Chapter 140 Mathematics? It’s nothing more than a creator’s game!
Chinese people have a special affection for red.
In fact, in other cultures, red is used to alert the world because it is eye-catching.
For example, in most Western stock markets, red means falling and green means rising.
But for China, a rising star in finance, although the stock market was established a hundred years later than those financial giants, from the beginning, red was defined as rising.
Otherwise, Chinese people think red is festive.
At the Beijing Airport, the players who got off the plane saw a bright red color in their eyes. Most of them were arranged by sponsors.
Many people don’t know that China has always been the source of platinum sponsors of IMO.
This is why even IMO's management is reluctant to offend Qiao Yu easily.
After all, to some extent, many people have regarded Qiao Yu as the future representative of the Chinese mathematics community.
Of course, this time the Chinese team's five gold medals and a perfect score of 248, the third best result in history, are indeed worthy of a grand welcome ceremony.
After the excitement, the team partially disbanded in the capital.
Because the members of the team this time have several activities during the summer vacation, such as accepting interviews with some media. But Qiao Yu does not need to participate.
Naturally, this was not requested by the media. It was requested by both Tian Yanzhen and Yuan Zhengxin at the same time.
Letting Qiao Yu attend IMO is already a compromise between the two bosses. It is impossible to go around and participate in various interviews and activities.
At least in the eyes of the two bosses, Qiao Yu doesn't need this meaningless exposure now.
Especially in the eyes of the two big guys, there is no need for meaningless praise from the outside world.
Qiao Yu had no objection to this arrangement.
Anyway, he doesn’t plan to debut... and he really doesn’t know what to say during the interview.
Well, you play games every day in the IMO competition circle and challenge players from all over the world. Not only did you win the IMO gold medal with a perfect score, but you also won the award for the most awesome mental arithmetic game?
And what Qiao Yu is most looking forward to is not these things, but that Qiao Xi is coming to the capital.
Qiao Xi has already sent him the ticket booking information on WeChat. The high-speed train will arrive at West Beijing Station at 2:30 pm tomorrow morning.
He could finally let his mother see his life in the capital with her own eyes. For Qiao Yu, this was much more interesting than being interviewed.
So after a simple celebration ceremony at the airport and a few more group photos, Qiao Yu was taken back to Yanbei University by someone called by Tian Yanzhen.
…
"Director Tian, ​​I'm back."
In the car, Professor Luo who went to pick him up said that Tian Yanzhen was waiting for him, so Qiao Yu went back first to put his luggage and then came to Tian Yanzhen's office.
"Well, sit down..."
Without Tian Yanzhen's instructions, Qiao Yu walked in consciously and sat down opposite the instructor.
"Did you enjoy going to Australia?" Tian Yanzhen asked.
"Happy." Qiao Yu nodded and replied honestly.
There is nothing to hide. Professor Zhou and Professor Zhang will probably report every move he makes in Australia to Director Tian and Mr. Yuan across from him.
He did let himself go a little bit this time when he went out to participate in IMO. However, Qiao Yu felt that there was nothing wrong. People always need to relax. The string in his heart was too tight some time ago.
The main reason is that the man still puts too much pressure on him.
If the problem in the proof of the geometric Langlands conjecture cannot be found in time, that man will be in the limelight at the World Congress on Algebraic Geometry.
Of course this is intolerable.
"Well, just be happy. Then you have to calm down. Take a look at these first."
With that said, Tian Yanzhen took out three beautifully bound documents from the drawer of his desk and handed them to Qiao Yu.
Qiao Yu took it curiously and saw that there were three offers from different companies.
They are all from big manufacturers...
For example, little Li Baba had an encounter with Qiao Yu.
He opened it and looked at it casually, and it was a letter of appointment with advance payment. If he was willing to accept it, the other party would be willing to pay for all his expenses during his studies, and even get a salary.
This way, after he graduates with his Ph.D., he can directly start working. The treatment offered is quite exciting.
Qiao Yu looked at Tian Yanzhen without knowing why.
Logically speaking, it is impossible for these big companies to not have his contact information, but they did not contact him privately and directly sent the offer to Tian Yanzhen.
"How's it going? Are you interested?" Tian Yanzhen looked at Qiao Yu and asked.
Qiao Yu shook his head slightly and said honestly: "I'm not interested. I think if I really want to work for someone after I graduate, they can offer me a higher price."
"Ha ha……"
Tian Yanzhen smiled happily: "Well, I think so too. Then I'll refuse it for you."
Qiao Yu nodded and handed all the offers back casually.
He has no interest in working part-time, but it would be fine if it was a consultant position.
Anyway, if there is a problem, send him a copy, and if he can solve it, he will earn a share of the money.
But just as Tian Yanzhen said, Qiao Yu also felt that it was too early for him to consider making money.
After all, he can only make a small amount of money now.
Now that we no longer have to worry about food, clothing, housing and transportation, there is no need to waste energy on this aspect. It is better to lay a solid foundation quickly so that in the future, like Schultz, he can make big money by directly cooperating with large enterprises like Microsoft on projects.
Tian Yanzhen put several offers aside casually, then looked at Qiao Yu and said, "While you were attending IMO, I talked to Mr. Yuan twice about your future."
Qiao Yu's ears perked up instantly.
The two instructors don't follow martial ethics, and they actually engage in liaison in private.
"I won't go into the specific communication process, because you are very interested in the distribution of prime numbers, so we all have full confidence in your ability to solve the Riemann Hypothesis."
Qiao Yu nodded subconsciously, then shook his head and said blankly: "Riemann Hypothesis? Well... isn't my next task to complete my undergraduate studies?"
Tian Yanzhen nodded and smiled: "Yes, undergraduate studies are the foundation, and it is indeed what you need to do in the next stage. But this is not inconsistent with your research.
In fact, we all agree that your energy is strong enough to support you in conducting targeted research while consolidating your foundation. This is also related to your previous study habits and results.
While solving a problem, you will take the initiative to read relevant literature, and you will always gain a lot. This is actually part of basic learning.
For example, you have actually accumulated a lot of relevant basic knowledge in the fields of algebraic geometry and mathematical analysis. What you lack is other related basic knowledge."
Qiao Yu looked at Tian Yanzhen blankly.
Although he didn't mind doing the research, it still seemed to be looking down on him too much.
"Um... Director Tian, ​​what you and Mr. Yuan mean is that you want me to solve the Riemann Hypothesis as an undergraduate, right? Isn't this a little too high of a view of me?"
Qiao Yu couldn't help but said.
Even though he is very confident in himself, this is no joke.
In the past, he said he was going to do the Riemann Hypothesis just because he wanted to dawdle. Now he doesn't plan to dawdle anymore, and the instructor is full of energy again!
If you really want to play like this, let alone graduate in one year. Qiao Yu doubts whether he can graduate in ten years.
"What are you thinking about? If the Riemann Hypothesis is so easy to prove, is it still your turn? Do you really think the $1.5 million reward from the Clay Institute is unattractive?"
Tian Yanzhen shook his head and said: "Don't worry, Mr. Yuan and I will not assign you tasks that you cannot complete at this stage. The Riemann Hypothesis is the ultimate goal, but the road is built step by step.
In fact, compared to the big proposition of the Riemann Hypothesis, there are many small propositions in related fields that can support it. For example, the Montgomery log pair distribution conjecture, the small prime gap conjecture, the Modell conjecture, and Landau-related problems.
This also includes the twin prime conjecture, Legendre conjecture, the cumulative properties of Möbius function values, etc.
Especially the twin prime conjecture. If you are interested in prime numbers, you should know Professor Zhang Yuantang's paper "Bounded Intervals between Prime Numbers", which proved that there are infinite pairs of prime numbers with gaps less than 70 million. This is already a great breakthrough.
And his proof of the Landau-Siegel zero-point conjecture can also give you some reference. And I have already contacted Professor Zhang. If you are interested in the twin prime conjecture, he is willing to help you.
Of course, we are not asking you to prove the twin prime conjecture. Even if you push this gap further, it is still an achievement. What we value most is your idea."
Qiao Yu nodded subconsciously, and then became more deeply aware of the value of a good mentor.
Whether it is Tian Yanzhen or Mr. Yuan, as long as he wants to research and study, he can directly find the best people to help him.
Tian Yanzhen continued: "But these are suggestions from Mr. Yuan and I. It is up to you to decide from which point to start formal research.
You have to know that the Fields Medal pays more attention to those novel mathematical ideas. Coincidentally, we all agree that this is exactly what you are good at."
"Fields Medal? This should be something I only consider after I turn twenty, right?"
Qiao Yu said blankly.
"When most mathematicians around the world think that you are already eligible to compete for the Fields Medal, you can start to consider it. It has nothing to do with your age. There is no age limit for the Fields Medal."
Tian Yan said truly.
Teacher and student looked at each other. When Qiao Yu realized that Director Tian was extremely serious today, he understood.
Is he afraid that his mentor and grandpa think he has a pressure-bearing personality? The greater the pressure, the higher his achievements?
But it’s quite challenging to think about it.
"So what you are saying is that I can choose one of the above propositions as the main research direction in the next stage?" Qiao Yu asked.
"Yes, if you need to collaborate with someone on research, you can also tell us. Mr. Yuan and I will do our best to help you contact the other party. Of course, you can also choose the co-researchers you can contact."
Tian Yanzhen added.
Qiao Yu took a deep breath, then nodded, and solemnly agreed: "Okay, Director Tian. I understand. I will report my research plan to you and Grandpa Shi as soon as possible."
When something is arranged, if you can't refuse, why not just keep working hard.
Not to mention that when the research produced results, the beneficiary was actually himself. It was just an extra burden.
Moreover, both Director Tian and Grandpa Shi were actually very humane towards him. They assigned him tasks based on what he was previously interested in.
It's like he once told his deskmate Zhou Shuang that when you work hard at something but seem to gain nothing, you should quickly give up and leave.
His situation obviously does not fall into this category. He worked hard and gained a lot.
"Yes, before the semester starts, make the topic selection and planning first. This way, after the semester starts, you can more easily allocate your energy between study and research.
You should know that both we and the opposite Huaqing have scientific research training programs for outstanding undergraduates. Most of them start in their sophomore year, so you are just one year ahead of schedule. Okay, you can go back and rest quickly."
Tian Yanzhen said with a smile, obviously very satisfied with Qiao Yu's statement.
Of course, this analogy is not that appropriate. After all, the scientific research training program at the undergraduate level actually starts with professors.
The task assigned to Qiao Yu was to be responsible for a topic independently, which was also a cutting-edge research topic in number theory. The difficulty was not the same as that of Qiao Yu.
Qiao Yu nodded, but still sat there steadily and did not leave.
Tian Yanzhen waited for two seconds and asked, "Is there anything else?"
Qiao Yu nodded and said coyly: "Well, I would like to ask you to help me arrange a car to pick up a few people at the train station tomorrow."
Tian Yanzhen agreed: "I'll have someone contact you directly later. Oh, the summer camp is about to start, right? Go pick up the classmate you talked about last time?"
Qiao Yu shook his head and replied: "It's not to pick her up, the main reason is that my mother will come with her to see me, and her teacher seems to be with another classmate from their school who was selected for the summer camp, but he is a sophomore in high school.
"
"Hmm? Your mother will come with you tomorrow? When will she arrive?" Tian Yanzhen became serious.
Qiao Yu replied: "Yes. We agreed before. We should arrive at Beijing West Station at 2:30 in the afternoon."
Tian Yanzhen ignored Qiao Yu, but picked up the phone and started looking at it. After half a minute, he raised his head and said, "I don't have any plans tomorrow afternoon, so I'll go pick her up with you. We'll leave at 1:30 p.m.
If there are four people, just arrange two cars.”
Qiao Yu was a little surprised and said, "Ah? Um...are you going too? Will it waste your time too much?"
Tian Yanzhen said: "This is the most basic courtesy. I have to thank her for raising such a good child. By the way, you should also tell Mr. Yuan about your mother coming to the capital. Okay, it's settled.
.You go and rest."
"Oh, I'll leave now, see you, Director Tian."
Qiao Yu walked out of the office, feeling very emotional. He still had to learn the style of a big boss.
Even though I know this is a way to win people's hearts, I still can't help but feel warm in my heart...
With the dignity of an academician, he went to pick up Qiao Xi in person, which not only gave his mother face, but also allowed him to intuitively feel the importance he received... Well, no matter what, my mother should be very happy, right?
Qiao Yu thought to himself, but he was really not sure how Qiao Xi would react.
For many years, he felt that Qiao Xi's mood had always been very stable, with almost no emotions of being too excited or too depressed.
If I had to describe it, it would probably be - it's good just like this, and it's not like I can't survive anyway.
But Qiao Yu has nothing to worry about.
Unless she is drunk, Qiao Xi doesn't actually have to deal with many inappropriate situations in social circles. At most, she just talks less outside.
Forget it, never mind.
However, Qiao Yu still followed Director Tian's instructions and sent a message to Mr. Yuan, telling him that he had returned to school. By the way, he also told Mr. Yuan that his mother would come to the capital tomorrow.
But after returning to the room, before Mr. Yuan could reply, Qiao Yu rushed into the bathroom and started taking a shower.
After nearly a day of flying, my body stinks.
…
In Huaqing and Qiuzhai's office, the old man is entertaining guests, but the way he treats guests is a little different.
The two of them held a magazine in their hands and read it silently.
The tea next to it has obviously cooled down, and there is no longer any elegant steam coming out...
The magazine is exactly the sample magazine Ann.Math specially sent to Qiao Yu by Qiao Yu.
Lot Dugan mailed a total of five copies to Qiao Yu. Qiao Yu gave two copies to his mentor and two copies to Mr. Yuan, and kept one for himself as a souvenir.
It's obviously not the first time Mr. Yuan has watched it, but he still smiles when he sees the wonderful parts.
Because I thought of what happened when Zhang Shuwen was in Huaqing at the beginning of the year and was invited to Yanbei to listen to Qiao Yu's lecture.
Zhang Shuwen also called him afterwards.
Neither of them expected that Zhang Shuwen just taught the boy a few words, but Qiao Yu actually wrote the paper.
The results given are still so simple and beautiful. Especially this unified set parameter constraint theorem is simply a stroke of genius.
This idea is actually not difficult, but the difficulty is to use this idea to unify four extremely complex parameters with different weights into a basic geometric structure.
Every time he sees this, Yuan Zhengxin can't help but want to admire Qiao Yu's genius idea!
At this time, he couldn't help but feel a little show off, and subconsciously looked at the junior next to him.
He is said to be a younger generation, but in fact, like Tian Yanzhen, he is also nearly seventy years old.
"Lu Yuan, have you seen the unified geometric parameter constraint theorem? How is the proof?"
"What a genius idea! Oh...Yan Zhen is so lucky." Tan Luyuan broke away from his concentration and looked at Mr. Yuan next to him with emotion.
As a mathematician of the same generation as Tian Yanzhen, Tan Luyuan was indeed quite unconvinced by Tian Yanzhen.
In fact, when it comes to which of the two has more knowledge and who has less knowledge, history is really hard to judge.
But there is no way, life's fate is like this sometimes. I have been working on a project for decades, but someone else has stepped ahead of me.
The glory naturally belongs to others.
In recent years, Tan Luyuan, who found it difficult to make academic achievements, like Mr. Yuan, put more energy into education.
In recent years, we have produced several relatively proud students, but to be honest, they are still in the stage of scientific research accumulation.
Who would have thought that Tian Yanzhen would discover another 16-year-old evil genius without saying a word.
No, it is said that he was only fifteen years old when he was discovered. How can others compare this?
I can't compare with myself, and my students can't compare with me either... Maybe having such a student in my life is enough.
"If nothing else, his luck has always been good." Yuan Zhengxin smiled and agreed with this statement.
Tan Luyuan put down the paper in his hand and said with emotion: "It seems that Teacher Yuan, you have really put aside that grudge."
Yuan Zhengxin smiled self-deprecatingly and said, "What else can I do? My grandson insists on calling him mentor and me calling him grandpa. You can't make it difficult for your child to be caught in the middle, right?"
Tan Luyuan was stunned at first, and then the corners of his mouth couldn't help but curl up. He probably understood how Mr. Yuan's temper was reversed.
If a child like this comes up and calls him Master, who can withstand it?
Could it be that he revealed that the relationship between the two was not good and told the grievances of the previous generation to a sixteen-year-old child?
Neither Yuan Zhengxin nor Tian Yan would be able to do such a thing. In other words, whoever does such a thing to a child first will lose.
"This kid is really... very interesting." Tan Luyuan sighed again.
"More than just fun."
The old man shook his head and continued: "You don't know that he is not only talented, but also very self-disciplined. He takes the initiative to send me his reading and learning experiences every week.
By the way, I introduced him to Li Lixing's research group, and within a few days he helped him solve a problem that had been bothering him for half a year. He didn't tell me, but Li Xing came to express his gratitude, and I didn't know until he came."
Tan Luyuan asked attentively: "Is there anything else? Could the topic you are talking about be the one that Professor Lixing applied for the Natural Science Foundation of last year?"
Yuan Zhengxin smiled and nodded, saying, "Exactly."
Tan Luyuan sighed with emotion: "It seems that he really has a deep understanding of the geometric Langlands conjecture."
Yuan Zhengxin nodded slightly and continued: "By the way, I learned about this from Li Xing that day, and on a whim, I wanted to see what this little guy would do after he made such outstanding achievements in silence.
Without notifying anyone, I made a special trip to Yanbei's Digital Research Center. Guess what I saw my grandson doing when I went there?"
Tan Luyuan looked at Mr. Yuan's expression across from him and said with emotion: "You've already asked me this question. I'm afraid you haven't relaxed at all and are still studying seriously?"
Yuan Zhengxin laughed and said: "Haha, that's right! Sixteen years old is the age when you are young, frivolous and high-spirited. You can make achievements and immediately devote yourself to studying knowledge."
After saying that, Mr. Yuan's face changed and he said in a low voice: "Look at other students. They complain if the requirements are a little stricter. They feel that the teacher is too demanding!
The difference is more than just talent? Therefore, the requirements for Huaqing’s elite class this year must be raised. Those who are dawdling can no longer be admitted!"
When Tan Luyuan heard these words, he picked up the cup and took a sip of tea to hide his embarrassment...
He understands the education model of Huaqing Talented Class, but he still thinks that the requirements of Huaqing Talented Class are low? Then other schools should simply stop offering basic mathematics classes...
Putting down the tea cup, Tan Luyuan simply changed the subject: "Teacher Yuan, what do you think of Qiao Yubi's comparison with Tao Xuanzhi?"
Yuan Zhengxin waved his hand and said decisively: "Qiao Yu will soon surpass Xuan Zhi."
Tan Luyuan was stunned...
Of course, he was already very aware of Qiao Yu's status in the old man's heart, but he did not expect such a high evaluation.
After all, Tao Xuanzhi won the Fields Medal at the age of thirty-one and is also recognized as one of the geniuses in mathematics.
"It's passed, it's been... Qiao Yu is only sixteen years old, this will pass quickly." Tan Luyuan shook his head and said.
The old man smiled and said: "It's passed? It's a long way. Believe it or not, I can see Qiao Yu solve the Riemann Hypothesis."
Tan Luyuan looked at Mr. Yuan in surprise and didn't know how to reply to this sentence.
Could it be said that it depends on how long you can live?
Wait, Riemann Hypothesis?
"You plan for Qiao Yu to start doing the Riemann Hypothesis now?" Tan Luyuan couldn't help but ask.
"It's not our intention, but Qiao Yu is actually more interested in number theory. He once said that the study of geometric Langlands conjecture, Langlands program, quasi-complete spaces and other theories is all in the hope of creating more tools .
This is where his interest lies. Qiao Yu has big ambitions! When he talked about the future with Tian Yanzhen before, he said that he wanted to do this conjecture. Forget it, you won't believe me if I tell you this. Today He just came back and wanted to rest.
In this case, I will send him a message and ask him to come to Huaqing to meet you tomorrow. You will know after chatting with him. It’s a long way to go. I dare say that you are not as bold as this kid to think about some research! He is not like that The kind of person who murders his own time with inaction."
With that said, Yuan Zhengxin put on his glasses and picked up his phone. When he opened WeChat, he saw that his beloved grandson had sent him a message.
After seeing it, I laughed.
"What a coincidence, Qiao Yu's mother is coming to the capital tomorrow. She is going to prepare a reception banquet. It just so happens that by being your host, I can be considered a reception for you."
Tan Luyuan smiled bitterly.
Good guy, he's here today, and the reception banquet is scheduled for tomorrow? It seems that he got this meal because of the little guy's mother!
This old man is extremely biased.
To prepare a feast for Qiao Yu’s mother’s arrival…
Tan Luyuan suspected that Mr. Yuan regarded Qiao Yu as his grandson...
…
Qiao Yu opened his eyes suddenly.
He woke up, but it was still dark outside the window. Qiao Yu was lying on the bed without moving.
But his body didn't move, and his mind began to think about what Director Tian said to him after he came back yesterday.
The Riemann Hypothesis was a subject that Master Shi did not want to get involved in before. This probably explains its difficulty, but it is also very interesting.
Of course, neither Director Tian nor Master Shi across from me was actually that harsh.
At least he was not required to prove the Riemann Hypothesis within a certain period of time.
But then again, even if it is just those predicate propositions, it is not that simple to solve them.
Otherwise, it wouldn’t be a series of conjectures. By the way, Director Tian also said that we need to have new ideas.
In fact, when he wanted to study prime numbers, Qiao Yu had already roughly understood the Riemann conjecture. Of course, it also included the twin prime conjecture.
There is no doubt that this belongs to the research scope of traditional number theory. At present, the main research methods are also focused on techniques such as prime number theorem and sieve method.
In fact, Qiao Yu has also read the paper written by Professor Zhang Yuantang that Professor Tian mentioned yesterday. The sieving method is one of the main mathematical tools.
To put it bluntly, it is to identify prime numbers by eliminating non-prime numbers through step-by-step screening.
However, Professor Zhang's method is indeed novel. For Qiao Yu to evaluate it, it uses a new application of the weighted screening method to control the spacing between prime numbers.
But obviously this is not enough, otherwise Professor Zhang would directly solve the twin prime conjecture.
In addition, Qiao Yu feels that the screening method is still too troublesome and lacks beauty.
The paper was written for more than fifty pages. Moreover, the method cannot be expanded, for example, it cannot be applied to triplet prime numbers and larger sets of prime numbers.
Moreover, Qiao Yu had a feeling that if he continued to study along this method, at most he could limit the gap between infinite pairs of prime numbers to a very small number, such as a single digit greater than 2.
But if you want to narrow it down to 2, it is definitely impossible to do it just by relying on known tools such as the prime number theorem or the sieve method and the functional analysis and Fourier analysis, accumulation functions, smoothing weights, etc. used by Professor Zhang.
There isn't much theoretical reason, it's just Qiao Yu's feeling.
Then again, if the existing tools can solve this conjecture, are so many talented mathematicians just doing nothing?
"Well, I can't follow the methods of my predecessors. I still have to create a new framework."
Qiao Yu muttered to himself on the bed, and then climbed out of the bed.
Although it was still dark, Qiao Yu was used to getting up as soon as she woke up, and it was impossible to fall asleep even if she continued to lie in bed.
Even if you do fall asleep, you will not be more energetic because of the long sleep. On the contrary, you may become more depressed.
He ran into the toilet and washed up. After coming out, Qiao Yu looked at the time. It was already 5:37 in the morning.
This time is pretty good...it's equivalent to him sleeping for about ten hours yesterday. No wonder he's so energetic.
After scrolling through WeChat, Grandpa Shi on the other side responded to the message. Hmm... Do you want to hold a reception banquet for Qiao Xi?
The private rooms have been reserved at the Jiasuo restaurant owned by Huaqing alumnus Lin. Qiao Yu has heard of this restaurant and it is very famous within Huaqing, but he heard that it is difficult to book private rooms.
I don’t know whether it was because of the holiday or because the old man was so proud that he was able to book a private room after receiving the news at the last minute.
However, Qiao Yu felt that this treatment was a bit exaggerated. Although he knew that most of it was doting on him, how could Comrade Qiao Xi be so virtuous...
A big-shot academician went to pick up the car, and another big-shot academician held a banquet to pick him up...
This is somewhat excessive.
You must know that when he came to the capital at the beginning of the year, he came alone with a bag on his back.
The person who went to pick him up was Lao Xue, and the first dinner he had at Yanbei University was a casual meal between the two of them in an ordinary canteen of Yanbei University.
On the day he arrived, he didn't even see Director Tian.
Okay, this is indeed an injustice to Tian Yan. In fact, the instructor originally wanted to meet him that night, but he had already arrived at the door of his dormitory.
I just saw Qiao Yu reading the paper too seriously and didn't come in to disturb him...
Forget it...the two bosses are giving mom face like this, after all, it's all about his face.
Thinking of this, Qiao Yu became proud again. He decided not to tell Qiao Xi the news just yet so as to scare her later.
Hey, just thinking about it made Qiao Yu feel a little envious of his mother.
Qiao Xi is so good at giving birth to a son as outstanding as him. He can easily have things that others can only dream of without working hard in life...
This seems to highlight how stupid that man is. He ran away with a good thing that he could have easily owned. He must have regretted it so much that his intestines are blue, right?
You have obviously recognized him, but you still have to pretend that you don't know him. He probably has the most promising result in your life, and you must feel very bitter in your heart, right?
It's such a pity.
Qiao Yu sighed in his heart, and then picked up the book.
No way, the fastest way to get into a learning state every morning is to read a math book.
If you keep thinking about the happiness during this period of time, you don't have to do anything all day long.
For example, his book "Analytic Number Theory" co-authored by Henrik Ivanets and Emmanuel Kowalski is definitely a good medicine for treating burnout.
The only drawback of any advanced topic is that it is too old. In Qiao Yu's opinion, it is only suitable for general reading, but it is still very useful to clear the brain.
Especially about the Dirichlet L function.
What can I say? Regarding the analytic continuation of the Dirichlet L function, the derivation process is very detailed and its domain of definition is directly extended to the entire complex plane.
I can only say that the two authors are really very patient.
Some of the special relationships, feature summation techniques, etc. are explained in great detail. It is simply a standard textbook for fools.
It is no exaggeration to say that Qiao Yu feels that even people who know nothing about analytic number theory can already get started after reading the derivation steps and application examples in this book.
Just like this, until the sky lit up, Qiao Yu went out to have breakfast, returned to his small study, stretched, picked up a pen, and then drew a frame on the manuscript paper...
Since we want to use a new method to solve the twin prime conjecture, we can't follow other people's old methods.
Qiao Yu plans to start with the seemingly complete space and the Langlands program that he is most familiar with.
The Langlands Program is to establish profound connections between different fields of mathematics, which is inseparable from symmetries in number theory and representation theory.
So of course we can consider directly treating the properties of twin prime numbers as symmetry and mapping problems in some kind of geometric or algebraic mechanism.
These are obvious.
The problem now is that if he wants to do this, he needs to construct a new category, whose object is naturally a pair of twin prime numbers.
Then define appropriate morphis to express the structural relationship of these pairs of numbers.
The next step is to build a topology.
Schultz's quasi-complete space theory contains an almost complete structure, which means it can be used to capture boundary behavior.
Coincidentally, the core of the twin prime conjecture is to study the limiting properties and distribution boundaries of pairs of prime numbers.
That is to say, combine the two to create a quasi-complete space of twin prime pairs.
Theoretically, all pairs of twin primes can be mapped into this quasi-complete space, so that each pair of twin primes forms an approximately equidistant sequence in this space.
Then we introduce topological tools to find ways to find topological invariants of the relationship between possible twin prime numbers.
Then directly define new algebra and geometric objects to construct twin prime number clusters. You can consider defining the relationship between twin number pairs through group structures or modular structures.
Or build a twin prime modulus space and map all pairs of twin primes so that the geometric features in the space can reflect the properties of the twin primes.
In this way, tools such as the Hodge structure can be used to find the periodic law of the distribution of twin prime pairs...
Soon, the manuscript paper in front of Qiao Yu was filled with content, followed by arrows and marked shapes, representing his thinking path.
Of course, this is just a rough idea. Which ones are useful and which ones are just his imagination. Qiao Yu himself doesn't know until he starts to deal with it.
However, there is no need to rush these tasks. Director Tian’s request is just to submit the project before the start of school. In other words, he only needs to complete the feasibility report.
To be honest, Qiao Yu felt that his mentor looked down on him a little bit.
As long as he is not allowed to give a complete proof, he can write and submit this kind of purely deceptive project idea report in a day without any duplication.
Anyway, Qiao Yu feels that whether it is to solve the twin prime number conjecture or the Riemann Hypothesis, it is necessary to introduce tools that can capture more delicate number theory structures.
Traditional number theory research is mostly limited to algebraic methods, which is obviously outdated.
If you want it to be delicate enough, you still have to find a way to introduce the idea of ​​​​geometric mapping and directly transform the arithmetic properties of number theory into changes in geometric space.
Of course, if you want to achieve other goals, it would be best to construct a calculable tool.
It is best not only to verify the zero point distribution of the L function, but also to directly check whether the zero point is located on the critical line within a limited evolution step, so as to maximize the utilization efficiency of supercomputing...
There were so many ideas at the same time that Qiao Yu recorded them all.
When he planned to pick up Qiao Xi in the afternoon, he happened to have a chat with Director Tian in the car. By the way, he showed his ambition.
Since we have to do it, we don’t need to deduce a more precise position. Professor Zhang has deduced it to 70 million digits, although this number is very large.
But what if his method can reduce the difference between infinite pairs of prime numbers to 6?
K can still only be equal to 3 instead of 2, which does not fully prove this conjecture. It’s boring!
Thinking of this, Qiao Yu suddenly had a realization - isn't mathematics just a creator's game?
Nothing is difficult!
Although this sentence is currently said to be pretentious, this is what Qiao Yu really thinks.
Yes, at this moment Qiao Yu felt that the twin prime number conjecture and even the Riemann Hypothesis were not difficult, but he had not yet figured out how to create it.
In this way, while thinking and feeling proud, the appointed time soon arrived, and Director Tian called him out with a phone call.
Director Tian actually prepared two cars and parked them at the entrance of the Digital Research Center, one behind the other.
Director Tian sat in the back seat of the first car, pressed down the window, and waved to him: "Why are you standing there? Get in the car."
"Oh, here we come."
Qiao Yu responded, quickly went around to the other side, opened the door, and got in. After the car started to move, he couldn't help but ask: "Director Tian: Why do we need two cars? One can accommodate more people. Isn’t a car enough?”
"Is it convenient to talk if we are all in the same car?" Tian Yanzhen glared at Qiao Yu and said.
"That's it."
Qiao Yu thought for a while and then said: "Actually, it's not inconvenient. You can brag about me more in front of my mother and let others hear how good I am. There doesn't seem to be anything wrong with it, right?"
Before Tian Yanzhen could say anything, the driver in the front seat suddenly couldn't help laughing, but it was just a laugh and he stopped it immediately.
Qiao Yu glanced at the driver, why did this man look both professional and unprofessional at the same time?
"Stop talking nonsense! I can only praise you with reasonable praise!" Tian Yanzhen glared at Qiao Yu and said.
"Oh, then let me give you some reasons to praise me. I have completed what you asked me to think about during the summer vacation yesterday. Just do the twin prime number conjecture. I feel that I can directly solve this problem." Qiao Yu said with confidence. .
Then he expressed his feelings in a very arrogant tone: "Mathematics is actually very simple, it is nothing more than a game for the creator!"
Thanks to eugenehowel for the tip and encouragement!
The November 10,000 word update was completed on the 9th day.
Chapter completed!