Chapter 143 Yes, that’s it!
The next day, early morning, Shaoyuan Canteen.
"I thought about it for a long time last night. I am definitely not a math genius. Because I am different from you, and I am different from that man.
For example, you can easily get full marks in high school math , but I can't. I often make mistakes, both in the past and now.
And at my age, I can't be as shameless as you, so don't expect me to say nice things in front of Academician Yuan like you did with Coco.
If Academician Yuan asks me a question, I will say yes if I know it, and if I don’t know it, I won’t. I don’t know how to pretend not to understand, nor do I know how to pretend to understand. Don't get your hopes up too high. ”
While eating breakfast, Qiao Xi gave Qiao Yu a vaccination.
What she said made Qiao Yu, who was originally confident, a little uneasy.
< br>Qiao Xi thinks Qiao Yu is a bit boring, so fart The matter will also alarm the academician
Qiao Yu really wants Qiao Xi to be valued by Mr. Yuan and come to the capital in the future. Not only will he be closer to Qiao Xi, but the key is that he can discuss it with Qiao Xi in the future. Mathematical content and then despise her
Anyway, no matter how strong Qiao Xi is, she can't be stronger than him.
"I know! We are all wild people anyway, but I still think that people who can casually read Schulz's papers must be talented."
Qiao Yu ate with a dull head. Congee and steamed buns, no longer too lazy to argue with Qiao Xi. Anyway, you will know it when you get to Huaqing.
The two sides were very close and they were not in a hurry. Qiao Yu did not use the number given to him by Director Tian and took Qiao Xi directly to Qiuzhai in Huaqing.
Actually, apart from the road section, the scenery on both sides of the campus is pretty good, especially the road from Huaqing to Qiuzhai.
But the most important thing is that even though it is already July, the mornings in Star City can already make people sweat on their foreheads. The temperature in the capital is only around 20 degrees, making it very comfortable to walk on the road.
Twenty minutes later, Qiao Yu led Qiao Xi into Mr. Yuan's office.
What surprised him was that Professor Tan was also there.
After the greetings, the four of them sat on the sofa where the old man was entertaining guests, and each had a cup of still-smoking hot tea in front of them.
Qiao Xi also immediately sincerely apologized to the old man on behalf of Qiao Yu: "Mr. Yuan, Qiao Yu was really reckless yesterday. In fact, I can only say that mathematics is a hobby at best.
I really don’t think he has much talent. More than ten years ago, when I was in high school, I didn't show much ability in mathematics. It was even difficult for me to get full marks on high school exam papers. "
Mr. Yuan smiled and shook his head and said, "Apart from this, whether you have mathematical talent or not is a trivial matter. But the idea you proposed yesterday, Lu Yuan and I both find it very interesting. I just invite you to come and have a casual chat today. ”
This sentence also made Qiao Xi feel relieved and she became more relaxed.
The mother is still afraid that because of herself, the boss will treat Qiao Yu a little more. Harsh.
So the four of them chatted about something, and then the old man praised Qiao Yu again, and then slowly turned to the topic of mathematics.
"By the way, Qiao Xi, I heard Qiao Yu say yesterday that you could understand Schulz's paper independently?"
Professor Tan asked casually.
Qiao Xi thought for a while and replied pertinently: "Part of it. I can't say that I fully understand it."
"Do you have a foundation in advanced mathematics?" Professor Tan asked.
"I occasionally looked through the mathematics books that Qiao Yu borrowed before, such as linear algebra, calculus and mathematical analysis. I have read more documents during this period."
Qiao Xi answered casually.
“Oh, if you were asked to choose one between linear algebra and calculus, which one do you think is more interesting, relatively speaking, which one do you think it would be?”
“That should be linear algebra. "
Qiao Xi thought for a while and said.
Professor Tan smiled, then looked at Mr. Yuan, thought for a while, and said: "There is such a sequence, the first three numbers are, 1, 3, 7... Do you think according to this rule , what should the fourth number be? ”
When Professor Tan started to ask questions, Qiao Xi was not doing well yet, but Qiao Yu sat upright first.
“23.” Qiao Xi gave an answer casually.
Tan Luyuan nodded and asked with a smile: "Think about it again, if there is a 3X3 square grid, the starting point is in the upper left corner and the end point is in the lower right corner.
The rule is You can only move right or down, don't draw a picture, your first impression is that there are several different paths from the starting point to the end point." Qiao Xi smiled and replied.
Tan Luyuan nodded, and then found that Qiao Yu seemed to glare at him secretly...
At first, he was a little stunned, but he figured it out in an instant. Maybe he thought the question he asked was too simple?
But he ignored it, just smiled and asked: "Qiao Xi, have you ever studied graph theory?"
Qiao Xi shook her head and said softly: "No, I’ve never been exposed to it.”
Tan Luyuan said with a smile: “It’s okay, let me explain two concepts to you. There is a basic structure in graph theory called an undirected graph, which is composed of vertices and edges, and the edges represent vertices. The connection relationship between them is characterized by the fact that the edges have no direction.
For example, if there is an edge u, v, then it can be connected from u to v or from v to u, and the relationship between the two is equivalent.
A loop refers to a path that starts from a certain vertex, passes through a series of edges and vertices, and finally returns to the starting point. Note that in a ring, vertices other than the starting point and end point in the path cannot reappear. Can you understand these two concepts? "
Qiao Xi nodded, it seemed that it was nothing rare for her.
"So now there is an undirected graph with nodes A, B, C, and D. The edges are A-B, B-C, C-D, D-A, A-C. So do you think there is a cycle in this undirected graph? How many rings do you think there are, if any? "
Tan Luyuan asked again.
Qiao Yu raised his head and looked at the ceiling. He even thought that Tan Luyuan was trying to test his mental retardation.
Fortunately, Qiao Xi didn't hesitate at all and answered: "There should be two, namely ABCA and ACDA."
"Well, not bad, not bad. Why don't I do it too? Just ask a question. You can answer it as you please."
Yuan Zhengxin, who had been listening quietly next to him, seemed to be surprised. I became interested and took the initiative to interject: "In this way, consider an irregular decahedron, and each face is an irregular triangle.
It is known that this decahedron has only seven vertices. The question is How many sides does this decahedron have? If possible, summarize the adjacent relationship of each face. ”
This time Qiao Xi thought for a while before answering: "There should be fifteen sides? In terms of adjacent relationships, because each face is a triangular decahedron, each face should be related to the other three faces. Adjacent relationship. "
Well, Qiao Yu found that he was confused because he was concerned.
Mr. Yuan probably made the arrangements with Professor Tan.
Although these questions are simple, the test items are not complicated, and they do not even involve very advanced mathematical knowledge.
But the things tested are actually the same. It's all abstract thinking and spatial imagination.
It seems pretty good to be able to come up with these questions in a short period of time.
Qiao Xi really did not disappoint him, the answers were all right. At least it seemed right to him.
As expected, he is still a bit tender. Although he felt that Qiao Xi must be talented in mathematics, he did not expect that he could be tested in such a simple way.
"Qiao Xi, your situation is very interesting. I guess you will never get lost."
After hearing Qiao Xi's answer, Mr. Yuan also smiled and gave A review.
Qiao Xi nodded, which she agreed with very much.
“Well, in our family, only Qiao Yu’s grandmother is blind and can’t always tell the direction. The others have a good sense of direction. As long as they have been to a place once, they can definitely find the way.”< br>
Old Yuan smiled and analyzed seriously: "Yes, you and Qiao Yu both have strong spatial imagination. This is indeed a rare talent. With strong spatial imagination and exposure to abstract algebra and geometry, You will often get twice the result with half the effort.
Especially when you are exposed to high-dimensional concepts such as gradient, divergence and curl, and when you need to perform optimization analysis, this ability can help you quickly understand the essence of the problem.
This is why you are more interested in linear algebra. The elementary content of linear algebra is actually more abstract than the elementary content of calculus.
But if you come into contact with multivariate calculus, you will find that this knowledge is actually very interesting and closely related. So there is no need for you to doubt yourself just because you can't get full marks on high school questions.
After all, the exam focus at different stages is different, and high school focuses more on specific application orientation. For example, I guess you must be able to handle functions, geometry, and sequence in high school.
At the same time, you will definitely get tired of questions that require a lot of calculations. I think this is why it is difficult for you to get full marks on high school questions. "
Qiao Xi frowned slightly and began to think about what happened in high school. It was a long time ago...
Qiao Yu kicked Qiao Xi without leaving any trace.
The two of them are really too familiar.
Qiao Yu knew that once Qiao Xi showed this expression, it would not take long before her attention would begin to wander, and her mind would wander.
No one reminds me of this state, or there is no alarm clock, and it usually lasts for several minutes...
Qiao Xi looked at Qiao Yu, and then looked at Mr. Yuan, who was still smiling. He smiled apologetically and replied: "Well, maybe. I actually haven't paid much attention to these."
"It's not possible, it must be like this. It's like you can understand Schulz's paper. ”
After speaking with certainty, Yuan Zhengxin paused and asked: "Since you know Schulz's paper, you should know the concepts of metric space, density, completeness, and Cauchy numbers, right?"
Qiao Xi nodded and said: "I didn't understand it at first. But there are I looked up the concepts I didn’t understand, and I gradually understood them.”
“That’s OK. I’ll ask you a question. You don’t need to prove it. You just need to use your first impression to answer my proposition. Just return the correct ones to the wrong ones."
Mr. Yuan continued.
Qiao Xi nodded slightly again.
"Suppose (X, d) is a metric space, and YX is a dense subset. Now assume that Y is a complete space, then X is also a complete space. Do you think this proposition is correct?"
Qiao Xi After thinking twice Seconds, then shook his head slightly and replied: "I feel wrong."
Yuan Zhengxin smiled even happier: "Look, this is the kind of jealous ability I mentioned. Really, you and Qiao Yu are both the same, you have a certain knowledge of mathematics. What is talent?"
After that, Mr. Yuan looked at Qiao Yu and continued, "Yan Zhen told me that Qiao Yu had complained to him. This is actually the reason why CMO competition questions only have skills but no beauty.
The most essential thing about mathematics is the exploration and expression of laws. The laws here are different from the laws of physics. They are not affected by the real world and are completely controlled by it. Mathematicians construct it themselves.
So people like you don't like those tedious techniques and calculations. Because you can see the underlying laws more easily than others.
The human brain instinctively gets tired of things it doesn’t like. This is why the two of you were able to understand Schulz's paper only by understanding the basic concepts. "
After a long speech, Yuan Zhengxin suddenly became serious and said: "Qiao Xi, do you know who your performance today reminded me of? "
"Ah, I'm sorry, Mr. Yuan, actually I don't know much about the mathematics world. "Qiao Xi shook her head in confusion.
Yuan Zhengxin revealed the answer nonchalantly: "Ramanujan, if you have time, you can find a movie called "Genius Without Limits" , this movie is about his life and achievements. ”
Hearing this, Qiao Yu grinned like a fool.
After all, he really knew Ramanujan, and he even knew how highly this Indian-born mathematician was rated in the mathematical community.
The only pity is that the mathematician’s life span was too short and he passed away at the age of thirty-two.
If he could live for seventy or eighty years, he might really be able to speed up the development of mathematics in India by several decades.
Qiao Xi glared at Qiao Yu and said sheepishly: "Yuan Laomiao praised me."
Yuan Zhengxin waved his hand and said: "This is not a compliment, I am just telling the truth. By the way, you only have a high school degree, right?"
Qiao Xi nodded and said: "Well, I am a high school graduate. I graduated. I just didn’t take the college entrance examination for some reasons.”
Yuan Zheng thought for a while and then asked: “Then are you willing? I am willing to be my student in the future."
Qiao Xi said hesitantly: "Mr. Yuan, you also know that I am old. Is it too late to start learning now?
Although I have recently. I plan to go to college, and I just want to have something to do. And you may not know that I have a big problem with concentration.”
After saying that, Qiao Xi glared at Qiao Yu again because the kid kicked him from below again.
Yuan Zhengxin noticed the little movements of the mother and son, then smiled casually and said warmly: "These are not problems. Since you said so, it is considered an agreement." Then Yuan Zhengxin looked at the man who was in a daze on the side. Tan Luyuan said: "Lu Yuan, I remember your Guangdong University is Can you provide a correspondence diploma? "
"For this, you should have to wait until March next year to register as a student, and it will be at least three years later, and you must take exams. The regulations of the superior department."
Tan Luyuan replied quickly.
Yuan Zheng thought for a while, looked at Qiao Xi and said warmly: "It doesn't matter, I will figure out the issue of student status. When school starts in September, you can first study with the leading planning class. This matter has been decided."
Qiao Xi was about to say something when she was interrupted by Qiao Yu who had been holding back for a long time: "Yes, yes, yes, grandpa, that's it. Don't change this arrangement." Okay!
You are my grandfather, and now she is your student. Once you are a teacher, you will always be a father. I think this is pretty good, right?"
Qiao Xi wanted to explain to Yuan Zhengxin that she might not be suitable for high-intensity study, but when she saw Qiao Yu's eyes with a little pleading, she finally softened her heart.
When I opened my mouth, it already turned into: "Thank you, Mr. Yuan."
"Why don't you call me Mr. Yuan? Qiao Xi, you have to call me teacher now." Tan Luyuan reminded him with a smile.
"Professor Tan said, thank you, Teacher Yuan." Qiao Xi immediately changed her tune.
Yuan Zhengxin smiled happily and said: "Okay, okay, this is a good thing. You are different from Qiao Yu. If he likes to do research on number theory, just let him. From now on, you will specialize in geometry."
Qiao Yu happily echoed: "That's right, Mom, what's so good about physics? Let me tell you, mathematics is more interesting. , Don’t be restricted by those rules. It’s absolutely fine to learn geometry from your grandfather.”
After hearing Qiao Yu’s words, Yuan Zhengxin said, “Oh? Qiao Xi, are you still interested in physics? No problem, you can study in depth the classification and structure of high-dimensional Karabi-Yuan manifolds in the future
This research direction is strongly related to the physical applications in string theory. You'll know when you get in touch with it. It's not only applicable to string theory, but also to high-energy physics. "
Looking at the cheerful Mr. Yuan, Tan Luyuan sighed in his heart, but still had a smile on his face.
"Congratulations, Mr. Yuan, for winning another Youtian points students. Congratulations to you too, Qiao Xi. If you can become Mr. Yuan's student, you will definitely be able to make a name for yourself in the world of mathematics in the future. ”
Really, after saying these words, Tan Luyuan just felt that the fate of life is so wonderful.
I originally thought that the two factions, Mr. Yuan and Tian Yanzhen, would probably be strangers to each other all their lives. .
Who would have thought that a mother and son pair, Qiao Xi and Qiao Yu, would suddenly appear. Now it was better.
The exchanges between the two parties will probably become closer in the future. To be honest, Tan Luyuan is not very optimistic about Qiao Xi's future achievements.
As Qiao Xi said, after all, she is old. It is impossible to accept basic knowledge as quickly as Qiao Yu. What she relies on is nothing more than her understanding ability and mathematical intuition that ordinary people do not have.
But Qiao Xi is Mr. Yuan’s student after all, and she is also Qiao Yu’s mother.
With Qiao Yu's current talent and attachment to Qiao Xi, if there are any important issues in the future, as long as he can get involved in the other party's research, he will probably take Qiao Xi with him.
If there are any major results, they will probably all be jointly produced by Yanbei International Research Center and Huaqing Yuan Zhengxin Mathematics Research Center...
Tan Luyuan seems to have seen the most powerful scholar in the Chinese mathematics community in the future. Valve is about to rise.
If Qiao Yu wins all kinds of mathematics awards again, especially the Fields Medal.
Coupled with the status of these two mentors in the domestic and world mathematics circles. Needless to say, Mr. Yuan and the influence of the living Philippine Prize winner in the international mathematics community need not be said.
Tian Yanzhen has always cooperated closely with the Academy of Sciences. He is also a judge of the Abel Prize, the world's most authoritative mathematics award, and an editorial board member of a top international mathematics journal...
Tan Luyuan simply couldn't imagine what Qiao Yu and Qiao Xi would develop if they followed this path in the future.
Integrating the Yanbei School and the Huaqing School, and establishing a good relationship with the Academy of Sciences, the future development of Chinese mathematics will probably only depend on the capital city.
If you add in the fact that professors such as Lott Dugan, Peter Schulz, Pierre Delini and others are said to have a good relationship with Qiao Yu...
Forget it, Tan Luyuan He was too lazy to think about it, but he had already decided to think of a way when he got back to see if he could cooperate more with Yanbei and Huaqing Mathematics.
Of course, the most important thing is that Tan Luyuan feels that now is the time to impress the mother and son in front of him.
So, after a pause, he said with a smile: "It seems that I can have another meal at noon today."
Although Tan Luyuan's status in the mathematics world is not as high as that of Yuan Zhengxin and Tian Yanzhen , but with the respect of an academician, naturally he will not miss a meal.
But this sentence can easily shorten the distance between them. Yes, Tan Luyuan is making compromises.
Even though the mother opposite is actually about the same age as his daughter.
"It's necessary. My mother and I should treat everyone to dinner today at noon. Let's go to the A restaurant! Grandpa, help book a box and I'll treat you." Qiao Yu said angrily.
You are not afraid of spending money, and you can use the Huaqing student card in Institute A...
"Well, Qiao Yu, send a message to your teacher and ask him to celebrate together." Yuan Zhengxin said.
"Oh, okay, grandpa."
......
"Huh? Mr. Yuan has decided to accept your mother as a student?"
"Yes, Director Tian. Mr. Yuan said that my mother has strong spatial imagination and abstract thinking skills, and is suitable for learning geometry. He said that he wanted my mother to inherit his mantle."
"Isn't that what you said yesterday? You also said you were going to take your mother to visit the capital today? Why did this suddenly happen? Is there something I don’t know about?”
< br>"Director Tian, I can't explain it clearly on the phone. Why don't you talk about it when you come for lunch? It's still in the same private room as yesterday in Office A."
"Okay, this time is quite coincidental. It would be later One day I’m going to Europe again.”
“Um? Why are you going to Europe again?”
"I have a meeting to attend, don't say anything anymore, I'll be there in a minute."
After hanging up the phone, Qiao Yu breathed a sigh of relief.
The instructor is obviously not very angry, which is good. But the tutor is going away again...
Although he has only been at Yanbei University for half a year, as far as Qiao Yu knows, his tutor has already traveled at least a dozen times, three of which were abroad.
Qiao Yu felt it was a bit hard to run around after being over sixty years old.
Of course, what Qiao Yu didn't know at this time was that Tian Yanzhen had actually minimized traveling as much as possible in order to spare half a day every week to check the progress of his homework.
I have put down many meeting arrangements, otherwise he will be even busier.
But Tian Yan, who hung up the phone, was really too lazy to think about the meeting.
I just feel that this world is ridiculous...
Mr. Yuan suddenly accepted Qiao Xi as his student? He has an extra junior sister inexplicably?
...
Just like that, at noon, the three-digit academicians sat at the same dining table with the Qiao family's mother and son again, except that Xia Keke was missing today.
Tian Yanzhen also learned the whole story from Qiao Yu. To be honest, he was very surprised...
From a theoretical point of view, it is possible for IQ to be inherited. Tian Yanzhen remembered reading an article before that analyzed the heritability of IQ from the perspectives of genetics and behavioral cognition.
The final conclusion is that a person's IQ is mainly the result of a combination of genetics and environment.
But this does not mean that if parents have high IQs, their children will definitely have high IQs.
Because Tian Yanzhen still remembers that the inheritance of IQ is not the result of the action of a single gene, but the joint action of multiple genes.
This means that the transmission process is very random. These include cerebral cortex thickness, gray matter density, brain neuron connectivity, etc...
In the same way, acquired environment is also extremely important as education.
So in theory, the combination of two people with high IQs often means that there is a higher chance of cultivating the next generation with high IQs.
But it's just a probability.
Especially according to research by scientists, Kochi people tend to get married and have children at a later age than ordinary people.
Many of them even miss the best nurturing period. In addition, parents with higher education are generally less willing to have multiple children.
So in the case of only one child, if there is a slight accident in the genetic process, the child's IQ may be mediocre.
This is also the reason why both parents have Ph.D.s from prestigious universities and their IQs are definitely not low, but their children are poor academics.
Like Qiao Xi and Qiao Yu, it is really unusual for mother and son to have the same mathematical talent, but it cannot be said that they are completely absent.
For example, the famous Marie Curie - Marie Curie, won the Nobel Prize twice, once in chemistry and once in physics.
Her daughter Irene Joliot probably inherited Marie Curie’s scientific talent and also won the 1935 Nobel Prize in Chemistry.
So at the lunch dinner, everyone soon started talking about the inheritance of IQ.
Especially Tan Luyuan, he was really curious about how this was inherited.
"I think it's not just genetic, right? I should thank my grandpa. Because my grandpa was actually responsible for educating my mother and me when we were young."
Listening to the three-digit academician chatting about this topic, Qiao Yu immediately found the commonality.
Mathematicians are very good at doing this, especially Qiao Yu.
“Oh? Your grandpa?”
“Yes, my grandpa’s name is Qiao Guozheng. He is a really great person. Not only can he repair everything on the railway, he can also do carpentry. ,painter.
My grandma said that after they got married, all the furniture in the house was made by my grandpa himself. Later, we moved to a new house, and my grandfather took care of the decoration of the house. Many of his colleagues asked him to help make furniture.
And he has a wide range of hobbies, such as chess, Go, Landlords, running beards, table tennis... and he is proficient in everything. When I was a child, I didn't go to kindergarten, and he took me everywhere to play. People invited him to dinner everywhere. ”
Qiao Yu was very proud to introduce the person he admired most in his life to the three academicians.
The three academicians did not say anything. Yuan Zhengxin and Tian Yanzhen both knew Qiao Yu very well.
Tan Luyuan learned about Yu's situation from Yuan Zhengxin's mouth.
I can only sigh secretly in my heart.
Tian Yanzhen felt that this was the right thing. If IQ is indeed related to acquired environment...
Comrade Qiao Guozheng is really a legend. After all, it is definitely not an easy thing to give such a precocious and talented child like Qiao Yu such heartfelt admiration.
Qiao Xi only felt sad...
The year she gave birth to Qiao Yu, her father had been ill once. After that, I retired due to physical reasons.
This makes it difficult for Qiao Xi not to blame her father's early death on her...
Looking back on the past, she was really too willful at that time.
It wasn’t until Qiao Yu next to her kicked her again that Qiao Xi came back to her senses and heard what Professor Tan said.
"...How about we have a drink today, so that each of us can have a beer. Qiao Yu definitely can't drink. Can Qiao Xi have a drink?"
Qiao Xi glanced at Qiao Yu. She showed her signature gentle smile, shook her head and said softly: "I'm sorry, Professor Tan, I'm allergic to alcohol."
Qiao Yu also smiled sweetly after hearing this. This alcohol allergy is very spiritual.
It’s not that he was bragging that if we were to compare their drinking capacity, everyone in the room would be drunk today, and they probably wouldn’t be able to make Qiao Xi burp...
The child is not feeling well, please ask for leave. Two days.
I went to the hospital again today. Hey... if the child gets better tomorrow, I should be able to make up for the two days he owes!
(End of this chapter)