Top academic

Chapter 143 Yes, that’s it!
The next day, early in the morning, in Shaoyuan Canteen.

"I thought about it for a long time last night. I'm definitely not a math genius. Because I'm different from you and that man.

For example, you can easily get full marks in high school math, but I can't. I often make mistakes, whether in the past or now. It's always the same.

Besides, I can’t be as shameless as you at my age. So don’t even think about me saying nice things to Academician Yuan like you did to Keke.

If Academician Yuan asks me a question, I will answer it if I know it, and I will not answer it if I don’t. I will not pretend not to know it, nor will I pretend to know it if I don’t know it. Don’t hold out too much hope.”

While having breakfast, Qiao Xi gave Qiao Yu a shot of prevention.

These words made Qiao Yu, who was originally full of confidence, a little nervous.

Qiao Xi felt that Qiao Yu was a bit boring. It was such a trivial matter that he had to disturb the academician.

Qiao Yu really hopes that Qiao Xi can be valued by Mr. Yuan and come to Beijing in the future. This will not only allow him to be closer to Qiao Xi, but more importantly, he can discuss mathematics with Qiao Xi and then despise her.

No matter how strong Qiao Xi is, he can never be stronger than him.

"I know! We are all amateurs anyway, but I still think that anyone who can easily understand Schultz's paper must be talented."

Qiao Yu ate his porridge and buns in silence, and was too lazy to argue with Qiao Xi anymore. Anyway, he would know when he got to Huaqing.

The two places were very close and there was no rush, so Qiao Yu did not use the number Director Tian sent him, and directly took Qiao Xi to Qiuzhai of Huaqing.

In fact, apart from that section of the road, the scenery on both sides of the campus is still nice, especially the road from Huaqing to Qiuzhai.

But the most important thing is that even though it is already July, when people can sweat in the morning in Xingcheng, the temperature in Beijing is only around 20 degrees, making it very comfortable to walk on the road.

Just like that, twenty minutes later, Qiao Yu and Qiao Xi walked 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 entertained guests, and in front of each of them was a cup of smoking hot tea.

Qiao Xi also apologized to the old man sincerely on behalf of Qiao Yu: "Mr. Yuan, Qiao Yu was really reckless yesterday. In fact, I can only say that I am a hobby in mathematics.

I really don’t think I have much talent. More than 10 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 exams.”

Old Yuan smiled and shook his head, saying, "Let's not talk about this. Whether or not you have a talent for mathematics is a small matter. But the idea you proposed yesterday was very interesting to Lu Yuan and I. Today, I just want you to come and chat casually."

This sentence also made Qiao Xi feel relieved and he became relaxed.

As a mother, she was still afraid that the boss would be more critical of Qiao Yu because of her.

So the four of them chatted about all sorts of things, and then the old man started praising Qiao Yu in various ways, and then slowly turned to the topic of mathematics.

"By the way, Qiao Xi, I heard Qiao Yu say yesterday that you can understand Schultz's paper independently?"

Professor Tan asked casually.

Qiao Xi thought about it and answered pertinently: "Partly. I can't say I understand it completely."

"Do you have a foundation in advanced mathematics?" Professor Tan asked.

"I occasionally flip through the math books Qiao Yu borrowed before, such as linear algebra, calculus, and mathematical analysis. I've been reading more literature recently."

Qiao Xi answered casually.

"Oh, then if you were asked to choose between linear algebra and calculus, which one would you find more interesting? Which one would it be?"

"That would be linear algebra."

Qiao Xi thought for a moment and said.

Professor Tan smiled, then looked at Mr. Yuan, thought for a moment, and said, "There is a number sequence. The first three numbers are 1, 3, and 7... What do you think the fourth number should be according to this rule?"

When Qiao Xi heard Professor Tan start asking questions, Qiao Yu sat up straighter instead of doing anything.

"23." Qiao Xi gave an answer casually.

Tan Luyuan nodded, and then asked with a smile: "Think about it again, if there is a 3X3 square grid, the starting point is at the upper left corner and the end point is at the lower right corner.

The rule is that you can only move right or down, and without drawing a diagram, you first have a sense of how many different paths you can take from the starting point to the end point.

"6 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 understood it in an instant. Maybe I thought the question he asked was too simple?

But he ignored it, just smiled and asked, "Qiao Xi, have you studied graph theory?"

Qiao Xi shook her head and said softly, "No, I have never had any contact with it."

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 consists of vertices and edges. The edges represent the connection between vertices, and the characteristic is that the edges have no direction.

For example, if there is an edge u, v, then it can go from u to v or from v to u, and the relationship between the two is equivalent.

A cycle is a path that starts from a vertex, passes through a series of edges and vertices, and finally returns to the starting point. Note that in a cycle, vertices in the path other than the starting point and the end point cannot appear repeatedly. Do you understand these two concepts? "

Qiao Xi nodded, as if this was not a difficult thing for her.

"So now there is an undirected graph with nodes A, B, C, and D. The edges are AB, BC, CD, DA, and AC. Do you think there are any cycles in this undirected graph? If so, how many cycles do you think there are?"

Tan Luyuan asked again.

Qiao Yu looked up at the ceiling. He even felt that Tan Luyuan was testing his wits.

Fortunately, Qiao Xi did not hesitate at all and answered: "There should be two, namely ABCA and ACDA."

"Well, good, good. Why don't I also ask a question. You can answer it as you like."

Yuan Zhengxin, who had been listening quietly, suddenly became interested and took the initiative to interject, "Well, 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, "Should there be fifteen sides? As for the adjacent relationship, since each face is a triangular decahedron, each face should have an adjacent relationship with the other three faces."

Well, Qiao Yu found that he was too concerned and confused.

Mr. Yuan probably had discussed this with Professor Tan.

Although these questions are simple, the content tested is not complicated and they do not even involve very advanced mathematical knowledge.

But the things tested are actually similar. They all require abstract thinking and spatial imagination.

It seems quite good to be able to come up with these topics in a short period of time.

Qiao Xi really didn't disappoint him, the answers were all correct. At least in his opinion.

Sure enough, he was still a little naive. Although he felt that Qiao Xi must have a talent for mathematics, he didn't expect that it could be tested in such a simple way.

"Qiao Xi, your situation is very interesting. I guess you never get lost."

After hearing Qiao Xi's answer, Mr. Yuan also smiled and gave an evaluation.

Qiao Xi nodded, she agreed with this very much.

"Well, in our family, only Qiao Yu's grandmother is directionally ill and always loses her way. Everyone else has a good sense of direction. As long as they've been to a place once, they can definitely find the way."

Yuan Lao smiled and analyzed seriously: "Yes, you and Qiao Yu both have strong spatial imagination. This is indeed a rare talent. With strong spatial imagination, you can often get twice the result with half the effort when you come into contact with abstract algebra and geometry.

Especially when you come into contact with 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 basic content of linear algebra is actually more abstract than the basic content of calculus.

But if you get in touch with multivariate calculus, you will find that these knowledge are actually very interesting and closely related. So there is no need to doubt yourself just because you can't get full marks on high school questions.

After all, the examination focuses at different stages are different, and high school is more focused on specific application orientation. For example, I guess you must be very comfortable with functions, geometry, and series in high school.

At the same time, you will definitely get tired of questions that require a lot of calculations, and 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. It was a long time ago when I was in high school...

Qiao Yu kicked Qiao Xi without leaving any trace.

The two of them are really too familiar with each other.

Qiao Yu knew that once Qiao Xi showed this expression, it wouldn't take long for her attention to become dazed and her mind to wander.

This state usually lasts for several minutes without anyone reminding you or an alarm clock...

Qiao Xi looked at Qiao Yu, and then at Mr. Yuan who was still smiling. He smiled apologetically and replied, "Well, maybe. I haven't really paid much attention to these things."

"Not maybe, but definitely. Just like you can understand Schultz's paper."

After saying this with certainty, Yuan Zhengxin paused and asked again, "Since you are familiar with Schultz's paper, you should know the concepts of metric space, density, completeness, and Cauchy sequence, right?"

Qiao Xi nodded and said, "I didn't understand it at first. But I looked it up when I didn't know a concept, and slowly I understood it."

"That's fine. I'll give you a question. You don't need to prove it. You just need to answer my question based on your first impression, whether you think it's correct or wrong."

Mr. Yuan continued.

Qiao Xi nodded gently again.

"Let (X, d) be a metric space, and YX be a dense subset. Now suppose Y is a complete space, then X is also a complete space. Do you think this statement is correct?"

Qiao Xi thought for two seconds, then shook his head slightly and replied: "I feel it is wrong."

Yuan Zhengxin smiled even more happily: "See, this is the kind of ability that makes people jealous. Really, you are the same as Qiao Yu, you have a natural keenness in mathematics. What is talent? This is it!"

After saying that, Mr. Yuan glanced at Qiao Yu and continued, "Yan Zhen mentioned this to me. He said that Qiao Yu once complained to him that the CMO competition questions only required skills but no aesthetics. This is actually the reason.

The essence of mathematics is the exploration and expression of laws. The laws here are different from physical laws. They are not affected by the real world and are completely constructed by mathematicians.

So people like you don't like those tedious techniques and calculations, because you can see the essential laws more easily than others.

The human brain is wired to get bored with things it doesn’t like. That’s why the two of you were able to understand Schultz’s paper with just 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?"

"Oh, I'm sorry, Mr. Yuan, actually I don't know much about the mathematical world." Qiao Xi shook his head blankly.

Yuan Zhengxin nonchalantly revealed the answer: "Ramanujan, if you have time, you can watch 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 knew how highly this Indian mathematician was regarded in the mathematical community.

The only pity is that this mathematician's life was too short and he passed away at the age of 32.

If he could live another 70 or 80 years, he might be able to accelerate the development of mathematics in India by several decades.

Qiao Xi glared at Qiao Yu and said embarrassedly, "Mr. Yuan, you are too kind."

Yuan Zhengxin waved his hand and said, "This is not a false compliment. I am just telling the truth. By the way, you only have a high school diploma, right?"

Qiao Xi nodded and said, "Well, I graduated from high school. But for some reasons, I didn't take the college entrance examination."

Yuan Zheng thought about it, then asked, "Then are you 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 do plan to go to 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 boy kicked him again from below.

Yuan Zhengxin noticed the little movements of the mother and son, then smiled and said gently: "These are not a problem. Since you said so, then it is agreed." Then Yuan Zhengxin looked at Tan Luyuan who was in a daze on the side and said: "Luyuan, I remember that your Yueshan University can provide correspondence diplomas?"

"Well, I should wait until March next year to register for school. It will take at least three years for graduation, and I must take exams. These are the regulations of the higher authorities."

Tan Luyuan replied quickly.

Yuan Zheng thought for a moment, looked at Qiao Xi and said gently, "It doesn't matter. I'll find a way to solve the enrollment problem. You can start studying with the Leadership Program class in September. This matter has been decided."

Just as Qiao Xi was about to say something, he was interrupted by Qiao Yu, who had been holding back for a long time: "Yes, yes, yes, Grandpa, it's decided. This arrangement couldn't be better!
You are my grandfather, and she is your student now. Once a teacher, always a father. This also clarifies the order of generations. I think it's great. 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 pleading eyes, she finally softened her heart.

When he opened his mouth, it had become: "Thank you, Mr. Yuan."

"Why are you still calling him Mr. Yuan? Qiao Xi, you should call him teacher now." Tan Luyuan reminded with a smile.

"Professor Tan is right. Thank you, Teacher Yuan." Qiao Xi immediately changed her tone.

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, let him do it. You can specialize in geometry in the future."

Qiao Yu agreed happily, "That's right, Mom, what's so good about learning physics? I tell you, mathematics is more interesting. Don't be restricted by those rules and regulations. It will be no problem to learn geometry from grandpa."

After hearing what Qiao Yu said, Yuan Zhengxin said, "Oh? Qiao Xi, are you still interested in physics? Actually, that's no problem. You can study the classification and structure of high-dimensional Calabi-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 can be used not only in string theory but also in high-energy physics. "

Looking at the excited Mr. Yuan, Tan Luyuan sighed in his heart, but still put a smile on his face.

"Congratulations, Professor Yuan, for accepting another talented student. Congratulations to you, Qiao Xi. Being Professor Yuan's student, you will definitely make a name for yourself in the mathematics world in the future."

Really, after saying this, Tan Luyuan just felt that life's encounters were so ingenious.

I originally thought that the two factions of Yuan Lao and Tian Yanzhen would probably be strangers for the rest of their lives.

Who would have thought that Qiao Xi and Qiao Yu, a mother and son, would suddenly appear. Now that's a big deal.

In the future, the exchanges between the two sides will probably become closer and closer. To be honest, Tan Luyuan is not optimistic about Qiao Xi's future achievements.

Just as Qiao Xi said, after all, she is old. It is impossible for her to learn basic knowledge as quickly as Qiao Yu. All she can rely on is her understanding ability and mathematical intuition that most people don't have.

But Qiao Xi is Mr. Yuan’s student after all, and also Qiao Yu’s mother.

With the talent Qiao Yu has shown so far and the degree of his attachment to Qiao Xi, if there are any important topics in the future, as long as they are related to the other party's research, he will probably bring Qiao Xi with him.

If there are any major achievements, they will probably be the joint achievements of the Yanbei International Research Center and the Huaqing Yuan Zhengxin Mathematics Research Center...

Tan Luyuan seemed to foresee the rise of the most powerful academic tycoon in the future of Chinese mathematics.

If Qiao Yu won all the major awards in mathematics again, especially the Fields Medal.

In addition, the status of these two mentors in the domestic and international mathematics community. Needless to say, Yuan Lao is influential, and the influence of the living Fields Medal winners in the international mathematics community is beyond words.

Tian Yanzhen has always had close cooperation with the Academy of Sciences. He is also a judge for the Abel Prize, the world's most prestigious mathematics award, and an editorial board member of a top international mathematics journal...

Tan Luyuan simply couldn't imagine how Qiao Yu and Qiao Xi would develop in the future if they continued along this path.

After integrating the Yanbei School and the Huaqing School and building good relations with the Academy of Sciences, the future development of Chinese mathematics may really only depend on the capital.

If we add the fact that Professors Lotte 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 made up his mind. When he returned, he would think of ways to see if he could cooperate more with the mathematics departments of Yanbei and Huaqing.

Of course, the most important thing is that Tan Luyuan feels that he should now improve his impression in front of the mother and son.

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 Yuan Zhengxin and Tian Yanzhen, as an academician, he would naturally not miss a meal.

But this sentence can easily bring them closer. Yes, Tan Luyuan is making a compromise.

Even though the mother opposite is actually about the same age as his daughter.

"Of course. My mother and I should treat everyone to lunch at noon today. Let's go to Room A! Grandpa, please help book a private room and I'll treat everyone." Qiao Yu said generously.

I am not afraid of spending money, and I can use Huaqing student card at Institute A...

"Well, Qiao Yu, send a message to your teacher as well and ask him to celebrate with us." Yuan Zhengxin said.

"Oh, okay, Grandpa."

……

"Hmm? Master Yuan decided to accept your mother as a student?"

"Yes, Director Tian. Mr. Yuan said that my mother has strong spatial imagination and abstract thinking ability, which makes her suitable for studying 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 the capital for a stroll today? Why did this suddenly happen? Is there something I don't know about?"

"Director Tian, ​​it's hard to explain over the phone. Why don't you come over for lunch at noon? Or in the same box as yesterday in the A-station?"

"Okay, this is a good time. If it's one day later, I'll have to go to Europe again."

"Uh? What are you going to Europe for again?"

"I have a meeting to attend. I won't talk any more. I'll be there soon."

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 on a long trip again...

Although he had only been at Yanbei University for half a year, as far as Qiao Yu knew, his tutor had already traveled at least ten times, three of which were abroad.

Qiao Yu felt it was a bit tiring to travel around at the age of over 60.

Of course, what Qiao Yu didn't know at this time was that in order to ensure that Tian Yanzhen could take out half a day every week to check his homework progress, he had actually tried to reduce his travels.

He turned down many meeting arrangements, otherwise he would be even busier.

However, after hanging up the phone, Tian Yan was really too lazy to think about the meeting.

I just think this world is ridiculous...

Did Master Yuan suddenly accept Qiao Xi as his student? He suddenly had a younger sister out of nowhere?

……

Just like that, at noon, the three-digit academicians sat at the same table with the Qiao mother and son, but Xia Keke was missing today.

Tian Yanzhen also learned the whole story from Qiao Yu. To be honest, she was very surprised...

From a theoretical point of view, IQ can be inherited. Tian Yanzhen remembers reading an article before that analyzed the heritability of IQ from the perspective of genetics and behavioral cognition.

The final conclusion is that a person's IQ is mainly the result of the combined effects 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 combined action of multiple genes.

This means that the transmission process is very random, including the thickness of the cerebral cortex, the density of gray matter, the connectivity of brain neurons, etc.

Similarly, the acquired environment and education are also extremely important.

So in theory, the combination of two people with high IQs often means a higher chance of producing an intelligent next generation.

But it's just a chance.

In particular, according to research by scientists, highly educated people tend to get married and have children later than ordinary people.

Many of them even miss the best breastfeeding period. In addition, parents with higher education levels are generally less willing to have more children.

So if you only have 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 are PhDs from prestigious universities and their IQs are definitely not low, but their children are poor students.

It is really rare for a mother and son like Qiao Xi and Qiao Yu to have the same mathematical talent, but it cannot be said that it is completely unheard of.

For example, the famous Madame Curie - Marie Curie, won the Nobel Prize twice, once in chemistry and once in physics.

Her daughter Irène Joliot probably inherited Marie Curie's scientific talent and also won the 1935 Nobel Prize in Chemistry.

So at the lunch, 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 grandfather. Because my mom and I were actually raised by my grandfather when we were young."

Listening to three-digit academicians talking about this topic, Qiao Yu immediately found common ground.

Mathematicians are very good at this, especially Qiao Yu.

"Oh? Your grandpa?"

"Yes, my grandfather's name is Qiao Guozheng. He is a really amazing man. Not only can he repair everything on the railway, he can also do carpentry and painting.

My grandmother once said that after they got married, all the furniture in the house was made by my grandfather himself. Later, when they moved to a new house, my grandfather also took care of the decoration of the house. Many of his colleagues asked him to help make furniture.

He also 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, and he took me everywhere to play, and people would invite him to dinner wherever he went. "

Qiao Yu was particularly proud to introduce to the three academicians the person he admired most in his life.

The three academicians remained silent. Yuan Zhengxin and Tian Yanzhen had both specifically inquired about Qiao Yu's situation and knew that this grandfather had passed away.

Tan Luyuan learned about this from Yuan Zhengxin.

I can only sigh in my heart.

Tian Yanzhen felt that this was right. If IQ is indeed related to the acquired environment...

Comrade Qiao Guozheng was truly legendary. After all, it was not an easy task to make a precocious and gifted child like Qiao Yu admire him from the bottom of his heart.

Qiao Xi just felt sad...

The year she gave birth to Qiao Yu, her father had been ill, and he retired due to health reasons.

This made it difficult for Qiao Xi not to blame her for her father's early death...

Looking back on the past, she was really too willful at that time.

It was not until Qiao Yu next to her kicked her again that Qiao Xi came to her senses and heard what Professor Tan said.

"...Why don't we have a drink today, one beer each. Qiao Yu definitely can't drink, but can Qiao Xi have one?"

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 smiled sweetly after hearing this. This alcohol allergy is very spiritual.

He's not bragging. If we were to compare drinking capacity, even if everyone in the room passed out today, it would probably be impossible to make Qiao Xi burp...

　My child is not feeling well, so I am taking the next day off.

　　I went to the hospital again today. If the child gets better tomorrow, I should be able to make up for the two days I missed!

　　
　
(End of this chapter)