Top academic

Chapter 109 Give roses to others and leave fragrance in your hands

Yuan Zhengxin was very satisfied with Qiao Yu's performance.

It’s even impossible to describe it as very satisfied... The old man is very sorry, sorry that Qiao Yu is not his biological grandson!

How great it would be if this child was his grandson.

Especially at this moment, when the sun was setting, a ray of sunlight leaked in from the window and sprinkled on the child's focused body, making Qiao Yu look like an angel covered with a layer of light.

The more I watch, the more I like it.

How much do you like it?

Let me put it this way, the old man got up and went to the bathroom, and when he came back he made some noise, which startled Qiao Yu. Qiao Yu raised his head blankly, glanced at the place where the noise came from with an unfocused look, then immediately lowered his head and continued to write and draw on the manuscript paper.

In fact, it didn't have much of an impact, but the old man didn't even dare to drink water for the next period of time, for fear that he would have to go to the bathroom again and affect Qiao Yu's thinking. He even breathed a little softer.

Time passed quietly as the old man looked at Qiao Yu from time to time, and finally the young man next to him stretched lazily.

However, the old man's originally kind eyes became solemn because of this stretch.

"How was your afternoon study session here?" the old man asked seriously.

Qiao Yu nodded vigorously, not caring about the old man's serious look, and answered loudly: "Report to Master, very good! I'm not bragging to you, I feel like I'm almost mastering Needham's Visual Differential Geometry and Forms!"

"Oh? You haven't asked me a single question, so I'm going to test you." The old man said seriously.

"No problem, you can take any test on this book except the last point!" Qiao Yu stood up confidently and handed the book to the old man beside him.

Yuan Zhengxin took the book from Qiao Yu, flipped through it casually, and then put it aside and asked, "Needham believes that geometric intuition can affect the study and research of differential geometry. What do you think of his point of view?"

Qiao Yu answered loudly: "I think Needham's point of view is correct. First of all, geometric intuition is a concept emphasized in Needham's book, which refers to the ability to understand geometric objects and their properties through visual and spatial perception.

This intuition can help us form concrete spatial images when faced with abstract mathematical concepts, making it easier to understand complex structures and relationships. Keep a focus on geometric intuition, especially when dealing with complex manifolds and surfaces.

Through geometric intuition, researchers can better propose conjectures and conduct verification, thus making progress in the derivation and application of theories. Let me give you an example..."

Qiao Yu's voice was loud, clear, and pleasant to the ear. The answer he gave was clear and logical, with opinions, analysis, and examples. Yuan Zhengxin roughly understood why this child could get so many full marks, and why Zhang Shuwen came to the conclusion that this child was incredibly talented after just one look.

Just like that, in the quiet little building full of ancient charm, two people, one old and one young, one asked and the other answered, as if they had traveled through a hundred years of time, just like the way students faced their teachers in ancient private schools.

The old man nodded slightly, finally smiled, and said, "The last question is, how do you understand the relationship between the tangent bundle and the tangent space on the manifold, and discuss the impact of the geometric structure of the tangent bundle on the manifold."

Qiao Yu answered loudly without hesitation: "The tangent bundle is the set of all tangent spaces on a manifold, usually represented by TM, where each tangent space TpM corresponds to a point p on the manifold M. The tangent space is a vector space, and the tangent bundle is the structure that combines these tangent spaces.

The geometric structure of the tangent bundle affects the manifold in that it allows us to define vector fields and differential forms. By studying the tangent bundle, we can analyze the local and global properties of the manifold, such as smooth mapping, the topological structure of the manifold, and how to define geometric quantities on the manifold.

Oh, and by the way, tangent bundles also play a key role in defining connections and calculating curvature, which helps us understand the curved nature of manifolds..."

The old man asked a total of six questions, covering all aspects of the part of the book that Qiao Yu had read.

He couldn't find any fault with Qiao Yu's answer. Really, every detail was almost perfect.

"Okay! Well, it's just a few minutes past five now, and we still have some time before dinner. Do you dare to challenge a differential geometry exercise paper I have here?"

"No problem! Master, if you want to test me, just come on!" Qiao Yu still looked confident.

"Are you so confident? I guess I have to pick a harder one." After saying that, Yuan Zhengxin stood up, pulled out a folder from the bookcase behind him, selected a test paper from it and handed it over.

Qiao Yu took the test paper, but did not start working on it immediately. Instead, he read it over from beginning to end, then said with a sad face, "Grandpa Master, I can do the test paper, but can I make a small request?"

"Oh? What's the request?" the old man asked patiently.

Qiao Yu held the test paper and said, "Look, some of the questions on this test paper are not difficult in themselves, but it is too troublesome to solve them using differential geometry methods. For example, the third question is to find the curvature and torsion of the parameterized curve at point P. If I use differential geometry methods, I have to calculate the derivative first, and then I can solve it using the curvature and torsion formulas.

But if I use the algebraic method, the direct parameter substitution method, that is, x=t, y=t^2, z=t^3, I can directly deduce the geometric properties of the curve through this relationship, and then substitute it into the geometric formula, saving the time of calculating the cross product. "

The old man glanced at the question and nodded repeatedly, then asked kindly, "Well, it can indeed be solved this way, but why are you thinking of being lazy when you haven't finished the paper yet?"

"Master, it's not that I'm lazy. I've been reading for the whole afternoon and I feel a little hungry. If I use the methods of differential geometry to solve it, it will take at least half an hour. I'll use a more labor-saving method and it will be done in 20 minutes. I can go back to eat!" Qiao Yu said, patting his stomach.

Yuan Zhengxin suddenly realized and said, "Yes, yes, yes, this is my fault. Oh, I forgot that you are only fifteen years old, and you are in the period of growth. I am not hungry, so I thought you were not hungry either. In this way, you don't need to write the whole question, just write down your ideas."

It's a pity that there are only Qiao Yu and Yuan Zhengxin in the office. If Yuan's students really saw their teacher looking so self-blaming, they would probably be shocked and doubt their lives.

You have to know that Mr. Yuan has always been known for his strictness. If it were someone else, let alone eating a little later, there is a high probability that he would not starve to death even if he skipped a meal...

"Master, you are so kind. It will only take fifteen minutes at most!"

"Okay, do the questions first. By the way, we'll eat here tonight. What do you want to eat?"

"Eh? Well, let's eat in the cafeteria! Anyway, the food in Yanbei University's cafeteria is delicious. I just want to try the food in Qingbei's cafeteria! And the food in the cafeteria is fast!"

"That can't be worse than the food in Yanbei Canteen. What kind of food do you like to eat? I'll have someone bring it over while you're doing your homework."

"Master, I'm not picky about food, just more meat would be fine. Oh, and mutton would be even better."

"it is good!"

……

"Mr. Yuan, are you sure the food will be packed directly to your office?"

"Yes, remember to order more mutton, all kinds of mutton."

"Yeah, okay, okay."

"be quick!"

"do not worry."

……

"How is it? Is the food in Huaqing Canteen okay?"

"Yeah, it's as delicious as Yanbei Canteen."

"If it tastes good, eat more."

"Grandpa, you eat too."

"I'm not hungry yet, you should eat more. By the way, are you used to it after coming to the capital?"

After hearing this answer, Qiao Yu blinked his eyes. It was good that the old man didn't correct him.

"I'm quite used to it, but the heating in the room is a little too strong, and I often wake up from the heat at night."

"Then it is better to leave the window open when sleeping to reduce stale air and allow for fresh air. Overheating is indeed not good."

"Okay, Grandpa. Let's try it tonight."

"Also, do you have enough living expenses in Beijing? I heard from Teacher Lan that you still have to earn money to support your family in Xingcheng?"

"That's enough! Grandpa, that's all old news! I won the gold medal in the Xiaolibaba International Mathematics Competition and received a bonus of 200,000 yuan. I won the first place in the IMO, and the school secretly awarded me 250,000 yuan. I left the school bonus to my mother for living expenses, and I still have 200,000 yuan myself. To be honest, I have never been so rich."

"Haha... you are very good, and your school is also very good. Speaking of which, I, your grandfather, also had a hard time back then."

"I know. I heard from my grandpa that his generation had a very difficult life, and your generation must have had it even harder. My grandpa was also a very nice person, but it's a pity that he passed away when I was in fifth grade."

"Alas, God has given me a long life, what a pity... Putting aside these disappointing things, are you still reading Schultz's paper?"

"I'm reading it, Grandpa. I'm studying his 2012 paper "Perfectoid Spaces" published in Publications mathématiques de l'IHS. This paper makes the definition of perfect space clearer.

Combined with the differential geometry I am reading, I think that on a complete p-adic body, as long as the structural ring of the complete space satisfies the characteristics of perfectoid, it can be used for those complex geometric analyses. And his tower structure is so shocking. "

“Yes, this is the way to read a paper, to connect it to what you have learned so far and do extended thinking. Schultz’s work is groundbreaking. As far as I know, many teams are currently using his results to do some basic research.

For example, Professor Gatesgory of the Max Planck Institute for Mathematics is leading a team to prove the geometric Langlands program. Professors from Huaqing University are also involved in this. If you have the time, you can learn about the Rosetta Stone problem, especially the geometry and number theory involved.

The hint was too obvious. Qiao Yu, who understood it, shook his head decisively and said, "Grandpa, I don't want to follow others to do the research that has already started. Besides, my foundation is too poor now! Once I make up for the shortcomings in the foundation, I will start from scratch and produce a result that will make you proud!"

"Yes, yes, it's really meaningless to follow others! My apprentice has great ambitions! All right, you should catch up on your basics in the next six months. Grandpa is waiting for you to make achievements."

……

"Grandpa, I'm full."

"Well, I have something else to do in the evening, so I can only ask someone to drive you back."

"No need, Grandpa, I can just walk back by myself."

"It's not easy to walk so far right after dinner. Besides, it's not convenient for me to ask someone to drive to Yanbei to pick you up, so can't I just drop you off? Just listen to my arrangements."

"Okay, Grandpa."

"By the way, take this card. You can come and go in Huaqing anytime in the future. There is still some balance in it. If you want to come to Huaqing for dinner, just swipe this card. If you feel unwell, you can also use the card directly at Huaqing's school hospital."

"Ah? Grandpa, this is not good, right?"

"You call me grandpa, and I didn't prepare any elder gifts for you in such a hurry. Just take it if you ask me to. Don't refuse. I also have this book for you. You can take it home and read it in your spare time."

"Thank you, Grandpa."

Qiao Yu took the book and the card, casually put the card into his pocket, and took the book in his hand and read it carefully.

"The Beauty of Mathematics" is an old book, but it can be seen to be well preserved. When you open the title page, there is an old man's autograph, which is so cool.

Qiao Yu put the book into his bag very solemnly.

"Come on, I'll take you downstairs to the car."

……

Yanbei University, Beijing International Center for Mathematical Research, Chen Zhuoyang was in his office with a book spread out in front of him, but his mind was obviously not on the book in front of him. From time to time, he would raise his head and look out through the window.

The position where he sat happened to allow him to see the only way to the building. This layout was originally chosen in order to observe whether the tutor would come over, but he didn't expect to use it to see his junior fellow apprentice today.

Come to think of it, he was already in this state three hours ago. He went to the cafeteria to have dinner at 5:30, and after coming back, he went to the junior brother's room to take a look. He found that the door was still locked and there was no one inside, so he went back to the office to wait. Now the time was almost 6:30.

Junior brother, have you run to the other side and lost your way?
Forget it. Chen Zhuoyang felt that he couldn’t stay in the office anymore. He was always restless. It would be better to go back to the dormitory to calm down and read well. After all, the academic pressure was still very great.

He tidied up his desk casually, picked up the books on the desk, and walked out of the office. Just as he walked not far from the entrance of the research center, he saw a black Audi car driving in this direction, and then stopped steadily at the intersection leading to the research center.

Chen Zhuoyang subconsciously glanced at the license plate. Well, it’s not the research center’s car.

Just as he was about to walk over, he saw Qiao Yu getting out of the car, and politely thanked the driver.

"Qiao Yu?" Chen Zhuoyang called out.

"Hey, Senior Brother Chen? Are you preparing to go back to the dormitory?" Qiao Yu turned around and walked naturally to his senior brother's side.

The car behind them started directly and left behind the two of them. Well, there are many gates in Yanbei University, so there is no need to turn around. There is a door in the front that can be used to go out.

"Ah, I just went out, and you came back from the opposite side? Is that Mr. Yuan's car?" Chen Zhuoyang looked at the car that had already left and asked curiously.

"I don't know. Master, you just arranged a car for me, right? And I have to come back, brother. I'm a student at Yanbei University and I don't have a dormitory in Huaqing. Should I just sleep in Master's office?"

Seeing Qiao Yu acting as naturally as if he had just gone out for a stroll and returned home, Chen Zhuoyang felt that his three views were overturned again. At the same time, his curiosity was overflowing. He naturally turned around and followed Qiao Yu back.

"Um, what did you do at the teacher's, ah, no, at Master Yuan's place this afternoon?"

"I just read. After I finished, my master tested me on some questions and asked me to do an exercise paper. Then, seeing that it was getting late, he invited me to have a quick meal at Huaqing. The food in Huaqing cafeteria is also delicious! Especially the boiled mutton.

Oh, by the way, before leaving, Master gave me a card, saying that I can enter Huaqing by swiping the card, and I can also use it to eat in the cafeteria. Next time, if you want to eat in Huaqing cafeteria, tell me, I’ll treat you! "

"No, didn't you talk about anything else with Mr. Yuan?"

"Yes, my master asked me to study the Rosetta Stone issue and wanted to introduce me to a research team. I refused. After all, it's not interesting to work with others. We should do our own research in the future."

"What? What team?"

"It seems that it is a team of a professor from the Planck Institute of Mathematics, and they are mainly studying the geometric Langlands program. There happens to be a professor from Huaqing University in the team. I think my senior wants me to help them and gain some experience, but I don't think it's necessary. Right, senior brother."

Chen Zhuoyang looked at Qiao Yu with his mouth half open, always feeling that this might be made up, but it seemed he couldn't make it up.

Although many people may know about this cutting-edge mathematical research team, they are definitely not many.

Of course, Mr. Yuan knew all about this, but he couldn't understand why he would specifically mention this to his junior fellow apprentice without bringing Qiao Yu into the research group.

It would be even more likely if Qiao Yu did some research on Schultz's paper recently.

It is said that although Schultz himself did not participate in the research of the geometric Langlands program, his theory is an important prerequisite for solving this problem, so it seems that the old man Yuan opposite may really want to give his junior apprentice a big hand.

Mr. Yuan is so confused!

Fortunately, the junior brother was clear-headed and refused. Otherwise, if he joined such a world-class research group at the age of fifteen, would they still be alive? !

Of course, he couldn't say that. Chen Zhuoyang could only lie and say, "Hey, Junior Brother, this is such a good opportunity... Just like you said, you can definitely go in and train and learn more from those big guys. Why did you refuse?"

Qiao Yu glanced at Senior Brother Chen and said seriously, "Senior Brother Chen, you are so superficial! Our Professor Tian is also a big shot, and when you join this kind of research group, when the results are signed, you are always at the end. It's hard to find the person you are, so who will remember you in the future?
If you have that much time, why not learn more from your teachers and then start your own project. If you have any research results, you will be the first author. How cool is that? So why rush?
Besides, there are so many difficult problems in mathematics. The problems in the millennium have been on the list for so many years, and no one has been able to solve them. There are even more problems that are not on the list. Are you still worried that there will be no research topics in the future? So, Brother Chen, you have to expand your vision. We must accumulate our strengths and then make a breakthrough. If we don’t make a splash, we will make a big splash! "

Listening to Qiao Yu's old-fashioned words, Chen Zhuoyang couldn't help but think of the abbreviation of China's national missile defense system. This is so simple...

The millennium problems...

Is it possible for a normal person to commit fraud?
How many people have chosen this kind of topic with great ambition, and then failed in their entire lives, wasting their best years, and not achieving any results, purely gambling with their lives...

He wanted to remind his junior fellow apprentice that his senior master across from him had rejected the teacher's suggestion and did not do research on the Riemann hypothesis in the Millennium Problem, which is why he successfully won the Fields Medal.

If Yuan had really chosen to pursue the Riemann hypothesis, he might have lost the Fields Medal.

but……

Forget it...

"By the way, Senior Brother, are you going back to the office again?"

Qiao Yu's voice called Chen Zhuoyang back to his thoughts. He looked at his junior fellow student beside him, feeling a little embarrassed. He was just busy eating melons...

I quickly followed Qiao Yu's words and said, "Yeah, that's right, I forgot to bring the half-written paper I just wrote. I have to go back and get it."

"Speaking of papers, I heard from the teacher that you are studying geometric analysis on complex manifolds?" Qiao Yu's tone suddenly became enthusiastic.

Chen Zhuoyang looked at Qiao Yu warily, nodded, and replied: "Yes, what's wrong?"

"Brother, I have an idea. You see, everyone is studying the geometric Langlands conjecture. You should also make it more difficult for yourself and add Schultz's theory of quasi-complete space. I have a feeling that as long as you understand Schultz's theory thoroughly, you will definitely be able to write something new in your doctoral thesis."

Qiao Yu said seriously.

Chen Zhuoyang was stunned for a moment, then looked at Qiao Yu with the same seriousness and said, "Well, Junior Brother, you'd better have your own ideas. Really, I admit that I was wrong. I shouldn't have treated you like air when I first met you. Please do me a favor and don't have any ideas about my thesis."

Qiao Yu insisted, "Believe me, Brother Chen, if you start researching this with me now, once the paper is finished, Professor Tian will definitely be proud of you! Are you really willing to just graduate from a research center with a Ph.D., then go to an ordinary key university, and start as a lecturer at an ordinary key university?"

Chen Zhuoyang said with joy: "Junior brother, there is such a good thing? To be honest, my goal is to be able to start as a lecturer in an ordinary key university. Can you help me ask our boss to recommend someone?"

Qiao Yu: "Brother, you..."

Well, this Senior Brother Chen didn't seem to have much ambition, which made Qiao Yu very disappointed.

What’s the point of being a lousy lecturer? You have to slowly get promoted to associate professor, then professor...won’t your whole life be wasted?

He originally thought that Director Tian’s students must all have great ambitions.

Chen Zhuoyang sighed and said, "Hey, Junior Brother, I used to have great ambitions. Really, I was no worse than anyone else back then, but when it comes to serious mathematical research... you can tell by looking at my hair now.

In fact, my teacher always said that my research was not original and only worthy of being published in some inferior journals. I knew that, but I had no choice, you know? Some things just can’t be learned! I also wanted to learn Schultz’s stuff, and I read his papers, but I couldn’t understand them, you know?
So why do you think I took the initiative to do all these miscellaneous things in the research center? Isn't it because the teacher saw that I had no credit but had worked hard, and he would help me when the time came? Alas, accepting a student like me is a shame for the teacher! "

Qiao Yu was shocked by this statement, and asked in surprise: "You don't understand? Brother, Schultz's paper proof process is very clear and logical, why can't you understand it?"

Chen Zhuoyang raised his head and glanced at Qiao Yu with a complicated expression: "Schultz's paper is about function analysis, probability theory, and mathematical physics. I won't talk about it. The key point is that completeness and those abstract concepts have no intuitive geometric explanation at all.

Not to mention those complicated theorems and formulas. For example, a formula to define the Cauchy sequence contains more than a dozen conditions and limit concepts. How can it be as easy to understand as you said? Professor Zhang also said at your seminar that the beauty of mathematics lies in simplicity.

But what he didn't say is that everyone can understand the simple ones, but the complex ones are difficult! For example, Euler's formula is simple, beautiful and easy to learn. It is even more intuitive in geometry. The complex number e^ix represents a rotation on the unit circle, and cos(x) and sin(x) represent the horizontal and vertical components of this rotation respectively.

Everyone can learn this easily. But those things that are extremely abstract are not ugly, but few people can really understand them except for a very few people. Do you understand? What you can easily understand may not be easy for others.

Let me put it this way, I didn’t understand a single thing about your seminar yesterday afternoon… Do you understand? This is probably why Professor Zhang criticized you… You don’t care about the vast majority of people. So I really gave up scientific research, but I think being a math teacher should still be okay.”

Qiao Yu nodded silently, looking at Senior Brother Chen who was almost bald, and a rare trace of sympathy rose in his heart.

But he couldn't feel any empathy in his heart, because he still didn't understand why he couldn't understand it. Isn't it something that anyone with a brain can understand?
But we can't say that Senior Brother Chen is stupid, right? After all, he is a PhD from the Mathematics Research Center and a student of Director Tian...

"Ahem, um, Senior Brother Chen, you didn't graduate from Yanbei University for undergraduate studies, right?" Facing the senior brother who was on the verge of emotional breakdown, Qiao Yu asked cautiously and tentatively.

"Well, I graduated from Linhai Jiaotong University for my undergraduate degree. I was first admitted to the Yanbei School of Mathematics for a master's degree, and then to the research center for a doctorate. At that time, I felt very lucky to be a student of Director Tian. But now...ah..." Chen Zhuoyang sighed and answered honestly.

So, maybe my senior brother’s development was delayed by a not-so-good university?

No, Linhai Jiaotong University is also okay. It was once one of the legendary nine schools alliance.

"Oh, okay. I'll definitely give you some advice from the teacher when I get a chance."

"Thank you, little junior brother."

"It's a small matter. By the way, when you finish writing your doctoral thesis, show it to me first and I'll help you revise it. To be honest, I'm good at revising papers. Otherwise, if you hand it in directly, Director Tian will get angry again. It will be hard to say what will happen then."

Qiao Yu decided to help this poor senior brother and help him escape from his suffering as soon as possible.

It was mainly for his own sake. He felt that Brother Chen's mood was indeed not very stable. The key point was that his office was just upstairs from him.

Of course, you can also do someone a favor by the way, which is not bad.

"Um...Okay, I'll show it to you after I finish writing it." Chen Zhuoyang said with a flushed face. He really couldn't say thank you for this.

Feeling that the senior brother's tone was a little strange, Qiao Yu suddenly realized that he was the younger junior brother. He had just been thinking that the senior brother couldn't understand the paper, so it was completely fine for him to give some guidance, but emotionally, it was indeed difficult for the senior brother to accept it.

The senior brother must have thought he was being too presumptuous.

Fortunately, it didn’t matter. After Qiao Yu reacted, he immediately found a solution and added: “Hey, brother, don’t get me wrong. If you think about it this way, even if I can’t finish your thesis, I have a good relationship with the senior teacher opposite.

I will secretly take your graduation thesis to my teacher to have a look, and then ask him to give you some suggestions, or even ask him to help you revise it. Even if he doesn't have time, he can still arrange a capable professor to help you, you know?"

After saying that, Qiao Yu patted Chen Zhuoyang's shoulder like an adult.

This one sentence made Chen Zhuoyang suddenly enlightened. The slight embarrassment and dissatisfaction he had just felt disappeared in an instant, and he became excited.

"Little Junior Brother, thank you so much! Now, if you are not satisfied with your life here, just tell me, and don't bother the teacher for everything. In fact, it's not good for a teacher to be too partial in some matters, but it's different between us brothers, you know."

Chen Zhuoyang said immediately.

"Okay, then I'd like to thank you, Senior Brother. Well, by the way, I'm not dissatisfied with my life. I actually think everything else about living here is pretty good. By the way, when I got up in the morning to wash my face, I felt the water was a little too cold."

"If you had told me earlier, I would have found a way to coordinate a solar water heater for this building tomorrow. That way, I guarantee that the toilets will have hot water by this week at the latest."

"Okay, thank you, Senior! I'm here, you can go up and get the paper."

"Okay, just study with peace of mind. Remember to let me know about any problems in your life, and I will help you with them."

Watching his senior brother rushing up the stairs in high spirits, Qiao Yu took out the key from his pocket, opened the door and entered his room.

There are many feelings. This is probably like giving a rose to someone, and the fragrance lingers on your hand, right? However, he felt that his senior brother's change was too fast and too abrupt, not smooth enough. If it were him, he would definitely not show his joy so early, and couldn't wait to give away benefits... Or maybe he stayed in school for too long!

However, after returning to the room, sitting on the stool, looking at the computer and printer on the table, Qiao Yu fell into deep thought again.

He really couldn't understand why the senior of Director Tian's student couldn't understand Schultz's paper. Was it really that difficult?

Although he had been in Class 13 for a long time and was well aware that some of his classmates were not very smart, his senior was obviously different from his classmates in Class 13. Those who could be admitted to Linhai Jiaotong University could probably be ranked in the top 100 of the key high schools in Xingcheng.

After thinking for a moment, he gave up and took out his cell phone to call Qiao Xi. After all, he had been there for two days and had just met a grandfather today, so he had to inform his mother.

Well, mainly because he missed his mother a little bit. No matter how strong he appeared to be on the outside, he was still only a fifteen-year-old boy after all.

The call was connected quickly, and Qiao Xi's signature lazy voice also made him feel warm.

"Hey, kid."

"Hey, Mom."

"Not bad, remember to call me. I keep seeing videos these days that say their kids go to college, just like a kite that has been let go. If you don't pull it, they will forget they have a home. I figured you're not short of money, and I don't even have a string to pull you through."

"Who is so irresponsible? You can post all kinds of messed up videos! Besides, am I that kind of person? By the way, let me tell you something. I found a grandfather today. That's amazing!"

"Hmm? Do you mean that you think recognizing a grandfather is amazing, or do you mean that the grandfather you recognized is amazing?"

"They are all amazing! After all, ordinary people can't recognize this grandpa!"

"Although your father is indeed a piece of shit, but to claim someone as your grandfather randomly..."

"My grandfather is the teacher of my academician teacher. He is now the No. 1 in the School of Mathematics at Huaqing University and a leading figure in the domestic mathematics community. This means that I not only have the protection of a teacher at Yanbei University, but also a grandfather from Huaqing University. In the game, this is equivalent to stacking two layers of legendary armor. Tell me, isn't that amazing?"

"Tsk tsk tsk, your worthless father doesn't deserve such a father!"

"What a wonderful day! Can we not talk about that man? Is it because after I leave, there is no one to argue with you, and you are too lonely at home? Why don't you come to the capital too?"

"Okay, if you hadn't argued with me, I could have lived ten years longer. But I really shouldn't have mentioned him. It's my fault. You can make your own decisions and don't have to report to me. Anyway, I think you won't suffer any loss wherever you go.

But I won't go to Beijing. Your grandfather has recognized you there. I don't know what to call him if I go there. Don't worry, the Xia family upstairs takes good care of me. By the way, now everyone in the community knows that you went to Yanbei University. The first thing they said to me when they saw me was that they could see that you were different from other children since you were young and very smart.

Congratulations, Qiao Yu, it only took you fifteen years to become the kid that everyone talks about."

"Heh..." Qiao Xi's rare compliment made Qiao Yu smile, and she said, "That's just the beginning! Oh, by the way, speaking of intelligence, Mom, when I was little, was there a moment when you felt that I was already a little abnormally smart?"

"Well, tell me the truth, Qiao Yu, do you think you have ever been normal? What normal kid can keep a bunch of old people of the same age as your grandpa busy every day? What normal fifth-grade kid didn't shed a single tear when his dearest grandpa passed away, but woke up his mother in the middle of the night, yelling in a serious face that he would support the family in the future?
You know what’s the most amazing thing? You actually did it! That’s why I always felt that I was never normal since I was a kid! ”

Well, thinking back on it, Qiao Yu suddenly realized that he had indeed been a little different from other classmates since he was a child. In short, he was indeed not normal.

The case is solved... It's not that the senior brother is too weak, it's mainly because he is too powerful!
"Hey, it seems that the main reason is that my IQ is too high, so I think other people's IQ should be the same as mine, and their poor grades are just due to lack of effort. Oh, I shouldn't bully that idiot in the group."

"What did I tell you? Don't cause trouble outside. Calling someone a fool is causing trouble."

"I'm serious. I've been studying a series of papers recently, and today one of my PhD seniors told me that he couldn't understand them. You have no idea how strange it felt when he said that. I always felt that the proofs were clearly written there, and I couldn't understand why he couldn't understand them."

"Is it possible that they just have a fixed mindset? Are you just younger and more flexible? Or maybe they are not very good at reading papers, but they are much better than you in other aspects. Although you are indeed very smart, you are still a person, right? Aren't all people's IQs about the same?"

“It seems to make sense.”

"Besides, I actually didn't think math was that difficult when I was a kid. At least when I was in high school, I was always second in the school in every math test."

"Oh? Then who is the best in the school?"

"The first one, um, is a man named Feng. He always gets full marks! I don't think he has ever failed once!"

"Cough cough..."

"So, I don't care whether you are smart or not, the most important thing is that you don't learn bad things. No matter where you are in the future, I won't allow your moral bottom line to be lower than that of a man named Feng."

"Don't worry, I have a great character! But mom, you had such good grades back then, you could have repeated your studies for a year after giving birth to me and taken the college entrance exam."

"Firstly, the environment back then was different from now; secondly, I didn't have the heart to study at that time."

"How about this, you start reviewing now. Anyway, the college entrance examination does not reject candidates from outside the society. It's just right for you and Keke to sign up for the college entrance examination together in three years. Then you can come to Beijing together. I will work hard and strive to graduate in three years. Then I will be your teacher."

"Qiao Yu, do you want to listen to what you are saying!"

"Well, being your teacher is of course a joke, but letting you study at home for the college entrance exam is serious. I left my freshman textbooks at home, you can look at them first, and I'll ask my senior to help get a few sets of review materials back, and you can study with Keke. You have to have something to do at home, right? Otherwise, it's so boring to be stuck at home every day!"

There was silence for a long time.

Qiao Yu thought that the other party would not agree, but unexpectedly, his mother asked quietly: "Do you really think I can do it?"

"Of course, you learn English very quickly! And you were always second in math in high school, so you just need to learn it all over again. By the way, I suggest you major in physics, chemistry and biology, so you have more options."

Moreover, these three courses are simple, as long as you understand them, it is not tiring to learn. Chemistry requires more rote memorization. These three courses require experimental exams, but it is not a big problem. I will tell Principal Zhang later that when you need to do experiments, you can go directly to Tieyi Middle School. He will definitely agree. "

"Then let me try?"

"What are you trying for? What did grandpa say? If you want to do something and it's the right thing to do, you have to act immediately. You may change your mind if you delay for even a minute! So act now!
So, I will arrange a study schedule for you later. You will start the evening self-study tonight. Well, today is the math evening self-study! Go to my room and find my math book to see if you still remember the questions. If you don’t remember, you have to start from the beginning of junior high school. "

"Oh, OK, I'll go to your room to study later. But you don't have to arrange the time for me. I'll ask Coco's mom to send me Coco's class schedule, and I'll roughly follow it."

"That's fine. You have to try to concentrate, but studying is not like cooking. It's not a big deal if you get distracted occasionally. Just come back to your senses and continue reading. Maybe studying can improve your concentration. Anyway, you don't need to take the entrance exams for Yanbei or Huaqing. When I came here, I saw a Normal University next to it, which is also quite close."

"Okay, I'm going to read. If you don't understand something, I can ask Coco when she comes back this weekend. Don't worry about it."

"No, shouldn't you ask me?"

"Except for the fact that you are slightly better at math, have you learned other high school knowledge?"

Although it made sense, Qiao Yu still felt despised and retorted righteously: "Please remove the words 'slightly' and 'a little bit'! Thank you!"

"Hang up, I'm going to read a book."

"Well, let's go."

After hanging up the phone, Qiao Yu thought about it and decided to ask Senior Brother Chen to get him some basic physics books tomorrow.

Forget about chemistry, but it is still necessary to learn physics.

After all, both my master's research and Schultz's thesis involve mathematical physics.

It was not about saving face in front of his mother who was preparing to take the college entrance examination. It was mainly because the conversation with Senior Brother Chen made Qiao Yu realize that the breadth and depth of knowledge are equally important.

Anyway, his relationship with Senior Brother Chen has become very close now.

Especially when he said goodbye to Senior Brother Chen today, he looked so excited. Qiao Yu felt that Senior Brother was probably afraid that he would not ask him for anything.

I can only say that although the teacher’s relationship with the master’s grandfather is not very good, the master’s grandfather is still the master’s grandfather, and the title is still very useful.

　The 24st day check-in for the -word update is completed!
　　
　
(End of this chapter)