Chapter 143 Yes, that’s it!
The next day, early morning, Shaoyuan Canteen.
"I thought 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 before and now.
And I can't be as shameless as you at my age. So don't expect me to say nice things in front of Academician Yuan like you and Coco did.
If Academician Yuan asks me something, I will say yes if I know it, and if I don’t know it, I won’t. I won’t pretend to understand, nor will I pretend to understand. Don’t have too much hope.”
During breakfast, Qiao Xi vaccinated Qiao Yu.
These words made Qiao Yu, who was originally confident, feel a little uneasy.
Qiao Xi felt that Qiao Yu was a little bored, and he wanted to alarm the academician with such a big deal.
Qiao Yu really wanted Qiao Xi to be valued by Mr. Yuan and come to the capital in the future. Not only would he be closer to Qiao Xi, but the key was that he could discuss mathematics with Qiao Xi 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 his porridge and steamed buns with his head down, and was too lazy to argue with Qiao Xi anymore. Anyway, he would know it when he got to Huaqing.
The two sides were very close to each other, and they were not in a hurry. Qiao Yu didn't use the number given to him by Director Tian and took Qiao Xi directly to Qiuzhai in Huaqing.
In fact, except for 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.
To his surprise, 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 I am interested in mathematics at best.
I really don’t think I have 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 the high school test paper.”
Mr. Yuan smiled and shook his head and said: "Don't talk about it, 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 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 her, the boss will be more harsh on Qiao Yu.
So the four of them chatted about something, and then the old man praised Qiao Yu in a fancy way, and then slowly turned to the topic of mathematics.
"By the way, Qiao Xi, I heard Qiao Yu say yesterday that you could independently understand Schulz's paper?"
Professor Tan asked casually.
Qiao Xi thought for a while and replied pertinently: "Part of it. I can't say I fully understand it."
"Do you have any 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 time."
Qiao Xi answered casually.
"Oh, if you were asked to choose between linear algebra and calculus, which one do you think is more interesting? Which one do you think it would be, relatively speaking?"
"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, the fourth number should What is it?"
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 that you can only move right or down, don't draw a picture, and your first impression is that there are several different paths to get from the starting point to the ending point."
"Six kinds." Qiao Xi smiled and replied.
Tan Luyuan nodded, and then found that Qiao Yu seemed to glare at him secretly...
I was a little stunned at first, but I figured it out instantly. Maybe I 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 have never been in contact with him."
Tan Luyuan smiled and said: "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. The edges represent the connection relationship between the vertices. The characteristic is 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 loop, the vertices in the path other than the starting point and the end point cannot be repeated. Can you understand these two concepts? ?」
Qiao Xi nodded, as if this was indeed nothing unusual for her.
"So now there is an undirected graph, the nodes are A, B, C, 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? If so, do you How many rings do you think there are?”
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 did not hesitate at all and answered: "There should be two, namely ABCA and ACDA."
"Well, that's right, that's right. Why don't I ask a question too? You can answer whatever you like."
Yuan Zhengxin, who had been listening quietly next to him, seemed to suddenly become 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 edges this decahedron has, and 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. Adjacency 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. They are all about 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 didn't disappoint him. The answers were all right. At least they were right in his opinion.
Sure enough, he was still a little naive. Although he thought Qiao Xi must be talented in mathematics, he didn't expect that she could be tested in such a simple way.
"Qiao Xi, your situation is very interesting. I guess you will never get lost."
After listening to Qiao Xi's answer, Mr. Yuan also smiled and gave an evaluation.
Qiao Xi nodded, she agreed with this point.
"Well, in our family, only Qiao Yu's grandmother is blind and can't always tell the direction. Everyone else has a good sense of direction. As long as they have been to a place once, they can definitely find the way."
Mr. 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 also the reason why you are more interested in linear algebra. The introductory content of linear algebra is actually more abstract than the introductory content of calculus.
But if you come into contact with multivariate calculus, you will find that these knowledge are actually very interesting and closely related. So there is no need to doubt yourself 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 will be able to learn functions, geometry, and sequence in high school with ease.
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 started thinking about what happened in high school, it was a bit long 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 wouldn't take long before her attention would begin to wander, and her mind would wander.
This state usually lasts for several minutes when no one reminds me or there is no alarm clock...
Qiao Xi looked at Qiao Yu, then looked at Mr. Yuan who was still smiling, smiled apologetically, and replied: "Well, maybe. I actually don't pay much attention to these."
"It's not possible, it's definitely the case. 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 if there were concepts I didn't understand, I would look them up, and I gradually understood them."
"That's fine. I'll ask a question. You don't need to prove it. You just need to use your first impression to answer my proposition. Do you think it is correct or wrong?"
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 thought for two seconds, then shook her head slightly and replied, "I feel wrong."
Yuan Zhengxin smiled even more happily: "Look, this is the kind of enviable ability I mentioned. Really, you and Qiao Yu are the same, with a natural acumen for mathematics. What is talent? This is it! "
After speaking, Mr. Yuan glanced at Qiao Yu and continued: "Yan Zhen mentioned to me that Qiao Yu once complained to him that the CMO competition questions only have skills and no beauty. This is actually the reason.
The most essential thing in 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 constructed by mathematicians themselves.
So people like you won't like those tedious techniques and calculations. Because you can see the essential laws more easily than others.
The human brain naturally 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 mathematics." Qiao Xi shook her head blankly.
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."
Upon hearing this, Qiao Yu grinned like a fool.
After all, he really knew Ramanujan, and he even knew how highly regarded this Indian-born mathematician was 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 it."
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 graduated from high school. I just didn't take the college entrance examination for some reasons."
Yuan Zheng thought for a while and then asked: "Then would you like 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 do plan to enter college recently, 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 Tan Luyuan who was in a daze and said, "Lu Yuan, I remember that your Yueshan University can provide correspondence diplomas?"
"Well, you should have to wait until March next year to register as a student. Graduation will take at least three years, and you must take exams. These are 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 program 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. This arrangement can't be better!
You are my grandfather, and she is now your student. Once a teacher, she will always be a father. This way, the seniority is smoothed out. I think it’s pretty good. Right, Mom!”
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 he opened his mouth, it already turned into: "Thank you, Mr. Yuan."
"What else are you calling Mr. Yuan? Qiao Xi, now you have to call me teacher." Tan Luyuan reminded him with a smile.
"What Professor Tan said is, 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 number theory research, just let him do it. 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 and regulations. It's absolutely no problem to learn geometry from grandpa."
After hearing Qiao Yu's words, Yuan Zhengxin said: "Oh? Qiao Xi, are you still interested in physics? In fact, it's 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 of string theory. Once you get in touch with it, you will know that it is applicable not only to string theory, but also to high-energy physics."
Looking at Mr. Yuan who was in high spirits, Tan Luyuan sighed in his heart, but still had a smile on his face.
"Congratulations to you, Mr. Yuan, for recruiting another talented student. Congratulations to you too, Qiao Xi. If you can become Mr. Yuan's student, you will definitely be able to make a mark in the world of mathematics in the future."
Really, after saying these words, Tan Luyuan just felt that the fate of life was so wonderful.
I originally thought that the two factions, Mr. Yuan and Tian Yanzhen, would probably be strangers to each other for the rest of their lives.
Who would have thought that a mother and son pair, Qiao Xi and Qiao Yu, would suddenly appear. Now it's 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 older. She cannot 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 the talent Qiao Yu has shown so far and the degree of attachment to Qiao Xi, if there are any important topics 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 be jointly produced by Yanbei International Research Center and Huaqing Yuan Zhengxin Mathematics Research Center...
Tan Luyuan seems to have seen the rise of the most powerful scholar in the future of Chinese mathematics.
If Qiao Yu could win various awards in mathematics 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.
It has integrated the Yanbei School and the Huaqing School, and is building 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, etc. are said to have a good relationship with Qiao Yu...
Forget it, Tan Luyuan 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 was that Tan Luyuan felt that now was the time to brush up on 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 community is not as high as that of Yuan Zhengxin and Tian Yanzhen, with his status as an academician, he will not miss a meal.
But this sentence can easily shorten the distance between them. Yes, Tan Luyuan is making a compromise.
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 also 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 his 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 legacy."
"Didn't you say yesterday that you were going to take your mother to visit the capital today? Why did this happen all of a sudden? Is there something I don't know about?"
"Director Tian, ​​I can't explain it clearly on the phone. Why don't you talk about it when you come over for lunch? It's still in the same private room as yesterday in the A office."
"Okay, this time is quite coincidental. I will leave for Europe one day later."
"Um? Why are you going to Europe again?"
"I have a meeting to attend. I won't say anything anymore. I'll be there later."
After hanging up the phone, Qiao Yu breathed a sigh of relief.
The instructor is obviously not very angry, which is good. But the instructor is going away again...
Although he has only been at Yanbei University for half a year, according to Qiao Yu's knowledge, his tutor has already traveled at least a dozen times, three of which have been abroad.
Even at the age of over sixty, Qiao Yu felt it was a bit hard to have to run around.
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.
He canceled many meeting arrangements, otherwise he would be even busier.
But after Tian Yan hung up the phone, he really didn't want to think about the meeting.
I just feel that this world is ridiculous...
Mr. Yuan suddenly accepted Qiao Xi as his student? He got a junior sister inexplicably?
…
Just like that, at noon, the three-digit academicians sat at the same dining table with the Qiao family and their 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, IQ is likely to be inherited. Tian Yanzhen remembers 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 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. This includes the thickness of the cerebral cortex, gray matter density, brain neuron connectivity, etc...
In the same way, the acquired environment and education are equally important.
Therefore, in theory, the combination of two people with high IQs often means that there is a higher chance of nurturing the next generation with high IQs.
But it's just a chance.
In particular, according to research by scientists, highly educated people tend to get married and have children at a later age than ordinary people.
Many of them even miss the best nurturing period, and parents with higher education are generally less willing to have multiple children.
Therefore, 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 certainly high, but their children are poor academics.
Like Qiao Xi and Qiao Yu, it is really strange that both mother and son 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 genetics, right? I should thank my grandpa. Because my grandpa was actually responsible for educating my mother and me when we were young."
Listening to three academicians 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 grandfather's name is Qiao Guozheng. He is a really good person. Not only can he repair everything on the railway, he can also do carpentry and painter.
My grandma said that after they got married, all the furniture in the house was made by my grandpa. Later, when they moved to a new house, my grandpa also took care of the decoration of the house. Many of his colleagues asked him to help make furniture.
Moreover, he has a wide range of hobbies, including chess, Go, Landlords, running beards, table tennis... and he is very proficient in all of them. When I was a child, I didn't go to kindergarten, so he would take me everywhere to play, and people would treat him to dinner wherever I went. "
Qiao Yu was particularly proud to introduce the people 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's situation and knew that his grandfather had passed away.
Tan Luyuan learned about this from Yuan Zhengxin.
I can only sigh secretly in my heart.
Tian Yanzhen felt that this was the right thing. If IQ is indeed related to the acquired environment...
This Comrade Qiao Guozheng is truly legendary. After all, it is definitely not an easy thing to give such a precocious and talented child such as Qiao Yu such heartfelt admiration.
Qiao Xi only felt sad...
When she gave birth to Qiao Yu, her father was ill once. After that, he 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.
"...Why don't we have a drink today, so each of us has a beer. Qiao Yu can't drink it, can Qiao Xi have a drink?"
Qiao Xi glanced at Qiao Yu and showed her signature gentle smile, shook her head and said softly: "I'm sorry, Professor Tan, I'm allergic to alcohol."
Qiao Yu also laughed sweetly after hearing this. He is allergic to alcohol and 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 and needs to take the next day off.
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 I owe!
Chapter completed!