In Beijing, Qiao Yu put down the phone and excitedly looked at the formulas on the computer, and began to re-examine the geometric background of the parameters and constants in the formulas.
Qiao Xi is right. There are many parameters and complex formulas. Now he needs to find the commonality of these parameters, so what is the commonality behind the current conditions? No, not just the commonality, but the essential commonality!
Otherwise it is not enough to link these parameters together.
So naturally, Qiao Yu put forward a hypothesis: Whether it is modular form, p-adic geometry or quantized homology category, their parameters can be uniformly represented by a single geometric quantity. The most critical part of this hypothesis is to find
A unified geometric quantity that can capture parameters reflecting the complexity of curves in different geometry tools.
Next is the most troublesome and critical step.
Qiao Yu began to analyze the core parameters of each geometric tool one by one, then listed its core parts, and then found the common points of all these parameters.
To put it simply, it is whether these parameters are controlled by a common constraint parameter. Of course, this is only the first step.
After finding the common constraints, you still have to find the connection between these parameters and the common constraints. This is another extremely complex proposition, but how can I put it, it fully meets Professor Zhang's requirements, complicating the proof process and simplifying the results.
.
And it can also make this formula a truly universal formula. When solving the problem of upper bounds of rational number points on curves, everyone does not need to think about anything else, just use his Qiao Yu-Qiao Xi theorem.
Immersed in the proof of the theorem, the sky turned dark before I knew it.
It wasn't until there was a knock on the door that Qiao Yu woke up from his tedious work.
Qiao Yu raised his head and looked out the window, then stretched on the spot, and then went to open the door.
Senior Brother Chen was standing outside the door. When he saw Qiao Yu standing in front of the door, he immediately raised the lunch box he had just packed in the cafeteria and said, "When I went to eat just now, I saw that you were not moving in the room, so I was afraid of disturbing you.
, I didn’t shout. I thought you must not have eaten yet, so I brought you a piece back.”
"Thank you, Senior Brother Chen!" Qiao Yu grinned and gave Senior Brother a sincere smile, then took the lunch box and turned around and walked into the room.
After spending an entire afternoon's brain cells, Qiao Yu felt really hungry.
This lunch box is very timely.
Chen Zhuoyang followed and walked in, still muttering: "Don't forget to sleep and eat all the time when you are studying. No matter how busy you are, you have to eat. No matter what you do, your body is the most important."
"I know, Senior Brother Chen. Today is a special situation!" Qiao Yu explained with a smile, then opened the lunch box and ate hungrily.
Although I didn’t do much exercise in the afternoon, I spent too much mental energy and felt very hungry.
Even more hungry than playing basketball all afternoon.
Chen Zhuoyang curiously looked at the content on Qiao Yu's computer. Oh my god, there were those complicated formulas and all kinds of messy custom symbols. This made the senior brother sigh inwardly.
It can't be compared, it can't be compared.
"Are you still studying your project?" Chen Zhuoyang pointed at the computer and asked casually.
Qiao Yu looked up at the monitor, swallowed the food in his mouth, and then said, "Yes, it's a pity that there are no results yet."
Before, he would have said a few words, but now that he had just found a clue and realized the difficulty of this problem, Qiao Yu became much more cautious.
He didn't want to talk too much before making results.
Chen Zhuoyang said with self-pity: "Don't be impatient. How can the results be so easy? My boss introduced me to a research group before, which mainly focused on the quantization of geometric structures and modulus spaces on high-dimensional algebraic varieties. The main goal was to publish An article exploring patterns
A paper on the relationship between equations and Kahler manifolds. Alas...
"Um? What are you sighing for? You couldn't publish your paper?" Qiao Yu asked curiously.
"Forget it, it took more than a year to work on it, but in the end, a team from Harvard did the same work and published several papers, which were better than ours. Then the project was hastily ended. In the end, the paper was casually published in a second-district water journal. The key is It’s true that I’ve only done three games.” Chen Zhuoyang said melancholy.
Qiao Yu probably understood the pain of Senior Brother Chen. He followed the top tutor and the tutor also gave resources, but he failed to grasp it... Of course, this cannot be entirely blamed on Senior Brother Chen. After all, a research group can be regarded as a whole.
But in other words, if Senior Brother Chen joins in and is able to turn the tide, the ending may be changed.
"Oh, Senior Brother Chen, what was your main job at that time?" Not knowing how to comfort him, Qiao Yu simply asked.
"Classification of modular forms of algebraic curves, research on the relationship with K stability. Hey, let's not talk about this anymore. In fact, I want to tell you that the first draft of my thesis is almost completed. When will you go to Huaqing? I can take advantage of you. Next time I go there and tie up the last bit." Chen Zhuoyang revealed his true purpose time and time again.
Still too thin-skinned.
Qiao Yu felt that if it were him, he had done so many things before, so he would definitely not talk so much at this time, and only then would the real purpose be revealed.
But he still thought about it and said: "Hey, what are you talking about, Senior Brother Chen? For such an important matter, I can just make a trip to Huaqing for you! But Grandpa Senior said that day that he was busy this week, maybe next time You are free this week. If you want Grandpa Shi to take a look at it in person, just give it to me before next Wednesday."
This time point actually has nothing to do with when Mr. Yuan has time. It is simply that Qiao Yu feels that if he is in the right direction, he should be able to almost complete the results before next Wednesday. At that time, he will help his senior brother to take a look first. Is it more convenient to take the thesis to Huaqing and let Grandpa Shi help me with my eyes?
Before he was sure that this direction was correct, he was not in the mood to care about other things.
Chen Zhuoyang said happily: "Next Wednesday? No problem! By the way, I don't ask Mr. Yuan to help me revise my paper. You just need to ask Mr. Yuan to help me see where there are problems and give me some specific comments." Qiao Yu nodded and said affirmatively: "OK! Just remember to give me the paper before Wednesday."
"Thank you so much, little junior brother, I'll go back and work on my thesis first." "Well, it's okay, you can go and do yours!"
"Hey..." After watching Chen Zhuoyang leave, Qiao Yu sighed and suddenly realized that he had more and more things going on now.
Study, read, coax the tutor and the tutor's tutor, do projects, write papers, participate in selections, and then go to IMO to get medals, while beating friends of the same age... Now I still have to worry about my senior's doctoral thesis.
How much does he have to do by himself? This is probably the legendary saying that a capable person works harder! Well, it seems that he must take on the task of revitalizing the Chinese mathematics community! After all, he is now sixteen years old.
He is no longer the fifteen-year-old brat he once was!
Thinking of this, the stuffed Qiao Yu became excited again, and sat down in front of the computer upright, working, working... In order to revitalize Huaxia Mathematics, and to show the tutor, senior master, and senior brother a little bit of Qiao's color
, he must work out Qiao’s upper bound theorem no matter what!
...
Mathematics research often has a very interesting characteristic, and it is a situation that countless mathematicians have encountered, that is, during the research process, it is likely to get stuck on a certain step, or on a certain problem, and be unable to make progress for a long time.
.Yes, it is stuck there alive.
Sometimes I have an epiphany, and when I have passed this hurdle, I feel suddenly enlightened, and the road ahead is smooth.
But it is a pity that for most mathematicians in the world, this obstacle may last a lifetime, so the project ends without any problem, and the previous work and data are stored there, dreaming that one day, they will suddenly have an epiphany and let these
Research will see the light of day one day in the future, but it is more likely that it will never happen again.
Qiao Yu is actually the same, it's just that his talent is a little higher than countless ordinary mathematicians.
When he realized the need to find commonalities in parameters under Qiao Xi's prompts, this problem no longer seemed to be a problem for him.
All the previous reasoning and proof processes have been done. It can be simplified by finding commonalities. The commonalities are hidden in the less obvious connections behind those parameters. As long as the work is detailed enough, Qiao Yu feels that this is definitely the right direction! Facts
And indeed it is.
For three days, Qiao Yu almost stayed at home except for eating. He didn't even read a book. He devoted himself wholeheartedly to this work, and then he really discovered the existence of commonalities. The higher the level of the model form, the steeper the curve.
Complex, so k~curve complexity.
The prime number p controls the local geometric behavior of the curve on the p-adic number field. Different prime numbers correspond to different geometric constraints. The prime number p is also related to the complexity of the curve, so the parameter q in the quantized homology of the local geometric complexity of p reflects the quantization.
The influence of geometric objects on the global complexity of the curve is a further quantification of the geometric complexity of the curve, so q~global geometric complexity. In other words, although different geometric parameters come from different sources, they all reflect the curve’s appearance under different perspectives.
complexity.
What is this? This is the defining condition for parameter unification.
So on Friday night, Qiao Yu designed a unified geometric constraint parameter 0, and put forward a second hypothesis: the geometric constraint parameter 0 is some kind of modular form level, p-adic field prime number and quantized homology parameter. Weighted combinations, which together reflect the global complexity of the curve.
Based on this assumption, it is obvious that Qiao Yu can get a basic structure: 0=f(g,k,p,q). Of course, at this step, it is obviously not enough.
Because the weight of each parameter is different, to make the structure mathematically reasonable, a combination method that can perfectly reflect the weight of each parameter is needed. The next step is the calculation and verification work, which is complicated, but not difficult.
But one night, Qiao Yu came to the conclusion that the growth of k increases logarithmically with the genus g, so: k ~ glog (g); the complexity of local geometry changes exponentially with the increase of genus, so p ~e^g/2; in quantized homology, the relationship between parameter q and genus g grows. Qiao Yu directly calculated an approximate value: q~g^3/2.
The formula comes out naturally: 0=f(g,k,p,q)=g-log(k) g^2.log(p) g·q
After directly bringing in the expressions of the three parameters, it is: 0=g·log(glog(g) g^2.log(e^g/2) g·g^3/2 At this step, there is only a loss. Grid g is an important parameter.
Next is the simplest simplification work: 0=g·(log(g) log(log(g)) g3/2 g^5/2
After working in front of the computer day and night for three days, Qiao Yu finally typed out the final formula for the rational point estimation of the curve on the computer at 11:37 pm on February 21, 2025: N(X)sC( 0)=0^gθ is the geometric constraint parameter he designed, and g is the genus.
This formula...is really beautiful!
After admiring it for a while, Qiao Yu immediately started to verify it. After all, the formula is useless only if it is beautiful. It must be useful. What he has to do is to find out whether it is accurate based on his own formula.
Qiao Yu chose the classic elliptic curve y^2=x^3 x
According to the known conditions of the BSD conjecture, it can be seen that the curve genus is 1, which can be directly introduced into the formula, and then simplified to get the result: 0=5, well, the 1st power of 5 is still 5. The conclusion is obviously correct.
Because this is the classic Hermitian curve. The rational number points on the curve have been calculated by someone more than ten years ago.
Next came the Model curve, special cases of the Fermat curve, various cases of the Kubert curve... Qiao Yu tried them all.
For example, the Model curve: y^2=x^3 k, k is an integer. Qiao Yu verified the cases of k=-1, k=2 and other known finite rational points, and the results were all correct.
Then Qiao Yu opened Professor Robert Green's paper and used his own formulas to conduct comparative calculations with the formulas derived by Robert Green. On certain points, his formulas were mostly the same as Robert's results, but some Not sure, there are still some differences between the two sides' calculations, but not big.
Well, Qiao Yu didn't bother to worry about who was right and who was wrong.
At least at this point, he can start writing the paper. This step is the easiest for him.
Because he had already written down the process of deriving the formula for more than half a month before, and because he had long considered completing a paper, Qiao Yuben had prepared the entire derivation process in detail, and the next step was just to use professional language to describe those The derivation process is integrated.
It's nothing more than lemmas, theorems, and the proof part. You can basically copy and paste it directly. The main thing is the subsequent proof process about the unified geometric constraint parameter 0, which needs to be written now.
Fortunately, Qiao Yu had a whole weekend to complete this paper.
In fact, of course there is no need to be in such a hurry. At Qiao Yu's age, there is no need to seize the day. It doesn't matter if the paper is completed a few days earlier or a few days later.
He doesn't need a professional title anyway, and he doesn't have the pressure of 3+3. To say the least, even if someone in the world of mathematics does the same research as him and publishes it first, it won't actually have much impact on him. It's just a change. Think about the topic. After all, there is no pressure to publish a paper when you are a student.
It's just that Qiao Yu's idea is very simple.
He didn't study or read papers this week, so naturally he couldn't write down any reading experience on the weekend, and naturally couldn't hand it over to his tutor or Grandpa Shi on Monday. Of course, if he explained it clearly, he believed that whether it was Director Tian or Grandpa Shi across from him, Everyone will believe him.
But how can a pale explanation be as convincing as throwing the paper directly into the mailbox of the tutor and grandpa Shi?
Send the paper to your email first, and then explain on WeChat: "I'm sorry, tutor/master, I didn't study as planned last week, so I can't send you my reading experience this week. The reason is that I spent all my time last week In order to improve my thesis, the paper has been sent to your email."
Qiao Yu doesn't know what others think, but he has understood a truth since the fifth grade of elementary school. Actions are far more convincing than words, and actions with results are far more convincing than actions without results. Trust or It is built up through fruitful actions, or it is consumed through repeated words or fruitless actions.
Why can he have a stable cash flow since he was in sixth grade? Isn't it because he spent more than half a year in fifth grade to establish a good reputation and full trust among primary school students, and accumulated a fixed customer group of primary school students? .As long as he helped write the homework and signed it, the teacher could not find out at all; whenever he agreed to take the exam for him and get high scores, he never failed.
In order to do this, he even gave up on his grades from the beginning. He wrote his homework blindly and got a C every time. He has low grades. He never skips class or makes trouble. He listens carefully during class performances and is busy doing homework for others during self-study... just to show the teacher that this child is quite diligent and obedient, but his grades cannot improve. impression.
The purpose is that even if a classmate secretly reports it to the teacher, the teacher will not believe that he is still capable of helping people with their homework and exams... Now it is just the same thing as in school in reverse.
In fact, Qiao Yu has always been like this, with a careful mind, clear goals, and strong action. Coupled with a relatively good IQ, he can naturally do things with twice the result with half the effort. So Qiao Yu completed the writing of the paper on Sunday afternoon, and then
Secondary review and revision time of the paper.
After reading the papers of Lao Xue's master's students, Qiao Yu understood how ridiculous some detailed errors in the papers were in the eyes of the reviewers.
Therefore, Qiao Yu's requirements for the paper are also to strive for excellence. At least it does not allow for obvious improper wording, ambiguity caused by grammatical errors, and logical loopholes. The content of the literature review and the citation format must be unified and meticulous.
Still busy until late at night, Qiao Yu completely sorted out the paper twice and made some minor revisions. After he was finally satisfied, he titled the paper "Algebra of modular forms and p-radical geometry based on quasi-complete spaces."
The paper "Derivation of Upper Bounds for Rational Points of Curves" was sent to two big guys, Tian Yanzhen and Yuan Zhengxin.
Based on the young man's desire to show off, Qiao Yu originally planned to send a copy to Professor Zhang Shuwen of Princeton.
But after thinking about it, he gave up. Although he was quite confident, it was his first time to write a paper on such a big topic, and it was completed entirely by himself. He was not sure whether his final result would be recognized.
It’s better to let his mentor and grandpa master help him palm his eyes first.
If there are any major problems, he will still have the opportunity to correct them. If Professor Zhang finds any major problems, he will be taught a lesson by an outsider.
Well, being taught a lesson by one's own tutor can also increase feelings, but being taught by an outsider can only be aggrieved when others are still doing it for his own good.
Not to mention that my tutor and my grandpa have a good relationship with Professor Zhang. If they approve this paper, Professor Zhang will definitely see it. It’s just a matter of time, so there’s no need to worry.
After sending the paper, Qiao Yu hurried out and ran to the second floor to take a comfortable bath. He returned to the room and blew his hair casually before falling asleep.
My body is not tired this week, but my mental energy has been consumed too much, making me prone to sleepiness.
Huaqing University, Qiuzhai.
Yuan Zhengxin walked into the office at 7:50 as usual, then turned on the computer and logged in to WeChat.
He planned to print out the reading notes Qiao Yu sent him and take a closer look.
The old man has become accustomed to Qiao Yu writing up his weekly readings and essays and his insights and achievements in a document and sending it to him on time around 7:30 every Monday morning.
This distance education method is not a student, it is better than a student
It is easy for people to fall for sweet words, especially the elderly.
Children always like to complain that their elders spend money indiscriminately, and are deceived by outsiders for health care, financial management, etc., but they never examine whether they are too perfunctory with their parents, and whether their children's identities are as good as others take them to be.
Careful and meticulous.
An excellent salesperson, he greets the elderly regularly every day and pays special attention to the emotional needs of the elderly. As long as it does not cost money, he can satisfy the elderly in everything. He even comes to the door to hammer the back and pinch the feet. He is closer than his own son or daughter, and he speaks nicely. Over time, it can really melt the heart of an iron man...
Nothing is wrong and I am chatting about home affairs: "Dad, you are sick and need...
The business will probably be over, and people's defensive psychology will always slowly disintegrate invisibly.
Not to mention that Qiao Yu has made some small upgrades here. He doesn't call him dad, he calls himself grandson...
"Grandpa, I didn't study this week, so I don't have any experience. But your grandson is not lazy. I finished the paper I have been studying for a long time this week, and it has been sent to your email. You must help me. I'll take a closer look to see if there's anything wrong! My goal is to publish it in one of the top four mathematics journals in the world!"
This sentence is followed by a serious expression, which fits the character of a grandson very well and looks very naughty.
The old gentleman smiled subconsciously, probably thinking: His grandson still wants to be published in the four top mathematics journals in the world. Isn’t publishing a section title enough for you?
Of course I'm still in a good mood.
After chatting with Lan Jie, the old gentleman had already downloaded Qiao Yu's paper and read it.
I am very satisfied, especially after I learned from Qiao Yu that the paper was almost written by me, my evaluation of Qiao Yu was naturally higher.
Originally, he planned to ask the corresponding author of the paper, Professor Xue Song from Yujiang University, to inquire about something, but when he learned that Xue Song had been transferred to Yanbei University, he gave up his thoughts.
Although he loved Qiao Yu to the core, it was still difficult to let go of some barriers.
After all, he is a teacher, and the other party hasn't said much yet. Should he be asked to bow his head and admit his mistake to the traitor first? But if it involves Qiao Yu...
Well, anyway, this child recognized him as his master and his family lineage, and that was enough for the time being. Soon, the paper was printed out.
The old man had heard Zhang Shuwen talk about Qiao Yu's ideas, so he was not surprised by the title of this paper. However, after reading the introduction and table of contents, the old man turned directly to the last two pages and saw the final result. He couldn't help but be stunned. He has become a lot more serious. Good guy, this kid really made a universal prediction formula?
This also made the old gentleman look a little more serious and even a little more excited when he read this paper.
Don't mention it, if this result is correct, at least if no obvious flaws can be found for the time being, this result is really qualified to be included in the four top mathematics journals.
If Qiao Yu's method is correct and applied to numerical applications, it can effectively assist in judging the convergence of the iterative process, help analyze errors, and optimize the convergence speed of related algorithms. Especially when solving optimization problems, it can help to set Constraints ensure that the solution is within the range of rational numbers and help simplify calculations.
After the old man became serious, he called the assistant directly into the office: "Go and inform me that I will not attend the group meeting this morning. Then just give me a summary of what was said at the meeting." "Okay, Professor. .”
At Yanbei University, Qiao Yu was doing morning exercises outside his dormitory and study room.
Last week, he was working on some papers, and felt like he was welded to a stool every day. He felt like he hadn't done any good exercise in a long time, so it was just a good time to exercise. He is only sixteen years old, and he can grow taller if he maintains a certain amount of exercise.
And for Qiao Yu, the new week is like being recharged for seven days, giving him the joy of squandering time. This is probably the benefit of living a fulfilling life. Occasionally being a little lazy can be enough. Full of happiness.
Unlike those who are used to fishing every day, after all, once a person is used to fishing, the happiness brought by fishing will become less and less, but once a person is unable to fish due to something, the harm caused will not be the same. There are tons... When Chen Zhuoyang came to the front of the building with energetic steps early in the morning, what he saw was the scene of his junior brother doing jumping exercises at the door, and he suddenly felt like he had seen youth.
"Qiao Yu, morning!"
"Senior brother Chen, morning!" Qiao Yu panted and replied.
Somewhat sighing, it seems that he has not done anything like exercise since he went to college, so it is easy for people to miss the youthful days of high school. Then he subconsciously remembered that the guy in front of him is only sixteen years old this year. , still a freshman in high school.
"At least I have more beautiful memories of high school life than he does."
Chen Zhuoyang thought to himself in his heart, and then suddenly discovered that he had not contacted his classmates in high school for a long time. He did have a group of classmates, but unfortunately few of them could talk to them all year round.
In addition, various class reunions have been almost demonized in recent years. It seems that no one has the intention to get together, and no one will organize such a thankless thing. Suddenly, the memories of those three years in high school feel like... It's not interesting. The only thing that makes him miss is probably that his grades were consistently ranked among the top five in the class. Every time the teacher reported the results for the exam, the envious eyes of the classmates around him, right?
It's a pity that after coming to Yanbei University, the feeling of being taken seriously by others has never been there again. Looking back now, Chen Zhuoyang feels that he should have woken up earlier. When he was studying for a master's degree, the classmates around him were already inhumanly powerful. The undergraduate level is completely different.
Really, he felt that with only seven points of effort in undergraduate studies, his grade point could be stable in the top 3% of his grade. When a brother in the dormitory was still worried about completing homework, he could quietly play games next to him. During the game, By the way, it is part of his daily routine to give advice to his dormitory brothers on their homework.
People who have never been a top student cannot understand that sense of superiority.
But after he was admitted to Yanbei to study for a master's degree, he had to go all out to gain a little status among the classmates led by his tutor. As for playing games? Are you kidding!
After arriving at the research center to study for a doctoral degree, except for the exciting day after passing the exam, he was constantly hit. His goal was to achieve results at the doctoral level, and he was recommended to exchange abroad. The academician organized his doctoral defense. After graduation, Yanbei University directly offered him a professor or researcher position in order to keep him...
Now, as long as I can graduate, it will be fine.
The change in mentality during this period has been a lifelong pain for Chen Zhuoyang. It can only be said that the person who was once full of yearning for mathematical research is dead. Many times, Chen Zhuoyang has begun to suspect that he may not be as good as he imagined, because he watched helplessly. I gradually couldn't keep up with the progress of my classmates.
But since Qiao Yu came, Chen Zhuoyang felt that it was no longer a matter of whether he was excellent or not. He began to suspect that he might be slightly mentally retarded. After all, the ignorant are fearless. If he hadn't been stupid enough, how could he have had the courage to take the doctoral examination under Director Tian? of?
Fortunately, the embarrassing days are about to pass.
If he can pass the thesis and prepare for the defense in two or three months, he can graduate. He can say goodbye to this place full of talented people and never come back again... He walked past Qiao Yu with complicated thoughts in his heart. , suddenly heard a cell phone ringing tone.
Subconsciously he took out his cell phone from his pocket, but it turned out it wasn't his, and then a youthful voice came from behind him.
"Hey, Director Tian, ​​good morning!... Well, I've eaten and I'm exercising... Oh, now?... Well, okay, I'll be there right away." Chen Zhuoyang turned around and asked: "Qiao Yu, the boss asked you to go to the office?"
"Yes." Qiao Yu nodded.
"Oh, do you know what I asked you to do?"
"I wrote a paper last week and sent it to my supervisor last night. Director Tian probably wanted to give me some advice, right? Or maybe he found something wrong with the paper and wanted to tell me clearly and then rewrite it." Qiao Yu said cheerfully. replied. "Oh, the paper is finished? Which one?"
"It's the issue discussed in the last seminar, about the accurate prediction of rational points on the upper boundary of the curve." "Has it been completed using Schulz's method?"
"Yes, um, senior brother, I'm sorry. Director Tian asked me to come over quickly, so I'll leave first. Let's talk back." After saying that, Qiao Yu waved casually to Chen Zhuoyang, and then trotted towards Tian Yanzhen's office. He ran towards the building he was in. Chen Zhuoyang looked seriously at Qiao Yu's quickly leaving back, and suddenly felt that it looked like his lost youth.
"Director Tian, ​​what do you want from me?" Qiao Yu knocked on the door, but did not go in directly. Instead, he opened the door a crack and only stuck his head in, looking at Tian Yan sitting at his desk. Zhen asked. He looked like he saw something was wrong and immediately ran away.
Tian Yanzhen raised his head and glanced at the funny Qiao Yu, and was so angry: "Come in, close the door!"
"Oh, okay, Director Tian." Qiao Yu then walked into the office honestly and closed the door.
Tian Yanzhen glanced at Qiao Yu, who had empty hands, and said, "Pick a book and sit next to it and read it. I will ask you any questions at any time." After saying that, Tian Yanzhen patted the paper on his desk.
"Okay!" Qiao Yu agreed readily, then came to Tian Yanzhen's bookcase, turned around and asked again: "Director Tian, ​​which book is the most expensive in your bookcase?" "Huh?" Tian Yanzhen Not knowing why, he turned to look at Qiao Yu again.
"Anyway, I will definitely read it today. You will give it to me when I leave. It will be more cost-effective for me to choose a more expensive one. After all, there are not many opportunities to come to your place to read." Qiao Yu explained seriously. Tian Yan was really happy: "Okay, don't worry about these books. If you want to read them, come and get them anytime. When you graduate, I will give them all to you."
Qiao Yu said excitedly: "Director Tian, ​​I'm taking it seriously! I will come directly to move books on the day I graduate. You can't stop me." Tian Yanzhen said casually: "No problem, you can come and move a few books It’s just a book, of little value.”
Qiao Yu casually took out a "Classic Introduction to Modern Number Theory" from the bookcase and retorted: "Ordinary books are definitely of little value, but the books placed in your office are different. The value of a book lies in its author. , The second one is a collector! When I get the books, I will go to the auction. These are all books collected by the masters of Chinese mathematics. How can the value be easily increased by hundreds or thousands of times? "
Tian Yanzhen was startled for a moment, then said with a straight face: "Where are there so many weird words? Sit aside and read a book. I didn't ask you, so don't talk." "Oh, okay, Director Tian." Qiao Yu immediately sat down and sat down. , began to flip through the book.
Flattery should not be too frequent or too deliberate. It is enough to make the instructor happy once in a while, otherwise the reputation will increase and it will be very troublesome in the future. As for whether the teacher will accept this trick, that is a matter of opinion. .
But from a human point of view, people all like to hear nice words, especially those from the most proud disciples. As long as you persevere and conscientiously choose the most favorable times to flatter occasionally, Qiao Yu believes that Director Tian no matter what Not with a straight face, but definitely happy in my heart.
Anyway, the teacher didn't let him talk, so he didn't argue and just read quietly. He just didn't stay quiet for a few minutes...
"In this paragraph, are you sure that k/p/q, the three parameters are truly independent? Is there enough data to support it?"
"Well, I have deduced this, introduced the parameters of multiple known curves, and fitted it. Anyway, it seems to be no problem so far."
"Manual fitting? You don't have a supercomputer to do numerical simulation? There are enough data samples in the LMFDB curve database to conduct batch verification. Numerical level verification and batch analysis can be done through supercomputer, so that it can be more convincing. "Ah? Get a supercomputer?" Qiao Yu was at a loss. He was just a little Karami who just wanted to publish a paper, so he still wanted to rent a supercomputer?
"Oh, you don't have an account for the school's supercomputer, right? In this case, you can use my account first. Okay, you can continue reading and I will continue reading." After saying that, Qiao Yu saw Tian Yanzhen pick up the pen and list. I made a note on the printed paper, and then continued to read.
The rest of the process was lackluster.
"Are you sure that the relationship between modular form level k and genus g can be universally applicable, especially in situations where high genus curves or moduli spaces are non-trivial?"
"Not just k, this part is actually a place where multiple tools meet. Professor Zhang said that the proof process can be complicated. The entire logic of this piece is based on the multi-level complexity of algebraic geometry. Here I used the formula of the weak BSD conjecture ..”
That's about it, one question and one answer.
Tian Yanzhen raised a question, and then Qiao Yu explained in detail as much as possible his thoughts besides the paper.
Unknowingly, the whole morning passed by. It wasn't until Qiao Yu felt his stomach growling that he finished reading the paper. "Last question, did you complete this paper by yourself?" Tian Yanzhen looked at Qiao Yu seriously and asked.
Then, without waiting for Qiao Yu's answer, he took the initiative to explain: "I'm not doubting you, but it's a very serious matter to submit such a paper after being verified by supercomputer.
If you have discussed with others in various ways, and the other party has indeed given you some effective suggestions or directly participated in the research of the topic, it may cause controversy if the author only signs your name after the paper is published. In this case, You'd better communicate clearly with the other party, such as whether you need to add the other party's name."
There was no need to think about it. Qiao Yu replied directly: "Well, indeed, I have only communicated with Qiao Xi about this paper. If it can be published, I originally planned to add her name as the second author. ." "Qiao Xi?" Tian Yanzhen was stunned, and then immediately said: "Your mother?"
"Yes, my mother, the most important part is the simplification of the results. I really couldn't think of how to effectively unify those parameters, so I called my mother. My mother told me that mathematics is to combine different conditions. Look for possible hidden logical connections.
I was inspired by this sentence to completely create the final result. That... is that my mother currently has no job, and she has been staying at home to take care of me, so she was added as the second author. , it’s not a big problem if the work unit column is left blank, right?
When I look at other papers, it seems that the authors are followed by their affiliations. If there is no affiliation, will there be any problems?"
Tian Yanzhen closed his eyes and thought for a while, sighed deeply and said, "It's not a problem that she doesn't have an employer, and she is not the first author. She just needs to indicate Independent Researcher or directly write Yanbei International Mathematics Research Center. I It means that you have not discussed this paper with anyone else in the mathematical community, including Mr. Yuan, right?"
"Yes, Teacher Tian. Grandpa Shi only received this paper from me last night, so there will definitely be no controversy in this regard. You can rest assured!" Qiao Yu replied with great certainty. Suddenly, the phone rang again. Qiao Yu took out the phone and looked at it. His expression was a little embarrassed, but he still said: "Hey, Grandpa Shi's phone number."
"Then why are you hesitating? Take it."
Chapter completed!