mobilized everyone's enthusiasm but found that he could not prove it, he would just watch the fun from the side, and from time to time he would come out to encourage everyone or drop some vague clues.

It was not until he died and his last words were exposed that mathematicians around the world learned that this conjecture was actually a theorem, which he had proved long ago. Alas, he just didn't tell anyone when he was alive, he was just playing around.

Then the bonus will naturally be given to him. Although he is dead, it can be left as an inheritance to the next generation.

Really, just thinking about this makes Qiao Yu feel very exciting, even feels like his blood is boiling.

And in reality, he was only three steps away from realizing this fun thing.

The first step is to become a world-renowned mathematician; the second step is to come up with this conjecture, and the third step is to prove it completely and accurately!
See, math is that simple.

Thinking of the stunned looks of the mathematicians, Qiao Yu couldn't help but smile knowingly. He looked at his masterpiece again, stood up, stretched hard, and then picked up his mobile phone.

Today's study ends here. Qiao Yu knows very well that the things he just came up with are impossible to prove with his current ability. But it doesn't matter, he hasn't finished reading Peter Schultz's related papers.

Maybe you will be inspired after reading this and solve the problem accidentally?
Just now, Qiao Yu checked and found that Professor Robert had published a paper in the Journal of the American Mathematical Society, which is one of the four top mathematics journals in the world that Lao Xue once mentioned to him.

In other words, the old man hasn't solved the problem completely yet, but his papers can be published in the world's top journals. If he can really solve this kind of problem, he must be more qualified to be published.

Although this is not the kind of difficult mathematical problem that will shock mathematicians all over the world once it is solved, the fact that so many mathematicians are interested in it shows that it definitely has an influence.

At least he can be considered to have caught up with the talented student named Zheng Zhiqiang who was trained in the school across the street, right?

In fact, it’s not entirely due to his desire to win. It’s mainly because Qiao Yu has always believed that he must do his best to realize the boasts he has made. If he slacks off because of some difficulties, how can he realize his dream?
If today he gave up the idea of ​​competing with the other party because the genius on the other side had achieved such amazing results, then wouldn’t he give up the idea of ​​acquiring the entire community tomorrow because it is too difficult to make tens of billions or hundreds of billions?
So what’s the difference between him and my grandfather’s drinking buddies who like to brag all the time?
As a man, you must face challenges head-on, in the literal sense, not just in the phonetic sense.

……

I opened my phone and checked the time. It was only ten twenty-three.

So Qiao Yu opened WeChat, thinking of sending a message to Qiao Xi to show off.

But the moment this crappy software was opened, a bunch of messages popped up in the friend group.

I clicked on it and took a look. Sure enough, it was Yu Yongjun who had been @ing him almost the entire day. Maybe he just couldn't help but @ him when he had some free time.

How should I put it? Qiao Yu had indeed not been in the group for the past two days. On the one hand, he felt that he was short on time and had a lot of work to do. On the other hand, he had already felt that it was not good to bully the kid in the group all the time...

Well, although they are actually of the same age, he is now a college student, and those two guys are still hanging out in high school, so doesn't the gap come out?

Qiao Yu now believes that those people on the Internet who say that college students are pure and stupid and that high school is the pinnacle of wisdom in life are either making fun of themselves or attending a fake university.

Not to mention anything else, just the document system of the Yanbei University library, which high school in the country can compare with it?
This thing can really broaden your horizons.

During the two months he was in high school, he stayed in the study room of Tieyi Middle School every day, trying to find some useful information. It often took him a lot of time to search for resources through search engines, and many times the resources he finally found were not of high quality, which was a complete waste of time.

After arriving in the capital, I used Yanbei University’s internal literature search system in this small room and was able to search for a large list of extremely high-quality resources in minutes!
I can’t finish it, I can’t finish it at all!
But since these two guys were so pious and insisted that he bully them...

Qiao Yu decided to click in and take a look. He had to respect his friends' desire to be abused.

Oh, it’s been two days and we’re still discussing his paper.

Yu Wei is still so resourceful. He only took a picture of half of the paper's title, but as the first author, this guy actually found the entire paper.

Of course, this doesn’t mean that this guy was scared. In the group chat, he was still as stubborn as ever.

To sum up, this guy argued with Yu Yongjun in the WeChat group for dozens of times. What he meant was that Qiao Yu had only an idea for this paper at most, and most of the article must have been completed, revised, and polished by others...

Also, this paper does not use any new tools, it is just the flexible application of many known mathematical tools. In essence, it is no different from their participation in the National Mathematical Olympiad, except that they are the flexible application of high school knowledge, while the paper is the flexible application of mathematical tools that only universities can come into contact with.

Because of the above reasons, Yu Wei believed that the reason why Qiao Yu did not show up was that he himself already understood that it was just a common paper and there was nothing to show off.

As for Yu Yongjun's expression, it is simple.

In fact, his lengthy and extremely hurtful expressions can be translated into just one sentence: If you say my elder brother is not good enough, then that is pure jealousy, otherwise You Can You Up!
Seeing his younger brother being bullied, Qiao Yu felt that he should occasionally show up to educate Yu Wei, otherwise, over time, this guy would really have some unrealistic illusions again.

"Ahem, you two can really chat? I've been too busy these past two days and have no time to deal with the group chat, but you guys have chatted for hundreds of times? Have you really been practicing the questions? In this state, I doubt whether you can be selected for this year's IMO!"

Yu Yongjun was still the first to rush out: "Damn it, Boss, you finally showed up. When you were away, Yu Wei was about to turn against Tian Gang!"

Qiao Yu: "I can't help it. I just arrived at Yanbei University and I'm too busy. Don't you know how strict Director Tian's requirements are? I have to attend a lecture by a professor from New York University tomorrow, and I have to finish reading at least two papers by that professor today. Hey, is it easy for me?"

Yu Yongjun: "Fuck, is it so high-end? Reading papers, attending lectures? This university life is a little different from what I imagined!"

After the two chatted for a few words, Yu Wei also popped up: "Ha...blow, you keep blowing!"

Qiao Yu: "Yu Wei, I know you are anxious, but don't worry. How about this, I will suggest to the instructor that we come to Yanbei University for the first phase of special training this year? Then I will let you experience my life at Yanbei University and you will know. Anyway, I forgive you first, because people can't imagine a life outside of their own cognition."

Yu Yongjun posted a picture of himself laughing out loud, and then asked: "Yu Wei, are you still not honest?"

Yu Wei: "Is the Chinese Mathematical Society founded by your family? So we're going to Yanbei?"

Qiao Yu: "Hey, you don't understand. Let me put it this way. Your evaluation of the paper I sent to you yesterday was actually correct. I also think its level is not high. It's just better than yours. It's meaningless. I really don't want to show off to you, but I have to tell you that I have just found a way to solve a world-wide mathematical problem.

Let me put it this way. As long as I show these things tomorrow, in order not to delay my research time, the special training in March must be held at Yanbei University. After all, it will save me time running back and forth, because this is saving time for mathematicians all over the world, understand?"

Yu Wei: "??? You went to Yanbei University to study bragging, right?!"

Yu Yongjun: "Well, Boss, although I think you are really awesome, at least much more awesome than Yu Wei, but to be honest, you did exaggerate a little bit this time, didn't you? How about we hold back for now and start by solving a small problem?"

Qiao Yu: "Alas, summer insects cannot talk about ice. First, search for the problem of accurately estimating the upper bound of the number of rational points on algebraic curves, and then search for the theory pioneered by Peter Schultz. And I, your eldest brother, am the first person who tried to combine the two and solve this problem. Do you understand?"

Yu Wei: “…”

Yu Yongjun: “…”

Qiao Yu: "Forget it, I don't have time to explain to you. I need to rest early today and I have to attend a lecture tomorrow. I know it's hard for you to accept the gap between us now, but time will prove everything.

So work hard! Try to pass the interview at Yanbei University in the future. After all, only when you come to Yanbei University can you know how big the gap is between you and me! "

After saying that, Qiao Yu directly exited the group chat and opened Qiao Xi's WeChat. There was no other way. The situation was different now. Some things were difficult to explain clearly to these two guys.

"Mom, I've completely gotten used to life at Yanbei University. You don't know how friendly the people here are! Not only did they arrange a special single room for me, but Director Tian also asked all the mathematics professors in Yanbei to come and train me. By the way, I also met a senior today. He's very nice and cute. Before I left, he said that I was as important to him as air."

Qiao Xi replied quickly: "Hmm? I can understand the other things, but why does your senior brother feel that you are as important to him as air? Are you sure this senior brother is normal?"

Qiao Yu was a little confused. He had only slightly processed Chen Zhuoyang's words. Qiao Xi's ability to understand was very strong, but how could he go so far astray? !

"Mom, you're wrong! He was affirming my mathematical talent! Because just a few words from me made him realize how important I am to the world of mathematics, and he hopes to receive my guidance in the future, so he said that."

"Oh, I see. It's good that you get used to it, but boys should remember to protect themselves when they are outside."

"This is Yanbei University. Do you know how strict the security at the gate is? I'll scare you to death if I tell you!"

"Okay, just take care of yourself and try not to scheme against others. I don't know how strict the security is at Yanbei University, but I know that there are very smart people there. Being clever will only make people dislike you."

"Don't worry, cleverness is only used in elementary school. In college, I will only use great wisdom to conquer them!"

"Okay, good luck! By the way, yesterday your eldest cousin heard about you from somewhere and knew that you went to Yanbei University, so he called to ask about you. He also asked if you were free during the summer vacation, because he wanted to take his son to Yanbei University to experience the atmosphere there."

This topic change was a bit awkward. Fortunately, Qiao Yu was used to Qiao Xi's way of chatting, so he immediately replied: "He is dreaming! I won't go home during the summer vacation?"

"Yeah, that's what I told him. I'm just reminding you in advance to stop showing off online."

Qiao Yu said disdainfully: "No, I'm not showing off. It's the reporters who want to report me. I can't do anything about it. It's difficult for a future great mathematician and China's rising star to keep a low profile.

Besides, I just like to see them say bad things about me behind my back when they see me become successful but can’t get any benefits. So I have to show off!”

"Yeah, that seems to make sense. Keke said the same thing today. She also said that if your eldest cousin dares to blackmail you, she will help us scold him."

Qiao Yu: "How can she curse? She just keeps repeating the same few words. Forget it, I'm going to sleep first. I have to attend a lecture tomorrow."

Qiao Xi: "Oh, good night, son."

Qiao Yu: "Good night, Mom!"

Putting down his phone, Qiao Yu stood up, picked up the toothbrush and towel, and planned to wash up and go to bed.

But when he reached the door and grabbed the door handle, he suddenly changed his mind.

Damn, he is so outstanding that the opposite sex is thinking about him every day and they all want to help him curse people, so why does he still pay so much attention to personal hygiene?

Forget it, let's just go to sleep. It's still pretty cold outside in Beijing at night in the winter...

So I put the toiletries back with peace of mind, jumped directly onto the bed and went to sleep!

……

The lecture on the second day was from nine to eleven in the morning, for two hours.

Qiao Yu regained his good habits and got out of bed at 6:30 in the morning.

You can be casual at night, but you still need to take care of yourself in the morning. After all, it was the first time for Qiao Yu to attend a lecture, so when he went out to wash up, he specifically took the facial cleanser that was still stuffed in the box.

Qiao Yu can use one bottle of this stuff for more than a year. It’s not that he is very frugal, but he never uses it except on important days.

Facts have proved that although washing your face with cold water is indeed painful at first, after shivering from the cold, your whole body will feel comfortable and refreshed.

Especially the one after using facial cleanser, it feels tight, dry and comfortable.

After washing up, Qiao Yu did a set of radio gymnastics outside the house. After stretching his whole body, he returned to the house, sat at the table, went over what he had thought about yesterday in his mind, then took a few sheets of manuscript paper and translated everything he had written yesterday into English.

There was no other way. When a professor from New York University came to give a lecture at the research center, Qiao Yu felt that he should assume that he did not understand Chinese. After all, Chinese is not easy to learn, especially for foreigners.

He took a stack of manuscript paper written in Chinese to ask the other party for advice, which seemed a bit unreasonable.

At half past eight, Lao Xue arrived at Qiao Yu's temporary dormitory on time. "So early, Mr. Xue."

"The lecture starts at nine o'clock, and it's half past eight now. Is that too early?"

"Isn't the lecture hall in the research center? Isn't it just a few steps away?"

Old Xue was speechless. He looked at Qiao Yu and asked, "So you plan to go in with the professor who is giving the lecture, right? The professor will go to the lounge in advance to wait for the lecture to start. Can't you wait in the conference room for a while?"

Well, considering that Qiao Yu is only fifteen years old, it is understandable that he doesn’t think things through, Xue Song reminded himself.

In fact, it’s not his fault that he is always strict with Qiao Yu. It’s just that Qiao Yu’s performance most of the time makes him subconsciously ignore this guy’s age.

"Oh, that's right. Please wait a minute. I'll prepare the things I need today."

After saying that, Qiao Yu quickly began to sort out the conjectures he had just sorted out in English and put them in order. If he put them in the wrong order, he was afraid that others would not understand his thinking at the time. To be honest, it was only one night, and when he was translating just now, he felt that his brain might have been a little too excited last night.

There is an indescribable messy beauty to these things that I came up with.

"Just bring a notebook and a pen, what else do you need to prepare? Wait, what is this?" Xue Song was very sharp and noticed Qiao Yu's densely packed manuscripts.

"This is what I thought after reading Professor Robert's paper yesterday. I plan to discuss it with the professor later. Maybe we can make a big step forward on this issue!" Qiao Yu said confidently.

"Let me see it first." Xue Song looked at Qiao Yu suspiciously. To be honest, he still didn't quite believe that Qiao Yu had any new insights into this research direction just by reading the paper for an afternoon. However, Qiao Yu had proved himself many times, so he couldn't just say it for sure.

"Okay, please read it from the beginning, otherwise it will be confusing."

After receiving the draft from Qiao Yu, especially the first proposition about constant C, Xue Song couldn't help but look up at Qiao Yu in surprise. No way? This is too outrageous!

I immediately looked away and continued reading, then I saw the big question mark following it, and then I calmed down.

Oh, just suggesting an idea... It startled him.

Then he quickly glanced over Qiao Yu's ideas without changing his expression, and Xue Song looked confused.

What was he just looking at? To be honest, he could roughly understand Qiao Yu's thoughts, after all, he was studying Diophantine equations, but this method...

He silently reorganized the manuscript, handed it to Qiao Yu, and then said in a calm tone: "Let's go."

"Okay." Qiao Yu took the goodies and followed Xue Song out the door. On the way to the lecture room, Qiao Yu couldn't help but ask cautiously: "Teacher Xue, is my idea wrong? Why do you feel weird after reading it?"

Xue Song took a deep breath and pondered for a while before answering: "I can't say whether it is right or wrong, because I don't know if you are further complicating the relevant issues. After all, I have not studied the results of Professor Peter Schultz in depth."

"Hmm? What does complication mean?" Qiao Yu asked humbly.

Xue Song thought for a moment and replied, "You should know from reading Professor Robert's paper yesterday that similar research we do is mainly based on the methods and tools of classical number theory and algebraic number theory. For example, the classical tools used are mainly class field theory, circle field theory, unit group theory, etc.

Even if it involves some modern tools, such as elliptic curve theory and modular forms, in short, this type of tool has already covered the key ideas of similar problems, so it does not rely on Peter Schultz's theory.

Similarly, Peter Schultz's theory is not necessary when studying problems such as prime number distribution, congruence theory, quadratic forms, integer rings over algebraic number fields, etc. Just like the proof of the classic Fermat's Last Theorem, before Weiers' work, it mainly relied on the basic concepts of elliptic curves, modular forms and Lich group theory.

So what can I say about what you are doing? Regardless of whether it will succeed or not, of course I cannot judge whether it will succeed or not, but what is certain is that the proof process will be extremely complicated. I don’t even know if success is a good thing or a bad thing.”

Qiao Yu blinked and asked, "Why would success be a bad thing? Aren't more advanced mathematical tools created to be used?"

Xue Song glanced at Qiao Yu and said expressionlessly, "Because that means that Schultz's theory may become indispensable for future research of this kind, but it is difficult to fully understand his theory. This means that the threshold for researching related issues will be raised again in our generation."

Qiao Yu suddenly realized and said, "Oh! I understand. That is to say, if I succeed, you might have to learn Peter Schultz's theory from scratch in the future, right?"

Xue Song glanced at Qiao Yu and was too lazy to say anything. This kid was getting more and more outrageous.

But Qiao Yu was obviously more excited, and said confidently: "No, Mr. Xue, you can't reject new things! We can only come up with new things based on other people's things after we have thoroughly studied them. If I succeed, and you want to learn this, I can teach you! Just like you teach me, I won't charge you any fees!"

Obviously, Professor Xue didn't appreciate it very much and directly scolded him: "Shut up!"

Qiao Yu felt a little aggrieved, but was too embarrassed to say anything.

But what came to my mind was the research topic of Senior Brother Chen that my tutor mentioned yesterday.

Old Xue is already a professor, so there is nothing we can do if he is not good at learning. But it is different for Senior Brother Chen. If he can find a method to solve the problem that Senior Brother Chen is studying, then doesn't that mean that Senior Brother will have to relearn Peter Schultz's theory before graduation?
I heard from Lao Xue that this theory is so advanced, I believe that the super talented Senior Brother Chen will definitely be grateful to him, right?
But he had to speed up, otherwise what if Brother Chen was unwilling to accept such advanced ideas when he successfully graduated with a Ph.D. and found a job? Wouldn't he have given his sincerity to a dog in vain?

Taking Qiao Yu up the stairs, Xue Song found that the boy really hadn't said a word, and he suddenly felt a little regretful.

Was I too harsh on this kid just now? It would be bad if I dampened his enthusiasm.

Although this kid's words are irritating, at least some of his words are not wrong. If more advanced tools can solve the problem, then you must learn them, otherwise you will only be left behind. And... he is only fifteen years old! It is the age for Feiyang to be lively and jumpy.

But Xue Song was too embarrassed to apologize directly, so he could only ask in a deep voice: "What are you thinking about?"

"Professor Xue, I'm wondering when Senior Brother Chen will be able to graduate with his Ph.D." Qiao Yu answered subconsciously.

"Why do you care about when Senior Brother Chen will graduate?" Xue Song asked with a frown. This was very puzzling.

"Uh..." Qiao Yu was a little hesitant. Although he was doing this for his senior brother's good, Old Xue's attitude just now made him unsure whether Old Xue could understand his painstaking efforts for his senior brother.

"Is this difficult to answer?" Xue Song couldn't help but ask again.

Qiao Yu quickly shook his head and replied, "No, I just thought that if I can apply this theory to things like surfaces and manifolds, and create more tools for my senior to solve problems, would it be easier for him to graduate?"

Xue Song opened his mouth, but was too lazy to say anything.

He had to admit that he had been worrying for nothing. This kid's enthusiasm was not so easily dampened.

No matter, he is Mr. Tian’s student anyway…

At this moment, Xue Song was even somewhat glad that he had not tried to trick this kid into becoming his disciple, otherwise his life would probably be very tiring. Really, after getting to know him, Xue Song no longer dared to guess what was going on in Qiao Yu's little head every day.

He even wanted to ask Qiao Yu for Lan Jie's contact information and ask how the high school teacher usually dealt with Qiao Yu.

"Teacher Xue, what do you think..."

"Stop talking nonsense, just follow me into this conference room."

Qiao Yu secretly stuck out her tongue behind his back, saying, "Old Xue has become so old-fashioned. I don't love him at all."

……

Today's lecture was scheduled in a medium-sized conference room.

As soon as you enter the door, you can see a blackboard in the middle of the podium and a screen on each side.

At this time, Brother Chen, whom Qiao Yu had been thinking about, was already debugging the equipment on the podium, probably to ensure that when the lecture began, Professor Robert's PPT could be projected normally on the screen.

This made Qiao Yu feel a little emotional.

He suspected that Peter Schultz obtained his master's and doctoral degrees so quickly probably so that he wouldn't have to work.

Turning his head and looking at the seats below the rostrum, Qiao Yu roughly counted and found that there were about fifty people sitting there. However, except for a row of tables in the first row, there were only stools in the back.

What surprised him was that he and Lao Xue were not the first to arrive. There were already more than 30 people sitting in the conference room.

Apart from the empty seats in the first row, there seemed to be not many seats left in the back.

Normally, I don’t know where these people hide. In any case, Qiao Yu feels that he hasn’t met many people in the past two days.

What surprised him even more was that he actually saw three senior sisters.

Qiao Yu almost couldn't help but take out his phone to take a photo for Lan Jie to see...

Who said there are no girls in the School of Mathematics? The good guy must have generalized.

Attending a math lecture, you can easily see three senior sisters. This is enough to show that the good guy didn't see girls when he was studying. It's not a math problem, but a school problem. Double-day universities must review...

Qiao Yu and Lao Xue also attracted a lot of people's attention, especially Qiao Yu.

Perhaps these guys didn't expect that a young college student like him would come to attend the lecture? Qiao Yu thought to himself, and then walked towards the back row of the conference room.

There was no way. When he was in Tieyi Middle School, he was used to sitting in the last row of the classroom, a position that the teacher didn't pay much attention to. But Xue Song grabbed him.

"Where are you running to? Our seats are over there, on the right!"

"Ah?" Qiao Yu was stunned for a moment, then obediently followed Xue Song and sat in the rightmost seat in the first row.

Well, it’s nice to have a table in front, not because of the mineral water on it, but mainly because it makes it more convenient to take notes.

Qiao Yu did not bring a laptop computer. He only brought a formal notebook that cost 12 yuan each and could only be used for taking notes, a fountain pen, and five sheets of A4 manuscript paper for summarizing his mathematical ideas.

When listening to a lecture, you mainly need to use your brain.

While Qiao Yu was sitting there, people came in from time to time. Teacher Xue was right. Qiao Yu observed that by 8:55, the entire conference room was basically full, and there were even people standing in the aisle.

This also includes first row seats.

Everyone who came in would look at him intentionally or unintentionally, and some professors would come over to greet Lao Xue and chat with him.

Brother Chen had also completed the pre-lecture adjustments and sat in a seat in the middle of the first row. There was an aisle between him and Lao Xue, but he left the seat closer to Lao Xue.

When Qiao Yu saw Senior Brother Chen coming down, he looked at him specifically. When their eyes met, Qiao Yu returned him a kind smile. It turned out that Senior Brother really treated him as important as air.

The lecture time was up, and Director Tian accompanied Professor Robert into the conference room.

The two walked to the podium together, and then Director Tian picked up the microphone first.

“Hello everyone, today we at the Yanbei International Center for Mathematical Research are honored to have Professor Robert Greene from New York University give this lecture. He is an outstanding scholar in the field of number theory, especially in the study of algebraic geometry and the distribution of rational number points. He has made many breakthroughs.

Today, he will give us a lecture on the exact estimation method of the upper bound of rational number points on special curves. This problem not only plays an important role in number theory, but also has close connections with many other branches of mathematics. Next, let us welcome Professor Robert with warm applause! "

After saying that, Director Tian walked down from the podium amid applause from the audience and sat next to Chen Zhuoyang, leaving the podium to Professor Robert on the stage.

At this time, Robert Green, after greeting the audience, had already sat down on the podium. After testing the microphone, he said in fluent English: "Thank you Professor Tian for your introduction, and thank you all for coming.

Today I will share with you the latest results of my team and I on the estimation method of bounds on rational points of a special type of curve. This problem has always been a very important topic in modern number theory, especially in understanding the properties of curves. I hope..."

Xue Song, who had been sitting there as steady as a rock, took the question prepared by Qiao Yu without hesitation while Robert Greene was still making his opening introduction on the stage and handed it to Tian Yanzhen, who was only separated from him by an aisle.

Before Qiao Yu could react, half of the things in front of him were gone.

Well, whoever is the teacher is right.

Qiao Yu turned his head to glance at Director Tian who was not far away, then looked obediently at the professor on the podium and listened to the report.

Fortunately, Professor Robert had already introduced the boring part at the beginning and got to the point. The PPT also directly showed the first example.

"We start with a familiar problem, the Mordell curve, which is an elliptic curve of the form y^2 = x^3 + k, where k is a constant. From Faltings' theorem, we know that for a non-singular algebraic curve of genus g ≥ 2, there are only finitely many rational points.

While this gives a finite number of rational points, it does not provide an exact upper bound. In recent work, we have further refined estimates of the number of rational points for certain classes of curves, such as superelliptic curves and some low-genus curves, by combining the Galois representation, Chabauty's method, and Coleman integrals..."

Qiao Yu listened carefully, and then roughly understood that the recent achievement of this big guy was to directly improve the upper bound of the number of rational points from the classic O(d^2) to O(d \log d), where d represents the degree of the curve.

For Qiao Yu, a newcomer who has just stepped half a foot into the world of mathematics, he is not quite sure whether this is a great progress in the world of mathematics.

However, Qiao Yu could see that the professor on the podium was obviously very proud when introducing this latest achievement.

Judging from one's own experience, this probably means that at least in this field, this achievement should be very impressive, right? Otherwise, why would he be so proud? It's like a math novice like him who is now too lazy to show off a paper he published in his friend group, because now looking back, he feels that the paper is really not that impressive.

Therefore, if this achievement is nothing, Professor Robert should not be interested in showing off in front of people like them.

Although Qiao Yu listened to the lecture very carefully, he was actually always keeping an eye on his tutor out of the corner of his eye.

As expected, our director Tian was only there out of courtesy.

He was there in person, but his heart was not there. He was reading his manuscript with great interest.

Judging from the situation, Qiao Yu suspected that Director Tian only came today out of courtesy and would not attend tomorrow's lecture at all.

Wait, there was some movement from Director Tian. Qiao Yu saw Director Tian ask for a pen from Brother Chen beside him, and then wrote a line on his manuscript.

After seeing Director Tian put down his pen, Qiao Yu immediately sat up straight and looked straight at Professor Robert on the stage. Sure enough, from the corner of his eye he saw Director Tian looking at him naturally and handing the manuscript back to Lao Xue.

Old Xue glanced at the handwriting on the manuscript, then casually put it back on the table without disturbing Qiao Yu who seemed to be listening to the lecture attentively.

But for Qiao Yu, who was always keeping an eye on everything, this obviously didn't bother him.

He could see clearly what was written on it.

"A small exchange meeting will be held in the P3 conference room from 3:45 to 2: p.m. Dr. Robert can be invited to discuss and demonstrate the feasibility."

See, he always said that his director Tian really has a keen eye...

And it turns out that's true.

　Thanks to the passers-by, book friends 20241005192534569, and Yishuiwangu for their rewards and encouragement!

　　PS: The 19th day of updating words has been completed!
　　
　
(End of this chapter)