Chapter 106 Mathematics is not that simple... but it is not difficult either!
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 algebraic curves. Specifically, the Riemann-Roch theorem applies to any Divisor D, 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)+1g+(KD). It has two parts that complement each other, describing the balanced relationship between the divisor D and the remaining part KD. But there are special cases when the degree of D is large enough, (KD). is zero, so in this case (D)=deg(D)+1g, do you understand what this means? "
"The degree of D is large enough, and the relationship between dimension and degree is linear." Qiao. Yu replied immediately.
"Then when D is zero..."
"(0)=1g+(K)...Oh, Professor Zhang, I understand what you mean...So this part of the proof does not need to be so It’s cumbersome, because the genus g(X) can be obtained directly through the Riemann-Roch theorem. Hey, then this part of the proof will not be so troublesome... Let me think about it..."
After that, Qiao Yu picked up the chalk and started writing on the other side of the blackboard.
"That is to say, when constructing a function... Well, dimQH1 (Cp is the dimension of the homology group after quantization, well, it depends on the genus g of the curve and the quantum operator Q... This part can By calculating the canonical factor, Obtain the dimension of H1(Cp)...
So the dimensionality relationship after decomposition is directly dimQH1(Cp)=gf(Q). Professor Zhang, do you think this is the derivation of this part? ”< br>
Zhang Shuwen took a deep breath, keeping his expression calm, and then nodded.
“Great, then the next step will be easy 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. The number of rational points will be limited, and the Jacobian can further affect the number of rational points...< br>
Genus is one of the core geometric invariants and cannot be simplified, so #C(K)≤f(g,Jac(Cp))? Huh, no, looking at it this way, I feel like this method Can you really deduce the formula of constant C? "
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 everyone really angry when they heard this?
How dare you accept a 45-minute seminar when you have nothing to prove with 100% confidence?
Just seeing that no one in the conference room cared, Chen Zhuoyang naturally couldn't say anything.
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? ? ! You have to at least simplify it to #C(K)≤f(g) One step only makes sense!
It is okay to introduce Peter Schulz’s theory. As long as the mathematical proof process is logical within the framework, it can be complex and abstract, but you must limit all complexity to An intermediate step in the proof!
The end result must be as simple as possible! Otherwise, even if you prove the constant C and derive the result, if you bring in so many set constants, think about how complicated the final formula will be? How can others take advantage of it?
The pursuit of real mathematics 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 researched, they will be rubbish! Mathematics is 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 come over and ask Said: "Professor Tian, what are Professor Zhang saying to that child? ”
Just now Qiao Yu used English when introducing his ideas, but when Zhang Shuwen came up to give Qiao Yu some advice, he had already started using Chinese.
"He taught Qiao Yu not to get carried away, and warned his children 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 can think up freely Such a creative idea, 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 Green said in confusion. Obviously from the perspective of the New York University professor, Zhang Shuwen was too harsh. Qiao Yu's requirements 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 currently a little difficult for this child to complete this proposition independently. So I am actually very grateful to Professor Zhang. At least he told Qiao Yu that subtraction at the mathematical level is sometimes much more difficult than the proof process itself. ”
Tian Yanzhen helped Zhang Shuwen explain with a smile on his lips.
"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 It was incomprehensible. After all, if Qiao Yu was his student, he would never 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 brings deep responsibility. If you are not particularly optimistic, given his character, you will not even bother to say nonsense to this child."
As he said this, 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. I originally said these words in my afternoon I also want to tell this kid, but I’m afraid it will dampen his enthusiasm.”
Robert Green shook his head. The Chinese people’s thinking mode is too weird, and he is incapable of understanding. Don't point out the problem yourself, but thank others for pointing it out more severely? So if others say it, it won’t dampen a child’s enthusiasm?
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 could not see any frustration. Still talking to Zhang Shuwen with a normal expression.
Damn, he can’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 was the one who solved the problem." It's too simple!
But I still insist that my idea is correct, and I will definitely prove the result. Without setting so many constants!”
Zhang Shuwen’s face brightened slightly, and he nodded and said: “Well, you are very talented in mathematics, but how to use this talent depends on your own efforts. And what kind of mathematical path to choose to take care of yourself."
After saying that, he turned around and returned to his seat.
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 good at the moment."
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 became lively.
Just as Tian Yanzhen said, Qiao Yu’s idea is very creative, but not mature. Most of the professors invited by Tian Yanzhen today have been immersed in the field of algebraic geometry for decades. You can There is still something to 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 you to Peter Schulz if I have a chance in the future. I believe he would also like to meet you.
Do you know why? Because I think your ideas are 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 gain a lot! ”
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 has given me a lot of help. I really enjoyed reading your paper. I only came up with these ideas after reading your paper. It just popped out of my head!"
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 the things in the bookcase You can read whatever you want."
After the seminar, Tian Yanzhen told Qiao Yu, then strode out of the conference room and caught up with Robert Green and Zhang Shuwen.
It’s hard to tell that Director Tian is already nearly seventy years old.
Qiao Yu glanced at Xue Song and asked, "Teacher Xue, will you go with me?" Go in. Just go and wait."
After that, Xue Song packed up his things and left.
Qiao Yu glanced at Senior Brother Chen who was doing the finishing work again...
Forget it, he should 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 have to admit that the first time I met my junior brother, 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 on foot from the research center. He declined Tian Yanzhen’s offer to send him to the hotel and left on his own. The main reason is that everyone is too smart, and the foreigner is very knowledgeable, and he can tell 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.
It’s not that I have nothing to talk about. Although the two universities are very close to each other, the campuses are huge. It takes two or three kilometers to walk back.
"No, it's good to walk back. It's not so delicate." Zhang Shu replied in a wan tone.
"Well, I'll give it to you?"
"No need."
"It's better to send him off. I won't go out when we get to the school gate." Tian Yanzhen insisted.
"Then take the east gate." Zhang Shuwen said.
“Don’t go to the lakeside for a stroll? It will be lively after school starts next week.”
“No, there will be a chance in the future.”
“Well, okay!”
After taking two steps in silence, Tian Yanzhen suddenly said with regret: "Mr. Hamilton passed away last year."
Zhang Shuwen was silent for a moment and said: "Well, respectable old gentleman. You must be in my heart. Complain, why wasn’t Simon Donaldson 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 was one year older than you.”
The two of them shared a few words of history in the world of mathematics.
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 Academy of Britain, and a double academician of the National Academy of Sciences of the United States. He has written numerous books.
However, there were indeed some minor conflicts between everyone back then.
From an ordinary person'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 recognition of papers submitted to pre-release websites.
For academic newcomers, well-known journals that still pursue double-blind review may reject papers that have been published on the pre-release website without hesitation, but it is different for these big guys. .
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. Made extensive revisions and cited their process.
This happened many years ago. What was the specific situation back then? Apart from the two parties involved, few outsiders can get a full picture.
Only 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 supported the opponent.
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. achievements. But it is also true that China’s voice is still not loud enough in the international mathematics community.”
Zhang Shuwen remained silent because this was indeed true.
Since the establishment of the Fields Medal, there has only been one mathematician from China who has won the Fields Medal, but his main academic experience was in Hong Kong Island and abroad, and he was of Chinese descent rather than Chinese nationality. Although it is only one mathematician, The words are different, but there is indeed a lot of regret hidden in it.
Any industry in this world is based on strength. If the results are not significant, the right to speak will naturally be weak.
Tian Yanzhen sighed and continued: "The general direction of Chinese mathematics research is still the development of scientific applications. Research must be combined with technological innovation and industrial implementation. Applied mathematics will inevitably receive more support. . Academic funds are limited, and funds for purely theoretical research projects will naturally be cut.
I. Not complaining. After all, this is never something that can be decided by one or two people, but it is the limitation of this era. But in terms of theory, we are already lagging behind, have insufficient funds, and do not pursue international cooperation. What should we 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. "
Tian Yanzhen nodded and said: "I have no intention of letting you get involved in any disputes, Qiao Yu. You should also understand his talent. I just want to say that although he is my student, first of all, he is also a child cultivated by our Chinese people.
It will be fine if he becomes unknown in the future, but if he really makes it. As a result, I have encountered some bad things in the international mathematics community. I hope everyone can help me. I don’t have much say. It would be meaningless if the child's future is delayed because of this."
Zhang Shuwen smiled and said: "Mr. Tian, if you don't have the confidence to train a child with such a talent, why not. Don’t be his teacher. And I think he may be more interested in number theory in the future, so he can leave it to me.”
Tian Yanzhen also laughed: "Haha, teacher is just a title. You also know that his understanding of mathematics is not deep enough, and this kid has a wide range of interests. I put him in the school where he came on the eighth day of the junior high school. I gave him my literature account to let him download Robert's papers and read them, so that he would not understand them at all during the lecture
As a result, this guy 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 went to train him yesterday, I honestly read Robert's papers in the afternoon.
As a result, something suddenly happened today. So, if you want to teach him, I have no objection at all. Why don't you give him your communication information, and I'll ask him to read more of your paper later and contact you directly if he doesn't understand anything? "
Zhang Shuwen frowned again: "What do you mean? He had just come into contact with the field of Peter Schulz's research in the eighth grade of junior high school, and then he had those ideas and directly implemented them? Professor Tian, are you really not joking? "
Tian Yanzhen suppressed a smile and replied seriously: "Yes, if you don't believe it, I have his ticket booking records and the background download records of the paper, which can be opened to you. look. Of course, don’t say you don’t believe it, I was also shocked at the time. If this weren't the case, I wouldn't be calling you today. "
Zhang Shuwen said seriously: "Okay, let me take a look. ”
"Huh?" Tian Yan was really surprised. Good guy, he was just being polite, but he really wanted to see it. But then again, this is really hard to believe. And the more experienced you are, the harder it is to believe it.
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 man 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...
"Take a 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 five articles in one go at seven o'clock in the evening. Let’s read Peter Schulz’s paper?”
After reading the record 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 complicated, including the most basic linear algebra, abstract algebra, real analysis and complex analysis; in algebraic geometry, in-depth study of projective geometry, affine geometry, algebraic varieties and schematic theory is required , homologous algebra ;
There are also more advanced p-adic and p-adic analysis, quasi-field theory in algebraic number theory, Galois representation, the basis of local fields and global fields, classical Hodge theory and p-adic Hodge theory Singular theory, complete congruence spaces, homology and derived categories.
By the way, there is also category theory.
Of course I have also studied Peter Schulz’s paper Zhang Shuwen, which used the language of category theory for 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 was not talking. He was just walking forward driven by instinct. Not long after, the east gate of Yanbei University was in front of him. Zhang Shuwen suddenly stopped and Tian Yan Shin 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 had switched places and he had attended a similar seminar in Huaqing, he would have said the same thing. Zhang Shuwen added: "Of course, I am 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 Send me an email to discuss at any time. Of course, you can also leave my personal phone number with him."
"Okay!" Tian Yanzhen said concisely.
There is no need to emphasize anything else. Mathematics also pays attention to the inheritance of a mantle. Not just China, but the whole world. Eastern European style, Soviet style, Dutch style, French style, Swedish style, American style... everything that should be included is available. It can even be divided into finer details.
With this statement, Zhang Shuwen and Qiao Yu already had a teacher-student relationship even though they were not named teachers and students. Sometimes the friendship between teachers and students is even stronger than the name of teachers and students.
If a student is really bullied in the future, how can a teacher not come forward to defend him?
Who doesn’t have a protective mentality anymore? Of course I, as a teacher, have the right to criticize my own gifted students, but do you deserve it?
When an agreement was reached, Zhang Shuwen couldn't help but ask: "Will the last question he asked for advice have to be forwarded from you before it is sent to me?"
Tian Yanzhen smiled and said confidently: "No, he is already my student."
"Goodbye." Zhang Shu said simply and concisely.
"No." Tian Yanzhen nodded.
After bidding farewell to Zhang Shuwen, Tian Yan turned around and walked towards the research center with great 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 and 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 way, he had to accept the old man's affection for many things back then.
"Come back."
"Hmm."
"Is there really such a student?" Obviously, the old man was also curious.
No matter how brilliant your life is, it cannot withstand the polishing of time.
Why is the Fields Medal only awarded to mathematicians under the age of 40? Because everyone knows that people are most energetic and their brains are most active before the age of forty. After the age of forty, even if the body is still healthy, the brain power begins to decline severely.
So there is no big achievement before the age of forty, but after forty, it becomes very difficult.
This is especially true after sixty and gradually entering old age. After time has settled, all that is left is experience. At this time, not only the brain power but also the energy cannot keep up with scientific research. I can probably only place my hope on the disciples who can inherit the mantle.
An excellent student will naturally make the bosses happy.
Of course Zhang Shuwen knew this mentality, because he was the same, so he chose to come back and answer his questions face to face.
“Yes, the talent is amazing! I kept thinking about what kind of talent it is that can read Schulz’s paper in one night without having much relevant background knowledge before, and he is just Fifteen years old.”
The old man said decisively: “It’s impossible. You have been deceived by such a person. I know my student, he is very experienced in cheating."
Zhang Shuwen was also very emotional, this teacher's inheritance...
Anyway, he is very experienced. The old man and Professor Tian opposite him ended up having extremely bad relationships with their mentors. The most embarrassing thing is that these two are the most accomplished students of their respective mentors. If viewed as a faction, in the process of inheritance, it has almost become a tradition for the best disciples to turn against their mentors...
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 do it quickly. Quickly understand what I want to express, and immediately make corrections and simplifications to the original derivation process. If you want to say this is fake... you can only say that this child is more talented!"
The old man! He was stunned, and then asked: "What was the problem, tell me, and how did the child correct it immediately."
Zhang Shuwen nodded.
This is also the reason why he did not reply directly to the message on WeChat, because he knew that when he truly affirmed the talent named Qiao Yu, this would definitely happen to him in the end.
So he roughly wrote down Qiao Yu's conjectures and the demonstration process.
“…here he did not use the Riemann-Roch theorem, but introduced constants to hard-deduct the result. I simply told him the content of the Riemann-Roch theorem, and he made the following modifications…”
“Is this an on-site modification?”
“Yes, on-site modification, mine The explanation will take no more than 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 understood something intrinsic to mathematics, but he didn’t understand it, or he didn’t fully understand it.”
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 responded: "Maybe, we can't see what is in that child's mind, but whether he understands it or not, it is enough to prove his mathematical talent. At least I can be sure that this child’s talent is at least no worse than Schultz’s.”
The old man nodded in approval. , sighed deeply, opened his eyes with fighting spirit, and said loudly and firmly: "Shuwen, how can Tian Yan teach such a student? How can he teach well? How can he teach well? He doesn't deserve it. Teach me! Are you right?"
Zhang Shuwen took a deep breath...
Good guy, how should he answer this?
But he can also understand the old man. He has trained seventy or eighty doctoral students in his life, so it is enough to turn against the most accomplished student at that time. Unfortunately, he has not yet trained a student whose achievements have surpassed the other's.
If it were him, he probably wouldn't be willing to accept it in his lifetime.
Of course, that’s fine if you just stay like this for the rest of your life, but after all, the world of mathematics also requires 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 mathematics, how will history evaluate these two people when the final decision is made in the future? The merits and demerits of
Ordinary people would not consider this because they are not qualified, 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 family matter belonging to his family. After all, Qiao Yu could be regarded as the disciple of the old man in front of him, so he naturally 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? !
But 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 studies number theory in the future, If you have any questions, you can contact me at any time.”
"Hey, you are confused! Then when do you have to wait? By the way, where did he find this child?"
Zhang Shuwen thought for a while, this probably couldn't be a secret, and then answered Said: "I discovered it from the CMO. When I came back, I checked and found that it was the CM of this year. O ranks first, one of the only two players with perfect scores."
"My name is Qiao Yu, right? I'll ask."
"Mr. Zhengxin, I will. Let’s go back to the hotel first.”
“Go and have a good rest first.”
...
On the other side of the street, at Yanbei University, Tian Yanzhen returned to the office.
As soon as he entered the door, he saw Qiao Yu curled up on the sofa and reading a book 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 said nothing.
After all, you are only fifteen years old, and 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.
"Director Tian, you are back." Qiao Yu greeted him proactively and enthusiastically.
"Well, what book are you reading?"
"Um..." Qiao Yu picked up the book again and looked at the cover before saying: "It's "Visualized Differential Geometry and Sums" by Needham. "Form"
"This book is very good as an introductory book on differential geometry. You can take it with you later." Tian Yanzhen said with a smile.
"Thank you, Director Tian." Qiao Yu thanked him 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 won't be so presumptuous when someone is 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 indeed of little use." Qiao Yu said seriously.
"Although I say this, it cannot be said to be completely useless. As I told you at noon, the thinking you made during the derivation process is actually a very valuable asset. Development of Mathematics Research Until now, not all propositions were invented just to solve practical problems like calculus.
Just like some mathematical results, we may not be able to see them in a short time. What's the use? But maybe hundreds of years later, it will be a standard fact and an exercise. For the mathematician himself, the result of the proof is like the beautiful box in which the pearls are returned, and the proof method is the pearl 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. I have a very stable mentality. 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 should not be afraid of tigers. Compared with the goal he hides in his heart, where is this!
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 wealthy.
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 don’t think we need to outline the course for you, You still have to make up for this. This is a book list I drew up for you last night by referring to the catalog of the Yanbei University Library. From now on, you can arrange your study time every day and read these papers. You must also 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 on two densely packed pages. They were all foreign works. The English titles written directly were not translations. , I couldn't help but muttered subconsciously: "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. Whether you are interested or not, you must read them all. The books in the second stage Books, you can choose the areas of interest for further reading
After a year at most, you should know which area of mathematics you are more interested in. You can't always move from one field to another. Your age is the best time to devote yourself to studying, and you cannot waste even half a year. "
Speaking of this, Tian Yanzhen became serious.
Qiao Yuze 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. Can you help me figure it out? ”
“What do we, master and disciple, do not want? As long as you think it will be beneficial to your study, feel free to mention anything you need. "Tian Yanzhen replied cheerfully.
"Look, isn't this the first phase of IMO special training that will begin next month? During this period, I want to take more time to think about this proposition. Do you think you can just do the special training at Yanbei University, so that I don't have to waste time running around? ”
Qiao Yu immediately made the request that he had wanted for a long time.
To be honest, this is 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 shook his head quickly He shook his head and said: "No, Director Tian, you told me to participate in IMO at the beginning, and our Xingtie No. 1 Middle School has never produced an IMO gold medal player before, so I don't I promised my alma mater that we must achieve this zero breakthrough."
Tian Yanzhen smiled and said, "Okay, this is indeed a serious matter. I will make a suggestion to the Mathematical Society, but let's make a deal first. I’m just going to make a suggestion. As for whether it will work, I don’t dare to give you a guarantee now. If the special training location has been determined and cannot be changed, there is nothing I can do.”
"It would be great if you could give me some advice. If it really doesn't work, there's nothing we can do about it. By the way, since you always have to give advice to the Mathematics Society, why not give me another suggestion by the way? Special training in late March. I might as well just choose a school in Star City.
This is not really what I want to do, it’s mainly because I agreed. Principal Zhang, when the second phase of special training is over, I will go back to my alma mater to give a motivating speech to the senior high school graduates. My alma mater has been very good to me, so I can’t keep my promise..."
It can only be said that using the alma mater complex as a reason is really too reasonable. It is so reasonable that Tian Yanzhen doesn’t know how to refuse.
After all, it must be a good thing if your students are grateful.
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. Activities, the Mathematics Society is not affiliated with local schools.”
"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... Oh, by the way, Teacher Xue asked me to tell you that I will definitely need a printer in the future. But I think there is no need to use this for the time being, right?" Qiao Yu said casually, thinking of Xue Song's explanation.
Tian Yanzhen said without hesitation: "This is really necessary. Professor Xue is a good and attentive person. Tell me directly to Senior Brother Chen about this matter. Just tell him what I said and let him coordinate with you." Let’s take one and let him help you install and debug it.”
“Um? It’s not a good idea to bother my senior brother about this, isn’t it?”
"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 book list as soon as possible. I will check them every week."
"Don't worry about that, Tian Director. 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 every Monday my reading progress and learnings on WeChat. , forget how you criticize me!”
Look, how can a tutor who is such a humble and obedient student not be confused?
Really, Tian Yan really tried his best to control his expression to avoid laughing too heartily.
Even Xue Song, who introduced Qiao Yu to him, became 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 actually be beaten away 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, eat more, and you must 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 will never be polite to the tutor. . ”
Well, Qiao Yu said this very seriously, literally.
Tian Yanzhen smiled as he watched the flying Qiao Yu turn around and leave.
Although Zhang Shuwen's personal email address has been sent to him, he was not in a hurry to give it to Qiao Yu today. After all, this child has not shown any special interest in number theory. He will wait until Qiao Yu finds his interest. Let’s talk about it later.
Thanks to Fenglin Wuhen, Book Friends 20210301106522696680, Zaizanglu_Delumengyu, and hikarusin for their rewards and encouragement!
PS: The 10,000-word update has been completed on the 21st day!
(End of this chapter)