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 Western stock markets, most of the colors are red for falling and green for rising.
But for China, a rising star in finance, although the stock market was established a hundred years later than those financial powers, from the beginning of its establishment, red was defined as rising.
Otherwise, Chinese people think red is festive.
At the Beijing Airport, the contestants who got off the plane saw a bright red color in their eyes. Most are arranged by sponsors.
Many people don’t know that China has always been the source of IMO’s platinum sponsors.
This is why even the management of IMO is not willing 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 this team have several activities during the summer vacation, such as accepting interviews with some media. But Qiao Yu doesn't need to participate.
Of course this is not what the media requires. Instead, Tian Yanzhen and Yuan Zhengxin made requests at the same time.
Allowing Qiao Yu to participate in 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 big guys, Qiao Yu doesn't need this kind of meaningless exposure now.
Especially in the eyes of the two big guys, the meaningless flattery from the outside world is unnecessary.
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 in the IMO competition circle every day 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 tomorrow morning will arrive at Jingxi Station at 2:30 pm.
He can finally let his mother see with her own eyes his life in the capital. For Qiao Yu, this was much more interesting than being interviewed.
So after a simple celebration ceremony at the airport and a few 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 to put his luggage first, 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.
This time he went out to participate in IMO and he really let himself go. But Qiao Yu didn't think there was anything wrong. People always need to relax. Some time ago, the string in my heart was too tight.
The main thing 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."
As he said that, Tian Yanzhen took it from the drawer of his desk. He took out three beautifully bound documents 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.
I opened it and looked at it casually. It was a letter of appointment with advance payment. If he is willing to accept it, the other party is 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 given is still very 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 others after I graduate, they can offer me a higher price."
" Haha..."
Tian Yanzhen smiled happily: "Well, I think so too. Then I will refuse it for you."
Qiao Yu nodded. Then he handed all these 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 make a profit.
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's better to lay a solid foundation quickly so that in the future, like Schultz, you can make big money by directly cooperating with large companies 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 Yu's ears perked up instantly.
The two mentors don't respect 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 He 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 with you The energy is strong enough to support you in doing targeted research while consolidating the 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 a part of basic learning.
For example, you have the relevant foundation in the fields of algebraic geometry and mathematical analysis. We have accumulated a lot of knowledge. What we lack is other related basic knowledge.”
Qiao Yu looked at Tian Yanzhen blankly.
While he didn't mind doing the research, it still seemed like it was looking down on him too much.
"Um...Director Tian, do you and Mr. Yuan mean that you want me to solve the Riemann Hypothesis as an undergraduate, right? Isn't this a little too high of me?"
< br>Qiao Yu couldn't help but say.
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 to dawdle. Now he doesn't plan to hang around anymore, the tutor is full of energy again!
If you really want to play like this, let alone graduate in one year. Qiao Yu doubted whether he could graduate in ten years.
"What are you thinking about? If the Riemann Hypothesis is so easy to prove, will it still be your turn? Do you really think that the $1.5 million reward from the Clay Institute is not attractive?"
< br>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 Riemann's hypothesis, there are many small propositions in related fields that can support it, such as Montgomery log pair distribution conjecture, small prime gap conjecture, Model's 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.
Also 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 matters most to us is your ideas. "
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 learn In any direction, 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 is more important. It’s those novel mathematical ideas. Coincidentally, we agree that this is what you are good at.”
“This should be something I will only consider after I am twenty? "
Qiao Yu said blankly.
“When most mathematicians around the world think you are already eligible to compete for the Fields Medal, you can start thinking about it. It has nothing to do with your age. The age of the Fields Medal goes down There are no limits.”
Tian Yan said seriously.
Teacher and student looked at each other. When Qiao Yu discovered that Director Tian was extremely serious today, he understood.
Is it possible that both his mentor and master think that he has a pressure-bearing personality? The greater the pressure, the higher his achievements?
But it is 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 promised solemnly: "Okay, Director Tian. I understand, and I will report my research plan to you and Grandpa Shi as soon as possible. ”
When something is arranged, if you can’t refuse, you might as well keep working hard.
Not to mention that when the research yielded results, the beneficiary was actually himself. It's just an extra burden.
And both Director Tian and Grandpa Shi actually treated him very humanely. They all assign tasks to him 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 You should know that both our school 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, go back and rest."
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. It was also a cutting-edge research topic in number theory, and the difficulty was completely different.
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 give it to you later. Someone contacted you. Oh, is the summer camp about to start? Are you going to pick up the classmate you talked about last time? "
Qiao Yu He 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. It seems that her teacher is also with another classmate from their school who was selected for the summer camp, but he is a sophomore in high school." br>
"Huh? Your mother will come together tomorrow? When will she arrive?" Tian Yanzhen became serious.
Qiao Yu replied: "Yes. It was 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: "Huh? Will you go too? Will it take up 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, that's it. You go and have a rest."
"Oh, I'll leave now. Goodbye, Director Tian."
Qiao Yu walked out of the office with emotion. He still has to learn how to behave like a big boss.
Even though I knew this was a way to win people's hearts, I still couldn't help but feel warm in my heart...
With the dignity of an academician, I went to pick up Qiao Xi in person, which not only gave my mother face, but also allowed him to intuitively I feel the importance I receive... 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 like this, and it's not like I can't survive anyway.
But Qiao Yu had 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 Mr. Yuan that he had returned to school. By the way, he also told Mr. Yuan that his mother would come to the capital tomorrow.
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.
……
Huaqing, the old man was entertaining guests in Qiuzhai’s office, but the way he treated guests was a little different.
The two of them held a magazine in their hands and read it silently.
The tea next to it has obviously become cold, and there is no more elegant steam coming out...
The magazine was the sample issue of Ann.Math specially sent by Qiao Yu to 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.
Obviously this is 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, I couldn't help but feel a little show off, and I subconsciously looked at the junior next to me.
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?"
"A genius idea! Alas... Yan Zhen is really 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 is indeed quite unconvinced by Tian Yanzhen.
In fact, it is difficult to judge who is more knowledgeable between the two. History is really difficult to judge.
But there is no way, life's encounters are like this sometimes. I have been working hard on a project for decades, only to be beaten to the punch.
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 him, and my students can’t compare with him either... Maybe having such a student in his 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 has really let go of that grudge."
Yuan Zhengxin smiled at himself and said: "What else can I do? ? My grandson insists on calling him mentor and me, master, but it can’t be difficult for the 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.
Who can withstand a child like this who calls him Grandpa Master?
Is it possible to reveal that the relationship between the two is not good and tell a sixteen-year-old child the grudges of the previous generation?
Neither Yuan Zhengxin nor Tian Yan would be able to do such a thing. In other words, whoever does this to a child first will lose.
“This kid is really... very interesting.” Tan Luyuan sighed again.
"It's more than just interesting."
The old man shook his head and continued: "You don't know, he is not only talented, but also very self-disciplined. He takes the initiative to send me his reading experience and learning experience every week. .
By the way, I introduced him to Li Lixing’s research group, and within a few days he helped him solve the problem that had been bothering him for half a year. He didn’t tell me, but Li Xing came here to express his gratitude.”
Tan Luyuan asked attentively: “Is this the topic you were talking about that Professor Li Xing applied for last year? The topic of the fund?"
Yuan Zhengxin nodded with a smile and said: "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 the other day. I On a whim, I wanted to see what this little guy would do after he made such outstanding achievements without saying a word.
No one was informed, so he made a special trip to Yanbei's Digital Research Center. Guess what "What did I see my grandson doing when I passed by?"
Tan Luyuan looked at Mr. Yuan's expression across from him and said with emotion: "You've asked me this, I'm afraid you haven't relaxed at all, and you're still studying hard, right?" ?”
Yuan Zhengxin laughed and said: “Haha, that’s right! Sixteen years old is a young and high-spirited age, and you can immediately concentrate on studying knowledge after making achievements.”
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!
This difference is not just about talent? So? This year’s Huaqing elite class must be more demanding. We can’t take it in any more!”
Hearing these words, Tan Luyuan picked up the cup and took a sip of tea to hide his embarrassment...
He knew the Huaqing Talent Class. In terms of education model, do you still think that the requirements of Huaqing Talent 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 startled...
Of course he was already very clear about Qiao Yu's position in the old man's heart. status, but such a high evaluation was something he didn't expect.
After all, Tao Xuanzhi won the Fields Medal at the age of thirty-one and is also one of the recognized geniuses in the mathematics community.
"It's passed, it's been... Qiao Yu is only sixteen years old, this will pass soon." Tan Luyuan shook his head and said.
The old man smiled and said: "Passed it? Lu Yuan, believe it or not, I can see Qiao Yu solve the Riemann Hypothesis."
Tan Luyuan glanced at Mr. Yuan in surprise, and didn't know what to say for a while. This sentence.
Could it be 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 his interest. Qiao Yu has big ambitions! When he talked to Tian Yanzhen about the future, he said that he wanted to make this guess. You won't believe this. Today he I just came back and need to rest.
In this case, I will send him a message and ask him to come to Huaqing to meet you tomorrow. You will have a long way to go. I dare say there is some research. You might as well dare to think like this kid! He is not the kind of person who would kill his time with inaction."
As he said that, Yuan Zhengxin put on his glasses and picked up his phone, opened WeChat and saw his beloved. His grandson had already sent him a message.
After seeing it, I laughed.
"What a coincidence, Qiao Yu's mother will also come to the capital tomorrow. This is to prepare a reception feast. Just in time, I am the host, which can be regarded as a reception for you."
Tan Luyuan smiled bitterly.
Good guy, he is here today, is this reception banquet scheduled for tomorrow? It seems that he got this meal because of the little guy’s mother!
The old man is extremely biased.
Creating a banquet for the arrival of Qiao Yu’s mother...
Tan Luyuan suspected that Mr. Yuan regarded Qiao Yu as his grandson...
...
Qiao Yu opened his eyes suddenly.
I woke up, but it was still dark outside the window. Qiao Yu lay still on the bed.
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 topic that Grandpa Shi did not want to get involved with before. That probably explains how difficult it is, but it’s also fun.
Of course, neither Director Tian nor Grandpa Shi on the opposite side is 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.
Otherwise it wouldn’t be a series of conjectures. By the way, Director Tian also said that we need new ideas.
In fact, when he wanted to study prime numbers, Qiao Yu had already roughly understood the Riemann Hypothesis. Of course, this also includes 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.
Qiao Yu has actually read the paper written by Professor Zhang Yuantang that Professor Tian mentioned yesterday. The sieve 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 sieve 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 sifting method is still too troublesome and lacks beauty.
The paper is more than fifty pages long. Moreover, the method cannot be expanded, for example, it cannot be applied to triplet prime numbers and larger sets of prime numbers.
And Qiao Yu has a feeling that by continuing to study this method, at most, the gap between infinite pairs of prime numbers can be limited to a very small number, such as a single digit greater than 2. number.
But if you want to reduce it to 2, it is definitely impossible to rely only on the prime number theorem or the sieve method and the known tools such as functional analysis, Fourier analysis, accumulation function, smoothing weight, etc. used by Professor Zhang. Do it.
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 he woke up, and it was impossible to fall asleep if he 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.
Run into the toilet and wash up. After coming out, Qiao Yu looked at the time. It was already 5:37 in the morning.
This time is quite good... it is equivalent to him sleeping for about ten hours yesterday. No wonder he is so energetic.
Looking through WeChat, Grandpa Shi on the other side responded to the message. Hmm... Want to hold a wedding banquet for Qiao Xi?
The private dining room has been reserved, and it’s at Huaqing Alumni Lin’s restaurant. Qiao Yu has heard of this restaurant. It is very famous in Huaqing, but he heard that it is difficult to book a private room.
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 I know that most of this is doting on him, how could Comrade Qiao Xi be so good...
A big-shot academician went to pick up the car, and another big-shot academician held a banquet...
This is somewhat excessive.
You must know that when he came to the capital at the beginning of the year, he came alone carrying a bag.
The person who picked 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.
He didn't even see Director Tian on the day he came.
Okay, this is indeed an injustice. In fact, the instructor originally wanted to meet with 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 gave my mother face like this, after all, it was for his sake. superior.
Thinking of this, Qiao Yu became proud again. And decided not to tell Qiao Xi the news now, lest she would be shocked.
Hey, thinking about it, Qiao Yu felt a little envious of his mother.
Qiao Xi is so good at giving birth to a son as good as him. He can easily have things that others want without working hard in life...
This seems to highlight the man's ability. How stupid, he actually ran away from a good thing that he could have easily owned. He must be so regretful now 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 results in your life, and you must feel very bitter in your heart, right?
What a shame.
Qiao Yu sighed in his heart, and then picked up the book.
No way, the fastest way to get into the learning state every morning is to read math books.
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 "Analytical Number Theory" co-authored by Henrik Ivanets and Emmanuel Kowalski is definitely a good medicine for treating burnout.
The only drawback of any advanced theme 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 DirichletL function.
How to say, regarding the analytic extension of the DirichletL 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.
It explains some of the special relationships, feature summation techniques, etc. 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.
Seeing the sky light up like this, Qiao Yu went out to have breakfast, returned to his small study again, stretched out, 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 number conjecture, we cannot follow the old path of others.
Qiao Yu plans to start with the seemingly complete space and Langlands Program that he is most familiar with.
The Langlands Program is to establish profound connections between different fields of mathematics, which cannot be separated from the symmetry 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 morphisms to express the structural relationship of these pairs.
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 prime number pairs.
That is to say, combine the two to create a quasi-complete space of twin prime pairs.
Theoretically, all pairs of twin prime numbers can be mapped into this quasi-complete space, so that each pair of twin prime numbers 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 you can establish a twin prime modular 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 number pairs...
Soon, the manuscript paper in front of Qiao Yu was filled with writing The content, with arrows following the meaning of the graphics, represents 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 only asked him 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 repetition.
Anyway, Qiao Yu feels that whether it is solving the twin prime 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...
I had so many ideas at the same time, 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, show his ambition.
Since you have to do it, don't go to a more precise position to deduce it. Professor Zhang derived 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 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.
Just like that, he was thinking and feeling proud at the same time. Soon the appointed time came and Director Tian called him out with a phone call.
Director Tian actually prepared two cars and parked them one behind the other at the entrance of the Digital Research Center.
Director Tian sat in the back seat of the first car, pressed down the window, and waved to him: "Why are you standing there stunned? Get in the car."
"Oh, here it comes."
Qiao Yu responded, quickly went around to the other side, opened the car door, and got in. After the car started to move, he couldn't help but ask: "Director Tian: Why do you have to do this? You need two cars? Isn’t one car that can accommodate more people enough?”
“Is it convenient to talk if we all sit in one 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 listen. Listening to 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, 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 solve this problem directly." 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 reward and encouragement!
November 10,000 words update was opened and completed on the 9th day.
(End of this chapter)