Zhang Shuwen hesitated for a moment, then stood up, walked to Qiao Yu's side, erased the last writing on the blackboard, and then started to explain on the spot.
"The Riemann-Roch theorem is a basic theorem in algebraic geometry, which is used to describe the dimensions of certain functions or forms on the algebraic curve. Specifically, the Riemann-Roch theorem applies to any divisor D on the algebraic curve X. The theorem states
The dimension of the function space L(D) associated with the divisor D on the algebraic curve.
Its specific statement is (D)=deg(D) 1-g (K-D). It has two parts that complement each other, describing the balance relationship between the divisor D and the remaining part K-D. ​​But there are special cases
, when the degree of D is large enough, (K—D) is zero, so in this case (D)=deg(D) 1—g, do you understand what this means?"
"The degree of D is large enough, and the relationship between dimension and degree is linear." Qiao Yu immediately replied. "Then when D is zero..."
"(0)=1—g (...., Professor Zhang, I understand what you mean.... So this part of the proof does not need to be so complicated, because the genus g(X) can be passed directly through Riemann—
Roch’s theorem shows that, hey, then this part of the proof will not be so troublesome... Let me think about it..."
After speaking, Qiao Yu picked up the chalk and started writing on the other side of the blackboard.
"That is to say, when constructing the function..., dimQH1 (Cp is the dimension of the homology group after quantization, well, it depends on the genus g of the curve and the quantum calculation... This part can be obtained by calculating the canonical factor, H1C
) dimension... So the dimensional relationship after decomposition is directly dimQH1(Cp)=g·f(Q). Professor Zhang, do you think this part of the derivation is correct?"
Zhang Shuwen took a deep breath, keeping his expression calm, and then nodded.
"Great, then the next step is to prove... After deriving the dimension of the homology group, the larger the dimension of the quantized homology group, the higher the geometric complexity of the curve, and the number of rational points on the curve is
will be limited, and Jacobian can further affect the number of rational points.
Genus is one of the core geometric invariants and cannot be simplified, so #C(K)sf(g,Jac(Cp)? Phew, no, looking at it this way, I feel that this method can really give the formula of constant C
Can you deduce it?" Qiao Yu sighed subconsciously.
Really, Chen Zhuoyang in the audience was stunned when he heard Qiao Yu's words.
Although he was also shocked by Qiao Yu's understanding, weren't you really angry when you heard this? How dare you accept a 45-minute seminar when you don't have 100% confidence in proving something? I just saw the conference room and didn't
Chen Zhuoyang naturally couldn't say anything if he seemed to care.
On the stage, Professor Zhang snorted coldly and said: "It's still early, I believe you can prove it and even get a formula you want! But are those really useful?! At least you can
It only makes sense to simplify it to #C(K)sf(g)! It is okay to introduce Peter Schulz's theory. The mathematical proof process can be as complex and abstract as long as it is logic within the framework, but you have to
All complexity is limited to the intermediate steps of the proof!
The final result must be as simplified as possible! Otherwise, even if you prove the constant C and derive the result, and bring in so many set constants, think about how complicated the final formula will be? Others How to use it?
What real mathematics pursues is to complicate thinking and simplify results. Only concise results are truly useful and elegant mathematical tools! Too many constants or parameters will only increase the difficulty of understanding and calculation, and even if they are studied, they will be garbage! Mathematics It’s not as simple as you think!”
Zhang Shuwen's tone was extremely stern, but Tian Yanzhen looked very happy as he sat there.
Robert Green finally couldn't help but came over and asked, "Professor Tian, ​​what are Professor Zhang talking to that child?"
Just now Qiao Yu was using English when introducing his ideas, but when Zhang Shuwen came up to give Qiao Yu some pointers, he had already started using Chinese.
"He taught Qiao Yu not to get carried away, and warned the child that what he was proposing now was just an idea, which was far from producing results, and that mathematical conclusions must be simplified." Tian Yanzhen explained with a smile.
"Oh! God, are Zhang's requirements so strict? Doesn't he know that this child is only fifteen years old? At fifteen years old, he can really understand Schulz's theory and come up with such creative ideas. Zhang still doesn’t think it’s enough? Is he crazy? I even think this is indeed a research direction worth looking forward to in the future.”
Robert Greene said in confusion. Obviously from the perspective of this New York University professor, Zhang Shuwen was too strict, and his requirements for Qiao Yu were even too harsh.
"Yes, this is why I must hold this seminar. I also think this is a possibility worth looking forward to. However, it is still a little difficult for this child to complete this topic independently. So I am actually very grateful to Zhang Professor, at least he told Qiao Yu that subtraction in mathematics is sometimes much more difficult than proving the process itself."
Tian Yanzhen helped Zhang Shuwen explain with a smile on his face.
"Although what Zhang said is very correct, there is no need to use such a harsh tone. This is unfair to a fifteen-year-old child." Robert Green still couldn't understand. After all, if Qiao Yu was his student, There's no way he could be so unkind.
Although he couldn't understand what Zhang Shuwen said, he could tell that the tone was even cold.
"We in China have a saying that deep love leads to deep responsibility. If you are not particularly optimistic, given his character, you will not even bother to say nonsense to this child."
As he spoke, Tian Yanzhen couldn't help but laugh out loud, although it was very suppressed: "Haha, Professor Zhang is probably regretting in his heart that he has never met such a student, right? In fact, I also want to thank Professor Zhang. Originally, these words made me I also want to tell this kid, but I’m afraid it will dampen his enthusiasm.”
Robert Green shook his head. The thinking mode of the Chinese people is too weird. He is incapable of understanding. He does not point out the problem, but thanks others for pointing it out more severely? So if others point out the problem, it will not dampen the enthusiasm of a child. ?In his opinion, students like Qiao Yu should be encouraged more. After all, he is only fifteen years old. Only in this way can he stimulate his love and confidence in mathematics instead of criticizing.
What surprised Robert Green even more was that the child on the stage didn't show any frustration. He was still talking to Zhang Shuwen with a normal expression. Damn it, he couldn't understand Chinese.
..
Yes, Qiao Yu did not feel any frustration on the stage. Facing the serious-looking Zhang Shuwen, he just said seriously: "Thank you, Professor Zhang. I understand. I thought of the problem too simply! But I
I still insist that my idea is correct, and I will definitely prove the result. And this is without setting so many constants!"
Zhang Shuwen's face danced slightly, and he nodded and said: "Well, you are very talented in mathematics, but how to use this talent depends on whether you work hard and what kind of mathematical path you choose to take care of yourself." After saying that, he turned back.
Arrive at your position.
At this time, Tian Yanzhen had already put away his uncontrollable smile, and said calmly as usual: "If you have any other ideas, please tell me. Qiao Yu's idea is definitely not mature enough. Everyone can help."
Help me, a student who is not very successful yet.
Then he turned his head and explained his words in a low voice to Robert Green beside him. The atmosphere in the conference room finally began to become lively.
Just as Tian Yanzhen said, Qiao Yu's idea is very creative, but not mature. Most of the professors Tian Yanzhen invited today have been immersed in the field of algebraic geometry for decades. There are still things that everyone can say.
.Of course, including Robert Greene who came all the way from the other side of the ocean.
In fact, the NYU professor really liked Qiao Yu so much that at the end of the meeting, he took the initiative to say: "Qiao Yu, your name is pronounced like this, right? Maybe you can leave me a contact information.
, I can introduce Peter Schulz to you if I have the opportunity in the future. I believe he also hopes to meet you very much.
Do you know why? Because I think your idea is very creative and very valuable! Oh, by the way, be sure to come to my lecture tomorrow. Believe me, there will be a lot of exciting content next, and you will definitely know it.
There are a lot of gains!" Robert Green expressed his attitude with practical actions, and encouraged Qiao Yu in front of Zhang Shuwen.
"Thank you very much, Professor Robert. In fact, your lecture today gave me a lot of help. I really enjoyed reading your paper. These ideas came to me after reading your paper.
!" Qiao Yu replied, which also made Professor Robert, who came from afar, smile.
When it comes to using processed truth to make people happy, Qiao Yu is even more expert than his mathematical talent, of course, if he is willing...
"I'm going to see off the two professors. You go upstairs and wait for me in Office 301. The door is unlocked. Don't touch the things on the table, but you can read the books in the bookcase as you like." After the seminar, Tian Yan
After Zhen confessed to Qiao Yu, he strode out of the conference room and caught up with Robert Green and Zhang Shuwen.
It was hard to tell from such a spirit that Director Tian was already nearly seventy years old.
Qiao Yu glanced at Xue Song and asked, "Teacher Xue, will you come with me?"
Xue Song shook his head and said, "Are you kidding? You can go to that place, but I won't dare go in without an invitation. Just go and wait."
After saying that, Xue Song packed up his things and left.
Qiao Yu glanced at Senior Brother Chen who was doing the finishing work... Forget it, he would go to the teacher's office by himself.
Senior Brother Chen is good at everything, but he is too serious.
Chen Zhuoyang finally breathed a sigh of relief when he felt Qiao Yu leaving the office. He had to think carefully about how to get along with his junior brother in the future. I must admit that when he met his junior brother for the first time, he seemed to speak a little louder. .On the other side, outside the research center, Tian Yanzhen was seeing Zhang Shuwen off.
Robert Green lived in a hotel just over 400 meters away from the research center. He declined Tian Yanzhen's offer to send him to the hotel and left on his own. The main reason was that everyone was too smart and the foreigner was very knowledgeable. , it can be seen that the two Chinese colleagues have something to talk about.
"Would you like to arrange a car to take you there?" Tian Yanzhen asked casually.
There was nothing to talk about. Although the distance between the two universities was very close, the campus was very big. It would take two or three kilometers to walk back. "No, it's good to walk back. It's not that delicate." Zhang Shuwen replied in a wan tone. sentence.
"Well, I'll give it to you?" "No need."
"Let's see him off. I won't go out until we get to the school gate." Tian Yanzhen insisted. "Then let's go through the east gate." Zhang Shuwen said.
"Aren't you going to hang out by the lake? It will be lively after school starts next week." "No, there will be a chance in the future."
"Well, good!"
After taking two steps in silence, Tian Yanzhen suddenly said sadly, "Mr. Hamilton passed away last year."
Zhang Shuwen was silent for a moment and then said: "Well, respectable old gentleman. You must be complaining in your heart why Simon Donaldson is not the one who died."
Tian Yanzhen smiled and said: "I'm not that mean. At our age, many things have been put aside. But then again, Donaldson is 69 this year!" Zhang Shuwen nodded and said: " Yes, I remember he is one year older than you."
A few simple words from the two of them are the history of the mathematical world.
Both Richard Hamilton and Simon Donaldson are internationally renowned mathematicians, especially the latter, who is a former Fields Medal winner, an academician of the Royal British Academy, a double academician of the National Academy of Sciences of the United States, and has published numerous works. However, There were indeed some minor conflicts between everyone back then.
From ordinary people's perspective, it is probably a very important research result of Tian Yanzhen, but Donaldson's team thinks it is theirs. But the actual situation is actually more complicated, involving the issue of the recognition of papers submitted to pre-release websites in advance. For For new academics, well-known journals that still adhere to double-blind review may reject papers that have been published on the pre-publication website without hesitation, but it is different for these big names.
The proof of an important proposition is often pre-released and reviewed by peers.
The situation at that time was that Tian Yanzhen was the first to publish the results, but Simon Donaldson believed that there were many problems in the proof process, so he published a new paper that solved the same problem, and insisted that Tian Yanzhen's paper was published after pre-publication.
They have made extensive revisions and quoted their process.
It happened many years ago, and apart from the two parties involved, very few outsiders can get a full picture of what exactly happened back then. It’s just that in that international debate, Simon Donaldson’s team had an absolute advantage.
After all, he is a real Fields Medal winner, with a higher rank, a higher reputation in the international mathematics community, and more followers. Even Tian Yanzhen’s mentor supports him.
Tian Yanzhen nodded and continued, "So we are old and need someone to take over. You have trained many young people over the years. I have paid attention to them. Many of them are very powerful and have achieved good results. But China is
It is also true that the voice of the international mathematics community is still not loud enough.
Zhang Shuwen remained silent because this was indeed true.
Since the establishment of the Fields Medal, there has been only one mathematician from China who has won the Fields Medal, but his study experience was mainly in Hong Kong Island and abroad, and he is of Chinese descent rather than Chinese nationality. Although there is only a one-word difference, among them
There are indeed many regrets hidden there. In any industry in this world, strength is valued. If the results are not significant, the right to speak will naturally not be strong.
Tian Yanzhen sighed and continued: "The general direction of China's mathematics research is still towards scientific application. Research must be combined with technological innovation and industrial implementation. Applied mathematics will inevitably receive more support. Academic funds are limited.
Yes, funding for purely theoretical research projects will naturally be cut.
I'm not complaining. After all, this is never something that can be decided by one or two people, but rather the limitations of this era. But in terms of theory, we are already lagging behind. We still have little funding and do not pursue international cooperation. What do you think we should do?
Not to mention that pure theoretical and mathematical research requires not only talent, but also a broad vision."
Zhang Shuwen shook his head and said: "Mr. Tian, ​​I study number theory, and you study geometric analysis. Although I am very grateful for the help you provided me with my doctoral thesis, you should know that I do not want to get involved in any ideas.
Fight."
Tian Yanzhen nodded and said: "I don't mean to let you get involved in any disputes. You should also understand Qiao Yu's talent. I just want to say that although he is my student, first of all, he is also a native of China.
The children who came out.
If he is unknown in the future, it will be fine. But if he really produces results and encounters some bad things in the international mathematics community, I hope everyone can help. He doesn’t have much say in the first place. If the child’s life is still affected by these things,
There’s no point in delaying your future.”
Zhang Shuwen smiled and said: "Mr. Tian, ​​if you don't have the confidence to train a child with such a talent, why not stop being his teacher. And I think he may be more interested in number theory in the future and can be given to
I."
Tian Yanzhen also laughed: "Haha, teacher is just a title. As you know, his understanding of mathematics is not deep enough, and this kid has a wide range of interests. When he came to school on the eighth day of junior high school, I gave him my literature
The account was given to him, and the original intention was to let him download Robert's paper and read it, so that he would not be completely confused during the lecture.
As a result, this kid downloaded five Schulz papers that night and started studying them. After reading them, he even gave himself an exercise on complete space theory. After I gave him a lesson yesterday, I started to read them honestly in the afternoon.
Robert's thesis. As a result, something suddenly happened today. So, if you want to teach him, I have no objection. Why don't you give him your communication method, and I will ask him to read more of your thesis later. What's the point?
If I don’t understand, how about contacting you directly?
Zhang Shuwen frowned again: "What do you mean? He just came into contact with the field of Peter Schulz research in the eighth grade of junior high school, and then he had those ideas and put them into practice directly? Professor Tian, ​​are you really kidding me?"
Tian Yanzhen suppressed his smile and replied seriously: "Yes, if you don't believe it, I have his ticket booking records and the records downloaded in the background of the paper, which I can show you. Of course, don't tell me about you.
I don’t believe it anymore, and I was shocked at the time. If this were not the case, I would not have called you today.”
Zhang Shuwen said seriously: "Okay, let me take a look."
"Huh?" Tian Yan was a little surprised. Good guy, he was just being polite, but he really wanted to see it. But then again, this thing is really hard to believe. And the more experienced you are, the harder it is to believe.
Tian Yanzhen even believed that if Peter Schulz knew that there was a fifteen-year-old child who could understand his proposition just by reading his paper for one night, he would probably find it unbelievable.
Just looking at the evidence so simply seems to show that there is too little trust between them.
This guy can really do it.
However, Tian Yanzhen still took out his mobile phone. Fortunately, the booking for Qiao Yu was not done by someone else...
"Look." Tian Yanzhen handed over the phone calmly: "This is the booking information... Let me show you the background document download record. You don't think I will download it in one go at seven o'clock in the evening.
Let’s read the five Peter Schulz papers?” After reading the records very carefully, Zhang Shuwen fell silent again.
With the thinking mode of a normal mathematician, it is really impossible to understand how a fifteen-year-old child who has not received systematic education can understand Peter Schulz's paper in one night.
After all, the mathematical knowledge involved is very complex, including the most basic linear algebra, abstract algebra, trial analysis and concentration; in algebraic geometry, in-depth study of projective geometry, affine geometry, algebraic varieties and schematic theory, homologous algebra and
More advanced p-adic and p-adic analysis, city-like theory in algebraic number theory, Galois representation, the basis of local domain and global domain, classical Hodge theory and p-adic Hodge theory, complete congruence spaces, homology
and derived categories.
By the way, there is also category theory.
Of course Zhang Shuwen has also studied Peter Schulz's paper, which uses the language of category theory in a large part. Concepts such as categories, functors, and natural transformations are indispensable for understanding his research.
"Of course, he only downloaded five articles and didn't read that much. I talked to him at noon and he only read the 2011 article for the time being." Tian Yanzhen explained again.
The phone was returned to Tian Yanzhen. Zhang Shuwen did not speak, but walked forward driven by instinct. Not long after, the east gate of Yanbei University was in front of him. Zhang Shuwen suddenly stopped, and Tian Yanzhen also stopped.
"Compared with such students, you, as a tutor, are a bit less interesting!" Zhang Shuwen said pertinently.
Tian Yanzhen smiled but said nothing.
If the two exchanged places and he had attended a similar seminar in Huaqing, he would have said the same thing.
Zhang Shuwen added: "Of course, I am also a little behind. But you are right about one thing. This child deserves to be carefully cultivated. I will send you a private email later. If he has any problems in the field of number theory in the future, you can Feel free to send me an email to discuss, and of course you can also leave him my personal phone number."
"Okay!" Tian Yanzhen replied concisely and concisely.
There is no need to emphasize other things. Mathematics also pays attention to the inheritance of a mantle. It is not only the Chinese school, but also the whole world. The Eastern European school, the Soviet school, the Dutch school, the French school, the Swiss school, the American school... all should be there. Yes. It can even be divided into more details. Even if there is no name of teacher and student between Zhang Shuwen and Qiao Yu, there is already a teacher-student friendship. Sometimes the friendship between teacher and student is even more important than the name of teacher-student. reliable.
If a student is really bullied in the future, how can a teacher not come forward to defend him?
Who doesn’t have the mentality to protect their own shortcomings? Of course I, as a teacher, have the right to criticize my own gifted students, but you deserve it too?
When they reached an agreement, Zhang Shuwen couldn't help but ask: "Will the last question he asked for advice have to be forwarded from you before being sent to me?" Tian Yanzhen smiled and said confidently: "No. As for, he is already my student."
"Goodbye." Zhang Shu said simply and concisely. "I won't send you off." Tian Yanzhen nodded.
After bidding farewell to Zhang Shuwen, Tian Yan turned around and walked towards the research center with genuine satisfaction. Qiao Yu was still waiting for him.
All the goals were achieved. Not only did he show off the talented students he discovered, but he also made the other party willing to tutor his students for free, and by the way, he protected Qiao Yu's future...
Zhang Shuwen returned to Huaqing University. He wanted to go back to the hotel to calm down, but he received a message from the old man on WeChat, asking if the seminar was over. After thinking for a moment, he simply came to the old man's office first. There was no other way. He had to accept this old man's favor for many things.
"I'm back." "Yeah."
"Is there really such a student?" Obviously, the old man was also very curious. No matter how brilliant a life is, it cannot withstand the polishing of time.
Why is the Fields Medal only awarded to mathematicians under forty years old? Because everyone knows that people are most energetic and have the most active brains before they are forty years old. After forty years old, even if the body is still healthy,
But his brain power began to decline drastically.
Therefore, there are no big achievements before the age of forty, and after forty, it becomes very difficult.
This is especially true when you are over sixty and gradually enter old age. After time has accumulated, all that is left is experience. At this time, not only can you not keep up with your brainpower, but also your energy. You can probably only put your hope in being able to do scientific research.
A disciple who inherits the mantle. An outstanding student will naturally make the big bosses happy.
Of course Zhang Shuwen knew this mentality, because he was the same, so he chose to come back and answer questions face to face.
"Yes, the talent is amazing! I kept thinking about what kind of talent would allow me to read Schulz's thesis in one night without having much prior exposure to relevant background knowledge, and he was only fifteen years old." The old man
He said decisively: "There is no way there is such a person. You have been deceived. I know my student. He is very experienced in cheating."
Zhang Shuwen was also very emotional, the inheritance of this master...
Anyway, the old man in front of me and Professor Tian across from him ended up having extremely bad relationships with their mentors. The most embarrassing thing is that these two people are both the most accomplished students of their respective mentors. If we look at it as a faction, this inheritance process
In the novel, it has almost become a tradition for the best disciple to turn against his mentor.
But he still shook his head and said affirmatively: "I can tell whether you were deceived or not. I believe that if you go there, you will come to the same conclusion. And even if it is a fraud, the other person is just a fifteen-year-old child.
You know, his mathematical derivation process is extremely rigorous.
And after I pointed out some errors and gave a brief explanation, he was able to quickly understand what I wanted to express, and immediately made corrections and simplifications to the original derivation process. If you want to say that this is a lie...that's just
It can be said that this child’s talent is even higher!”
The old man was stunned, and then asked: "What is the problem? Tell me how the child corrected it immediately."
Zhang Shuwen nodded.
This was also the reason why he didn't reply directly to the message on WeChat, because he knew that when he truthfully affirmed the talent named Qiao Yu, this would definitely happen to him in the end. So he combined Qiao Yu's guesses with the demonstration
The proof process is roughly written down.
"...here, he did not use the Riemann-Roch theorem, but introduced constants to derive the result hard. I simply told him the content of the Riemann-Roch theorem, and he made the following modifications..."Is this an on-site modification?"
"Yes, it will be modified on the spot. My explanation will not exceed three minutes."
The old man closed his eyes, thought for a moment, and said calmly: "There is probably only one possibility. His understanding of Schulz's theory is not at the technical level, but he has understood some essential mathematical things. He
I understand, but actually I don’t understand, or I don’t fully understand.”
This sentence was very mysterious, but Zhang Shuwen understood it, because the nature of mathematics is so mysterious.
However, Zhang Shuwen was not sure. He just nodded and replied: "Maybe, we can't see what's in the child's mind, but whether he understands it or not, it is enough to prove his mathematical talent. At least I can be sure.
The child’s talent is at least no worse than Schultz’s.”
The old man nodded in recognition, sighed deeply, opened his eyes with fighting spirit, and said loudly and firmly: "Shuwen, how can Tian Yan really teach such a student? How can he teach him?"
Can he teach well? He is not qualified to teach! Are you right?"
Zhang Shuwen took a deep breath...
Good guy, how should he answer this?
However, he can also understand that the old man has taught seventy or eighty doctoral students in his life, and it is enough to turn against the student with the highest achievement at that time. However, he has not yet trained a student whose achievements have surpassed him. It was his replacement.
Probably I will never be willing to accept it in this life.
Of course, that's fine if you just stay like this for the rest of your life, but after all, the world of mathematics is about strength.
If the student with whom I have the worst relationship wins the Fields Medal in the future and becomes a new generation leader in the field of mathematics in the future, how will history evaluate the merits and demerits of the two people when the final decision comes? Ordinary
People don't think about this because they don't have the qualifications, but this old man is really qualified to consider it.
As for whether they are qualified to teach, they are already their students, so they can’t be grabbed by force, right?
So Zhang Shuwen chose to remain silent. Speaking of this, it was a household matter belonging to his family. After all, Qiao Yu could be regarded as the disciple of the old man in front of him. Naturally, he would not make any comments. "You didn't ask for the child's contact information.
?" The old man asked again.
Very good, this question can be answered, but are you really trying to steal students?!
However, Zhang Shuwen could only shake his head and replied: "No, it's not convenient. But I left Tian Yanzhen my personal email address and promised that if Qiao Yu has any questions about number theory in the future, he can always contact him
I'll contact you." "Hey, you're confused! Then when do you have to wait? By the way, where did he find this child?"
Zhang Shuwen thought for a while and realized that this was probably not a secret, so he answered: "I was discovered in the CMO. When I came back, I checked and found that he was ranked first in the CMO this year and one of the only two players with perfect scores.
." "My name is Qiao Yu, right? OK, I'll go ask."
"Then Mr. Zhengxin, I'm going back to the hotel first." "Go ahead, you have a good rest first."
.
On the other side of the street, at Yanbei University, Tian Yanzhen returned to his office.
As soon as he entered the door, he saw Qiao Yu curled up on the sofa and reading quietly. When he saw him coming in, he jumped up quickly. Although Tian Yanzhen generally didn't like students with irregular sitting postures, he just smiled and didn't
What can I say? After all, you are only fifteen years old. It is normal to have some shortcomings. As the saying goes, no one is perfect.
Well, to put it bluntly, people love their homes and their homes.
This is human nature. If you change a nasty person, you may be sent to the eighteenth level of hell just by sitting in the same position.
"Director Tian, ​​you are back." Qiao Yu greeted him proactively and enthusiastically. "Well, what are you reading?"
"Um..." Qiao Yu picked up the book again and looked at the cover before saying, "It's "Visualizing Differential Geometry and Forms" by Needham." This book is a very good introductory book to differential geometry. You will bring it later. Let’s go.” Tian Yanzhen said with a smile.
"Thank you, Director Tian." Qiao Yu thanked her quickly, then looked around and said, "Do you want some water? I'll get you some water." "No, no, just sit down."
"Oh, okay." After saying that, Qiao Yu sat down opposite Tian Yanzhen in a polite manner. He still wouldn't be so presumptuous when someone else was around.
"What Professor Zhang said to you at the seminar today didn't shock you, right?" Tian Yanzhen asked.
"No, I think Professor Zhang is right. If the result is too complicated, it is of little use." Qiao Yu said seriously.
"Although I say this, it cannot be said that it is completely useless. As I told you at noon, the thinking you did during the derivation process is actually a very valuable asset. With the development of mathematical research to this day, not all Propositions, like calculus, were invented to solve practical problems.
Just like some mathematical results, we may not see any use within a certain period of time. But maybe hundreds of years later, it will become a standard fact and an exercise. For other scientists, the proven results are like buying Returning the elite box to Juli, the proof is that it is the bead inside.
For others, it's just the opposite. This is also the most charming part of mathematics, so you don't need to be discouraged at all, understand?" Tian Yanzhen taught patiently.
"Don't worry, Director Tian, ​​my mentality is very stable. I'm a newbie in mathematics anyway. What should I be afraid of, right? Besides, my goal is that my future results, whether for myself or for others, will be that good." A bead! Mathematics may not be that simple, but I don’t think it’s so difficult that it would make me despair!”
Qiao Yu said confidently.
A newborn calf is not supposed to be afraid of tigers. Compared with the goals he hides in his heart, where is he?
If he can't even become a great mathematician who is influential in the mathematics world, Qiao Yu doesn't think he will have a chance to realize his wish in the future. After all, in any industry, only by achieving the ultimate goal can one become rich.
Qiao Yu's good attitude obviously comforted Tian Yanzhen, and he couldn't help but put a smile on his face: "It's good that you have this attitude. In addition, you also felt today that the basic knowledge of all aspects of mathematics is also very good." important.
Although Professor Xue and I feel that there is no need to define a curriculum for you, you still have to make up for this. This is a book list I drew up for you last night with reference to the catalog of the Yanbei University Library. You can arrange it every day from now on. When you have time to study, you have to read papers, and you also have to read these books."
After saying that, Tian Yanzhen picked up two printed book lists from the table and handed them to Qiao Yu.
"Thank you, Director Tian." Qiao Yu took the book list and looked at it. Good guy, it was printed out in two densely packed pages. They were all foreign works. The English titles written directly were not translated versions. He couldn't help but subconsciously
I muttered: "So many?" "You don't need to read them all. This book list has two stages. The books included in the first stage belong to the basic category.
No matter whether you are interested or not, you must read them all. For those books in the second stage, you can choose the areas of interest for further reading. In this way, after one year at most, you should understand which area of ​​mathematics you are more interested in, and you will also
You can't always go here and there. Your age is the most suitable time to devote yourself to study, and you can't waste even half a year."
Having said this, Tian Yanzhen also became serious.
Qiao Yu rolled his eyes and immediately agreed: "Don't worry, Director Tian, ​​I will start reading these books tomorrow. But speaking of saving time, I have something to ask you. See if you can help me think of a solution.
?" "What do we, master and disciple, do not want? As long as you think it will be beneficial to your study, feel free to ask for anything you need." Tian Yanzhen replied cheerfully.
"Look, isn't the first phase of IMO special training about to begin next month? During this period, I want to take more time to think about this proposition. Do you think I can just do the special training directly at Yanbei University?
So that I don’t have to waste time running around.”
Qiao Yu immediately put forward the request that he had wanted for a long time. To be honest, this was indeed not an excessive request.
But Tian Yan really thought about it and asked, "Do you want to participate in IMO? In fact, based on your current situation, whether to participate in IMO is not that important."
Qiao Yu quickly shook his head and said: "No, Director Tian, ​​you promised me to participate in 1MO at the beginning, and our Xingtie No. 1 Middle School has never had a 1MO gold medalist before, so I agreed to my request.
My alma mater must achieve this zero breakthrough." Tian Yanzhen smiled and said:
"Okay, this is indeed a serious matter. I will make a suggestion to the Mathematics Society. But first, I am just going to make a suggestion. As for whether it can be done, I dare not give you a guarantee now, in case the special training location has been determined.
It can’t be changed, and there’s nothing I can do about it.”
"It would be great if you could give me some advice. If it doesn't work, there's nothing I can do about it. By the way, since you always have to give advice to the Mathematical Society, why not give me another suggestion by the way? The next sentence in March is special.
Just pick a school in Star City for training.
This is really not what I want. The main reason is that I promised Principal Zhang that after the second phase of special training is over, I will go back to my alma mater to give a mobilization speech to the senior high school graduates. My alma mater is very good to me, and I can’t keep my promise.
.........Hey." After all, it must be a good thing if your students are grateful.
I can only say that using the alma mater complex as a reason is really too reasonable, so reasonable that Tian Yanzhen doesn’t know how to refuse.
So Tian Yanzhen agreed without hesitation: "Okay, but again, I can't promise you anything now. After all, it depends on whether any school in Star City applies to host this event. The Mathematics Association and the local
The school I attended was not affiliated with the school.
Tie."
"Thank you, Director Tian."
"Are you still used to your life? Do you have any other needs?" Tian Yanzhen asked again.
"There's nothing else. In fact, I'm quite used to it, and the food in the cafeteria is also very satisfying. By the way, Teacher Xue asked me to tell you that I will definitely need a printer in the future, but I think it's okay for the time being. There's no need to use this, right?" Qiao Yu thought
After receiving Su Song's explanation, he said casually.
Tian Yanzhen said without hesitation: "This is really necessary. Professor Xue is a good and attentive person. Tell your senior brother Chen directly about this matter. Just tell him what I said and ask him to switch to one with you. By the way, He will help you install and debug it."
"Um? Isn't it too bad to bother senior brother with this matter?"
"It's okay, we are all senior brothers, what's the trouble? Forget it, I'll tell him later."
"Oh, then I have nothing else to do."
"Well, then you go to eat first. By the way, start reading the books on the list as soon as possible. I will check them every week."
"Don't worry, Director Tian. I know you are all doing this for my own good, so you don't have to worry about random checks in your busy schedule. From now on, I promise to report to you on time on WeChat before ten o'clock every Monday morning. My reading progress and experience gained during the week, I have forgotten how you can criticize me!"
Look, a student who is extremely talented and can be so humble and obedient, how can a tutor not be confused?
Really, Tian Yan really tried his best to control his expression to avoid laughing too heartily.
Even Su Song, who introduced Qiao Yu to him, became even more impressive in Tian Yanzhen's mind.
If he followed his original idea and waited step by step until the IMO results came out before going for the interview, he might really be beaten by the other party. Who could he talk to to reason with him?
"As long as you have this intention."
"Then I'm going to eat first, Director Tian."
"Go on, eat more, and be sure to keep up with your nutrition studies! If you don't have enough living expenses, just tell me first."
"Okay, Director Tian! Don't worry, I'm never polite to my teacher."
Well, Qiao Yu said this sentence sincerely, literally.
Tian Yanzhen smiled as he watched the flying Qiao Yu turn and leave.
Chapter completed!