United States, Cambridge, Areston Community.
This community is very close to MIT and Harvard University. It has a quiet environment, good schools, and its own park.
However, what Zhang Xinwen chooses to live here is that compared with other middle-class residential areas in Cambridge or Boston, the price here is lower, the quality of living is not bad, and the price-performance ratio is good. And many in the community are With faculty and staff from MIT and Harvard, you can feel comfortable living there.
There is no way. Although the profession of university professor in the United States has a certain social status, it is not considered a high-income group, especially when they are not well-known. As we all know, this country really takes advantage of birds of a feather to flock together. .
Middle-class and poor communities are mixed together, and knowledge and crime are often only one street apart. Even everyone has become accustomed to these.
In any city here, even a capital like Washington or a world financial center like New York, certain areas will have higher crime rates and social problems. Relatively speaking, Cambridge, home to Massachusetts and Harvard, is already very safe. .Especially at night, the community is very quiet, even quiet.
Basically, middle-class communities do not have the habit of traveling at night. There is no noise from cars on the streets, and there are no inexplicable carnivals by unknown people in the streets. If a family makes unscrupulous noises, there is a high probability that they will ask for a 911 door-to-door visit. This way In the early hours of the morning, cell phone ringtones tend to be particularly harsh.
Zhang Xinwen was awakened by the harsh ringtone. As soon as she opened her eyes, she heard the complaints of the woman next to her.
"Who is it? Are you still on the phone at this time? How many times have I told you to mute your phone and turn it on when you go to bed at night?" After saying that, the woman next to him had already turned on the light, got up angrily, hugged the quilt and walked out of the room. .Zhang Xinwen only felt a headache.
When people reach middle age, conflicts between husband and wife seem to increase all of a sudden, and mathematics professors are no exception.
I had just had a fight before going to bed, and I finally managed to coax myself to sleep. A phone call escalated the conflict again. I shook my head helplessly, picked up the phone, and became very angry when I saw the number.
It would be fine if it was the number of a colleague here in Cambridge. At least it proves that the person is still staying up late. But this is a Chinese number.
Don’t you know how to respect the time difference? Cambridge EDT is 12 hours slower than CST! It’s already 12:50 in the morning in Cambridge. Is Li Lixing crazy?
He answered the phone with resentment, but before he could speak, the person on the other end rushed to say: "Professor Zhang, go to the mailbox quickly, Qiao Yuzheng is here!" Being a little confused, Zhang Xinwen asked subconsciously: "Qiao Yu? What did he prove?"
"No? What else could it be? Of course it's the problem we are encountering now! I won't say it anymore, I have to inform Ronald!" "Dududu..."
The busy signal on the phone receiver made Zhang Xinwen stunned for a long time.
no…….....
Just hung up?
He seemed to be planning to scold this guy who disturbed people's dreams and ruined the relationship between husband and wife. Why did he just die?
etc……
Did Qiao Yu prove that problem?
His brain was finally fully activated. Zhang Xinwen suddenly became excited. Then he found some clothes and put them on. He quickly came to his small study room and opened his laptop. He quickly logged into his mailbox. Sure enough, there was an email from Li Lixing from Huaqing.
The email I sent had a small picture attached.
Zhang Xinwen clicked it in confusion, and the extremely concise proof process entered his mind.
After reading it carefully, Zhang Xinwen felt that it was a bit unreal. The problem that had troubled them for more than half a year was solved by Qiao Yu in only six lines?
After sighing in his heart for less than two seconds, Zhang Xinwen picked up the pen, then pulled out a stack of paper from the table and started to do the derivation.
For example, the proof of invariance in line 5.
The prover here ensures that the average of the global function under the action of the transformation group is a feature layer.
This is very important because it proves that the constructed feature layer W actually captures the main characteristics of the global function instead of changing with the change of the group. The logic of the proof is that by transforming the average effect of the group, the obtained
The result still belongs to the feature layer.
But Qiao Yu’s expression is: using the principle of categorization contraction, it can be proved that: vgEG,g-Φ(f)=Φ(f). Therefore, (f) is an invariant function and can be regarded as benefit
An automorphism of the Turk layer. This is obviously too concise.
Using the principle of categorization shrinkage, this sentence is easy to say but troublesome to prove. First, you need to define the average value: Ф(f)=1/1G1gEGΣg—f, and then verify the invariance: g—Ф(f)=g:
(1/1GigEGΣg—f) ..Time passed as Zhang Xinwen wrote hard and fast. Unknowingly, the manuscript paper used for the calculation had been written on three full sides, and then he came up with the same answer as Qiao Yu's proof process.
"Yes!" Zhang Xinwen couldn't help shouting excitedly, causing a burst of barking from dogs outside the house. He was shocked to realize that it was already early in the morning, and he was so frightened that he immediately shut his mouth.
Fortunately, except for the dog barking twice, there was no movement inside or outside the house.
Zhang Xinwen was relieved, but still emotionally excited.
It is hard for any mathematician not to be excited if something he has been thinking about for more than half a year is suddenly solved.
Excitement was followed by fear.
Fortunately, Mr. Yuan took the initiative and brought Qiao Yu into their research group...
Otherwise, what if this guy found out about their problem from another channel and then solved it easily?
In this situation, it can at least be said that their previous research was valuable, and it at least helped Qiao Yu sort out the context of this issue.
This problem was solved, and he could finally start the next step of research! The world is so beautiful.
Cambridge, Massachusetts, is about three thousand kilometers away from Berkeley, California, which is also the distance from the east coast to the west coast.
For many small countries whose weather forecasts can be summarized in just one sentence, they probably cannot understand why they are so far apart and what it is like to still belong to the same country. The answer is probably not good, especially when a country does not use when in the same time zone.
We belong to the same big family, but there is a three-hour time difference, which makes internal communication very troublesome. This is especially true for large companies and scholars who need to communicate frequently. When receiving an important meeting notice , and then confusion of time often happens.
Just when Zhang Xinwen felt lucky and excited, Professor Ronald from Berkeley had also completed the work of completing the missing steps. Different from Zhang Xinwen, Ronald completed the complete work while video chatting with Li Lixing. Proof process.
Although it was already 1:30 in the morning in Cambridge, it was only 10:30 in Berkeley at this time. Therefore, Ronald could express his emotions at this time more casually than Zhang Xinwen.
"You know? Li, when you said you wanted to add a child to the team, I actually wanted to refuse it directly. This would make academic research less pure! If it hadn't been for that Joe who figured out the geometric Langlands conjecture If the loopholes are proven, really, I will definitely reject it!
Now it seems that this was not the right decision. Fortunately, I was convinced by you at the time. Of course, it was not you who convinced me, but his perfect proof process that convinced me! You know? I really want to now I wonder how he came up with it! What a beautiful idea!"
Ronald said excitedly to the camera.
Obviously, this professor doesn't pay much attention to hiding his thoughts when he is excited.
But it didn’t matter. At that time, Li Lixing proposed to add a new blood to the research team, and when he was only a sixteen-year-old boy, Ronald was really not interested in this proposal. In fact, Berkeley would also accept many results and Ronald was disgusted that students who did not meet the standards applied for admission.
The only good thing is that these students often don't enroll in the mathematics department. Originally, Ronald thought that Qiao Yu probably belonged to this kind of student.
He felt that someone hoped to use the results of their project to pave the way for the future of this sixteen-year-old Chinese boy. This kind of thing is actually very common in the academic world. What made him angry was that there was no exchange of resources. .The other party seemed to really think that such a sixteen-year-old child could help with their project.
He had raised doubts at that time.
It wasn't until Li Lixing compiled some of Qiao Yu's achievements into an email and sent it to him, and vouched for his academic credibility, that he reluctantly agreed to the matter and allowed Qiao Yu to participate in the research. However, The two parties also agreed that if Qiao Yu never made any contribution to the research group, he would have the right to refuse Qiao Yu's signature on the paper when the results were finally produced.
But now it seems that that agreement has become invalid.
Qiao Yu has already made important contributions to the research group. Even if Qiao Yu makes no further contributions, he still has the qualification to sign the paper. If this project can really produce results, it will be eligible to be published in a top journal.
Based on the rigorous academic requirements of top journals, or at least the apparent rigor, the authors also need to explain each person's specific contribution to the results in the attachment.
There is no doubt that one of the most difficult theorems in this paper has been conquered. Not only does this sixteen-year-old boy, who he once didn't believe in, have the qualification to sign the final paper, but even when the project is completed, everyone will have to start. Think carefully about where you should put Qiao Yu's name.
Jump from one worry to another.
This is still based on the fact that Qiao Yu no longer pays attention to this subject. If Qiao Yu makes any important contributions in the future, Ronald even feels that the research team will start to consider whether it is appropriate to leave this embarrassing work to Qiao Yu. Question. "I don't know either, but I have told Qiao Yu that in about seven or eight hours, we will have a group meeting, and then you can hear him tell you personally about the inspiration for constructing this series of proofs." source."
"Okay, but why not now? You know? I was so excited that I couldn't sleep! You asked me to get up so early, which is cruel!"
"Ronald, you have to consider that Professor Zhang is in Cambridge, and there is still a three-hour time difference between you. If he misses this meeting, he will probably be irritable. Of course, if you need to ensure sleep, you can also set it to nine Hours later, at half past ten in the evening in Huaxia, I believe Qiao Yu is still awake."
"Oh, by the way, the damn time difference! Do you know? When I first learned that China spanned five time zones, how envious was I that there was no concept of time difference internally? Really, this is like a complete country! Rather than damn it like this, different states can’t even unify their time!”
Li Lixing didn't answer this sentence.
Many people will ridicule their own country, but cannot accept the ridicule of others. There is no way, human nature is such a double standard.
"Then the team meeting will be held in nine hours?"
"Well, no need. I can get up in eight hours. By the way, Qiao Yu is really only sixteen years old, right?" "Of course."
"Congratulations, Professor Li. China has produced a true and unquestionable mathematical genius! I can't even imagine what achievements he will have when he is thirty years old." "What are you congratulating me for? Hey... ..." In the video, Li Lixing shook his head and sighed: "But if you have the chance, you can congratulate Tian Yanzhen and Mr. Yuan in person."
It’s really hard to compete for students these days.
God knows how Tian Yan managed to dig out such an incredible guy from the CMO so quickly.
If you follow the procedures, you should first be screened by Huaqing and Yanbei and enter the elite classes on both sides. Then the professors will select ready-made talents from the elite classes.
"Okay, let's get here today, Professor Ronald. You should take the time to rest so that you can be energetic tomorrow morning." "Although I am still in a state of excitement, you are right. Goodbye, Professor Li."
After hanging up the video, Ronald stretched and looked at the complete derivation process again. He stood up with satisfaction and walked out of the study. "Hi, dear, today is such a lucky day..."
Hua Xia, Yanbei University, Qiao Yu waited for a while, but there was no news after Professor Li hung up the phone. He was too lazy to pay attention to Hua Qing's reaction. This was just a phased result.
After completing this proposition, there is still a lot of proof work to be done. Based on this conclusion, the existing theoretical framework can be expanded, and finally the two-dimensional generalization of Chevalet's theorem for reduced Lie algebras and reduced algebraic groups is completed. The next step is to wait for the group
After the meeting, everyone assigned tasks and started the next phase of research.
In any case, it was very satisfying to have figured out a proposition. Qiao Yu planned to take a half-day off for himself and go out for a walk. He picked up his phone and planned to check the time, but someone in his friend group happened to be @him. Click to check it out.
Suddenly, it was Yu Yongjun who showed off a pre-admission notice from Yanbei University.
For Qiao Yu, this thing was quite novel. He had never received it before. So he clicked on the picture to take a closer look.
The upper left part is the letterhead of the Yanbei University Admissions Office, and the upper right corner is three rows of small characters that also contain a phone number, fax number, and an email address. Then in the middle part is the pre-admission notice in red font, and there is a special
serial number.
The title of the text part is naturally the name. "Classmate Yu Yongjun:
Because you achieved excellent results in the 2024 National Mathematics Competition finals, after an interview with our school, we have decided to recommend you to study at the School of Mathematics (Elite Class) of Yanbei University. The official admission notice will be issued after the approval of the Education BU. I hope you will continue to work hard.
Study and strive to achieve better results in future studies."
In the lower right corner is the official seal of Yanbei University.
It looked very formal and awesome, and it didn't look fake. Qiao Yu replied directly: "No? When was the interview? Why didn't I know?" "Haha, I didn't inform you, did I? Boss, I will do it next semester.
I will officially join you!"
Qiao Yu thought for a moment and said encouragingly: "Well, that's awesome. I've never received anything like this."
After posting this sentence, Qiao Yu planned to end the communication with his younger brother, but who knew that two identical notices soon popped up in the group.
No, there is still something different. The number on the pre-admission notice is different from the handwritten name.
Qiao Yu was silent for a long time. Good guy, four of the six official IMO players this year chose Yanbei? I don't know if the other two chose Huaqing. If not, it would be very embarrassing.
After all, Huaqing is not bad...
Wait, what do Gong Jiatao and Yu Wei mean?
He said he didn't receive it, just because he wanted to show it off in front of him?
"Well, I really don't have this pre-admission notice, but I did receive an invitation letter for the World Congress on Algebraic Geometry in France next month, so I'm going to give a thirty-minute report at the conference in Paris next month.
"Although it is just a satellite meeting of the World Congress of Mathematicians, I think it can be considered a kind of exercise, right? The only pity is that it is not a number theory meeting. As you know, I am actually more interested in number theory."
"Hey, in short, don't come to play with me between the 17th and the 24th of next month, because I am not in the capital and have gone to France. Oh, by the way, Director Tian said, Peter Schulz from Germany The professor also asked me to meet at the conference to discuss the Langlands conjecture with me."
Qiao Yu quickly entered three messages in succession. No one bothered him in the middle.
After the last message was sent, no one responded after waiting for thirty seconds.
This made Qiao Yu feel a little unhappy, so he said: "@Everyone is not, please tell me something. For example, is there anything you need me to bring back from France? Or do you have any foreign mathematics idols who want me to get an autograph for you? What? You guys have no feedback at all. I don’t even know if you have seen my reply. This makes me feel very embarrassed, especially you @dayu.”
Yes, even though he @ everyone, Qiao Yu still didn’t forget to @ Yu Yongjun one last time. After all, he said so much in the group chat and no one responded, which was really embarrassing.
"Boss, that guy Gong Jiatao dragged me into another group he created. Two people are complaining about you there. They say you are not human!" So, Qiao Yu really didn't believe that the two of them could tolerate it. It’s not sour to live in.
"Oh, why don't you send a screenshot of their chat?" "Wait a minute, boss, I'll take a screenshot right now."
Gong Jiatao was the first to come out: "@dayu, I advise you to be kind." Yu Wei: "..."
Unfortunately, these two people are obviously not as intimidating as Qiao Yu.
Soon a long screenshot of the WeChat group chat was posted to the friend group.
After reading it once, Qiao Yu felt happy and quickly replied: "Tsk tsk tsk, it's so sour! But @ Chan Zhi Zhi Xue, this is not like your style? You haven't even tried hard yet, and you already want to surrender. ?How can we forget it? Last time you said you wouldn’t get married if you couldn’t catch up with me in grades... You can’t really plan not to marry for the rest of your life, right? So don’t give up!”
Yu Wei: "Yes, you win, I have decided not to marry for the rest of my life!"
Qiao Yu: "Don't say it so early. What if you meet a girl you like in the future?"
Yu Wei: "I only said that I won't get married, but I didn't say that I can't fall in love. If you like it, let's talk about it. If you don't like it, break up. That's it!"
Qiao Yu: "Scumbag! You don't understand that short-term, empty and boring happiness is nothing compared to the momentary feeling of solving a mathematical problem! What a real man pursues is the joy of controlling the truth! And Don’t let hormones take over your brain to pursue those superficial pleasures!”
Yu Wei: "If you take back what you said above, when I become an adult, I can guarantee that I will invest in a project that you are responsible for, as long as it is within 40 million yuan."
Qiao Yu, who had no idea that there would be an unexpected surprise, immediately retracted his previous statement, and then asked: "Forty million yuan? Can you make the decision?" Yu Wei: "My father will give me this amount when I become an adult. The money is completely at my disposal and he will not interfere in any way."
Obviously Qiao Yu was not the only one who was surprised by Yu Wei's words.
The two guys who had been peeking at the screen couldn't help but start showing off.
One sent three question marks in a row, and the other sent three exclamation points directly.
But obviously these two low-level guys who have no lower limit were ignored by Qiao Yu and Yu Wei.
Qiao Yu: "Um... Although this is not very polite, I still want to ask you, does your dad usually keep his word?"
Yu Wei: "My eldest brother gave me the 30 million when he became an adult, and my second brother gave me the 36 million when he became an adult. Now I'm the only one left." Qiao Yu: "Your dad is really fair. This can't be true."
Did you even take inflation into account?”
Yu Wei: "Yes."
Qiao Yu had a lot of emotions. He could only say that there was a huge difference between his father and his father in the human world.
He was about to ask Yu Wei why he suddenly changed his mind so drastically, but the atmosphere that he had managed to create in the group was directly ruined. Yu Yongjun: "@ Chan Zhi Shi Xue, brother, let me ask you something, our dad still lacks a son
No?"
Yu Wei: ".."
Gong Jiatao: "@dayu people can't, at least they shouldn't! If you just recognize me as a foster father, I can't speak up! @ Chan Zhi Zhi Xue, Brother Fu, let's get to know each other again. Do you need a sworn brother?"
Seeing the two shameless guys being so flattering, Qiao Yu didn't bother to chat in the group and directly clicked on Yu Wei's private chat interface.
"Weren't you willing to bet me a hundred dollars before? Forty million? Are you serious?"
"I don't bet with you because it's meaningless to lose money to you. I sponsor your research project, and I am the noble person who brings the funds into the group. These are two completely different things. Even if you are the project leader, when you see me
You should also call me boss! At least the results of your project cannot be achieved without my help!"
Yu Wei's words deeply impressed Qiao Yu, and he sighed sincerely: "I finally understand why capitalists have such a bad reputation! If the descendants of rich people have the same old-fashioned logic as you, how can you let an ordinary person like me
How else can you make money? Listen to my advice, don’t let yourself be so tired, and starting to lose money seriously is what you should do from today!”
Yu Wei: "Get out!"
Still ended the conversation with "Go away".
Qiao Yu really wanted to tell Yu Wei not to think that having a few bad money can show off in front of future great mathematicians. But after thinking about his bank card balance, he gave up. After all, people cannot be compared with others.
He was still thinking about how, when he had received several essay bonuses from the school in the past two years, the cash he received for his coming-of-age ceremony turned out to be tens of millions. Of course, it was just a small goal of 0.4. If it were on the Internet,
That's simply not worth mentioning. You might even be ridiculed as a poor guy.
But Qiao Yu believes that this is definitely not small money, because he has actually made money himself.
If he earns money according to the way he used to provide emotional value to his elder brothers in Internet cafes, even if an elder brother is willing to contribute 20,000 yuan on average, and the studio has to share 10,000 yuan, he can only get 10,000 yuan. This means that he has to serve 4,000 people.
Only the eldest brother can earn so much. According to the average studio that can send him three orders per month, which means a monthly income of 30,000, it will take him about 1,333 months to earn 40 million, which means he will need to work for about 111 years.
.
But in reality it is not possible to save so much.
After all, it is not a simple thing for a person to live for more than a century. Food, clothing, housing, transportation, and health care all cost money.
Qiao Yu originally planned to go out for a walk, but after talking to Yu Wei, he suddenly felt that he couldn't slack off anymore.
A family that can give out a total of more than 100 million as a coming-of-age ceremony to its three sons after they reach adulthood, their assets should probably start in several billions. The second generation of rich people work so hard, and they also have to study for the Mathematical Olympiad and participate in IMO. He is the only one. Children from poor families really have no right to slack off. After all, money will not disappear out of thin air if it is not used. Even if it is just thrown into the bank and depreciated, it is still money and the value is still there.
But if talent is not used, it has no value.
To paraphrase a good old man, Yu Wei is just a second-generation rich man. At most, he can only flirt with him until he is an adult. He wants to be a man of the rich generation! So Qiao Yu picked up the book that was thrown on the desk. I haven't read "Principles of Algebraic Geometry" for a long time after borrowing it from the library.
Starting this week, I will continue to share my reading experience with Director Tian and Mr. Yuan.
In addition, he cannot just ignore Lao Li's projects. He must continue to work on the projects assigned to him by Director Tian. At least he must give Director Tian a decent random prime number model before going to participate in IMO.
Thinking of this, Qiao Yu suddenly felt dizzy.
Just now I thought I could relax a little bit recently, but now that I think about it, his recent tasks are still very heavy! But there is no way, this is his responsibility.
Chapter completed!