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Chapter 140 Mathematics? It’s nothing more than a game for creators!

The Chinese have a special feeling for the color red.

In fact, in other cultures, red is used to alert people because it is eye-catching.

For example, in Western stock markets, red represents a fall and green represents an increase in most cases.

But for China, a rising star in finance, although its stock market was established a hundred years later than those financial powers, red has been defined as rising since its inception.

There is no other reason, Chinese people think red is festive.

At the Beijing airport, the athletes who got off the plane saw a sea of ​​red. Most of them were arranged by sponsors.

Many people don’t know that China has always been a source of platinum sponsors for IMO.

This is also the reason why even the management of IMO is not willing to offend Qiao Yu easily.

After all, to a certain extent, many people have regarded Qiao Yu as the future representative of the Chinese mathematics community.

Of course, the Chinese team's five gold medals and a perfect score of 248, the third best result in history, is indeed worthy of the grand welcome ceremony.

After the excitement, the team was partially disbanded in the capital.

Because the members of this team have several activities in the summer vacation, such as accepting some media interviews, etc. However, Qiao Yu does not need to participate.

This was of course not a request from the media, but rather a request made by both Tian Yanzhen and Yuan Zhengxin at the same time.

Allowing Qiao Yu to attend IMO was already a compromise between the two bosses. It was impossible for him 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 flattery from the outside world.

Qiao Yu had no objection to this arrangement.

Anyway, he has no plans to debut... and he really doesn't know what to say in an interview.

Well, I play games in the IMO competition circle every day, challenging players from all over the world. Not only did I win the IMO full score gold medal, but I also won the best mental arithmetic game award?

And what Qiao Yu was most looking forward to was not these, but Qiao Xi’s coming to the capital.

Qiao Xi had already sent him the ticket booking information on WeChat. The high-speed train would arrive at Jingxi Station at 2:30 p.m. tomorrow.

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 accepting an interview.

So after a simple celebration ceremony at the airport and a few group photos, Qiao Yu was taken back to Yanbei University by the people called by Tian Yanzhen.

……

"Director Tian, ​​I'm back."

In the car, Professor Luo, who came to pick him up, said that Tian Yanzhen was waiting for him, so Qiao Yu went back to put his luggage away 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 tutor.

"Did you have fun in Australia?" Tian Yanzhen asked.

"Happy." Qiao Yu nodded honestly.

There is nothing to hide. Professor Zhou and Professor Zhang will probably report his every move in Australia to Director Tian and Mr. Yuan across the street.

He did let himself go a bit this time when he went out to participate in IMO. But Qiao Yu thought there was nothing wrong with that, people always need to relax. The string in his heart was too tight some time ago.

The main reason was that the man put too much pressure on him.

If the problem in the proof of the geometric Langlands conjecture is not found in time, that man will be in the limelight at the World Congress of Algebraic Geometry.

This is certainly intolerable.

"Well, as long as you are happy. Then you need to concentrate. Take a look at these first."

As she spoke, Tian Yanzhen took out three beautifully bound documents from the drawer of her desk and handed them to Qiao Yu.

Qiao Yu took it curiously and saw that they were actually three offers from different companies.

They are all from big factories...

For example, Xiaolibaba, who had interactions with Qiao Yu.

He opened it and took a quick look. It was an employment letter with an advance payment. If he was willing to accept it, the other party was willing to cover all his expenses during his studies and even give him a salary.

This way, after he graduates with a Ph.D., he can directly start working. The salary offered is still very attractive.

Qiao Yu looked at Tian Yanzhen in confusion.

Logically, these big companies couldn't have been without his contact information, but they didn't contact him privately and sent the offer directly to Tian Yanzhen.

"How about it? Are you interested?" Tian Yanzhen asked Qiao Yu.

Qiao Yu shook his head slightly and said honestly, "I'm not interested. I think when I graduate and really want to work for someone, they will offer a higher price."

"Ha ha……"

Tian Yanzhen smiled happily: "Yeah, I think so too. Then I will help you reject them all."

Qiao Yu nodded and handed all the offers back.

He has no interest in working, but he would be fine if it were a position like consultant.

Anyway, if there is a problem, just send him a copy and you will earn money if he can solve it.

But just as Tian Yanzhen said, Qiao Yu also felt that it was too early for him to think about making money.

After all, he can only make a little money now.

Now that we have no worries about food, clothing, housing and transportation, there is no need to waste energy on this aspect. It is better to quickly lay a solid foundation so that in the future we can make a lot of money by cooperating with large companies like Microsoft directly like Schultz did.

Tian Yanzhen casually put a few offers aside, then looked at Qiao Yu and said, "During the time you were attending IMO, I talked to Mr. Yuan twice about your future."

Qiao Yu's ears pricked up instantly.

The two mentors have no moral principles and actually colluded with each other in private.

"I won't go into the details of the communication process, because you are very interested in the problem of prime number distribution, so we all have full confidence that you can solve the Riemann hypothesis."

Qiao Yu nodded subconsciously, then shook his head and said blankly: "Riemann hypothesis? Um... 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 does not conflict with your research.

In fact, we all agree that you have enough energy to support you in doing targeted research while consolidating your basics. This is also related to your previous study habits and results.

While solving a problem, I will actively read related literature, and I can always gain a lot. This is actually part of basic learning.

For example, you have already accumulated a lot of basic knowledge in 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 like too much of a compliment to him.

"Um... Director Tian, ​​you and Professor Yuan didn't mean to ask me to solve the Riemann hypothesis during my undergraduate studies, right? Isn't that a bit too high a value on me?"

Qiao Yu couldn't help but say.

Even though he was confident in himself, this was no joke.

In the past, he said he wanted to work on the Riemann hypothesis just to get by. Now he doesn't plan to get by anymore, because his advisor is excited again!
If he really wanted to do this, he would never graduate in one year. Qiao Yu doubted whether he could graduate in ten years.

"What are you thinking? If the Riemann hypothesis is so easy to prove, how could it be 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 won't assign you a task that you can't complete at this stage. The Riemann hypothesis is the ultimate goal, but the road is paved step by step.

In fact, compared with the big proposition of Riemann hypothesis, there are many small propositions in related fields that can support it, such as Montgomery's logarithmic pair distribution conjecture, small prime gap conjecture, Model conjecture, and Landau related problems.

These include the twin prime conjecture, the Legendre conjecture, the cumulative characteristics of the Möbius function value, and so on.

Especially the twin prime conjecture. If you are interested in prime numbers, you should know Professor Zhang Yuantang's paper "Bounded Gaps between Prime Numbers", which proves that there are infinite pairs of prime numbers with gaps less than 7000 million, which is already a huge breakthrough.

His proof of the Landau-Siegel zero-point conjecture can also give you some reference. And I have contacted Professor Zhang, if you are interested in the twin prime conjecture, he is willing to help you.

Of course, we don’t ask you to prove the twin prime conjecture. Even if you can push this gap forward a step, it will be an achievement. What we value most is your thinking. "

Qiao Yu nodded subconsciously, and then realized more deeply the value of a good mentor.

Whether it is Tian Yanzhen or Mr. Yuan, as long as he wants to research and learn in a certain direction, he can directly find the best person to assist him.

Tian Yanzhen continued, "But these are just suggestions from me and Mr. Yuan. It's up to you to decide where to start the formal research.

You know, the Fields Medal values ​​novel mathematical ideas. Coincidentally, we all agree that this is exactly what you are good at. "

"Fields Medal? This should be something I should consider after I turn 20, right?"

Qiao Yu said blankly.

"When most mathematicians in the world think you are qualified to compete for the Fields Medal, then you can start considering it. It has nothing to do with your age. There is no age limit for the Fields Medal."

Tian Yan said with a serious look.

The teacher and the student looked at each other, and when Qiao Yu realized that Director Tian was extremely serious today, he understood.

I’m afraid that his mentor and master’s uncle both think that he has a pressure-tolerant personality, and the greater the pressure, the higher his achievements?
But it is indeed challenging to think about it.

"So what you mean is that I can choose one of the above propositions as the main research direction for the next stage?" Qiao Yu asked.

"Yes, if you need to collaborate with others on research, you can also tell us, and 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 agreed seriously: "Okay, Director Tian. I understand. I will report my research plan to you and Master as soon as possible."

When something is arranged, if you can't refuse it, you might as well keep working on it.

Not to mention that if the research yields results, he will be the beneficiary. It's just that he has more burdens.

Moreover, both Director Tian and Master Shi were very humane to him. They assigned him tasks based on the content he was interested in before.

Just like he once told his deskmate Zhou Shuang, when you work hard on something but seem to get nothing out of it, you should just give up and walk away.

This is clearly not the case with him. He worked very hard and gained a lot.

"Yes, before the semester starts, I should choose a topic and make a plan. This way, I can allocate my energy between study and research more easily after the semester starts.

You should know that both we and Huaqing University across the street have excellent undergraduate research training programs. Most of them start in their sophomore year, and you just started a year earlier. Okay, go back and have a rest. "

Tian Yanzhen said with a smile, obviously very satisfied with Qiao Yu's statement.

Of course, this analogy is not that apt. After all, the research training program at the undergraduate level is actually just helping the professors.

The task assigned to Qiao Yu was to be responsible for a project independently, which was 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, "Anything else?"

Qiao Yu nodded and said shyly, "Well, I would like to ask you to arrange a car for me to pick up a few people at the train station tomorrow."

Tian Yanzhen agreed immediately: "I'll have someone contact you directly later. Oh, is the summer camp about to start? Go pick up the classmate you mentioned last time?"

Qiao Yu shook his head and replied, "Not to pick her up, but mainly because my mom will come with her to see me. It seems that her teacher and another student from their school who was selected for the summer camp will also be there, but she is in the second year of high school."

"Hmm? Your mother will come with you tomorrow? When will she arrive?" Tian Yanzhen became serious.

Qiao Yu replied, "Yes. We agreed on it before. We should arrive at Beijing West Station at 2:30 pm."

Tian Yanzhen ignored Qiao Yu and picked up her phone to check it. Half a minute later, she looked up and said, "I don't have anything planned tomorrow afternoon. I'll go with you to pick her up. We'll leave at 1:30 pm. If there are four of us, we can just arrange two cars."

Qiao Yu was a little surprised and said, "Ah? Um...you're going too? Will it take up too much of your time?"

Tian Yanzhen said: "This is the most basic courtesy. I have to thank her for raising such a good child. By the way, please tell Mr. Yuan about your mother coming to Beijing. Okay, it's settled. Go and have a rest."

"Oh, I'll be leaving first then. Goodbye, Director Tian."

Qiao Yu walked out of the office, feeling very emotional. He still had to learn how to behave like a big boss.

Even though I know this is a means to win people's hearts, I still can't help but feel warm in my heart...

As an academician, he went to pick up Qiao Xi in person, which not only gave his mother enough face, but also made him feel intuitively how much he was valued... Well, no matter what, mom should be very happy, right?

Qiao Yu thought to himself, but he was not sure how Qiao Xi would react.

For many years, he felt that Qiao Xi's emotions had always been very stable, and he was rarely too excited or too depressed.

If I have to describe it, it would probably be - it's fine like this, it's not like I can't survive anyway.

But Qiao Yu had nothing to worry about.

Unless he was drunk, Qiao Xi didn't have many inappropriate responses in social situations. The most he did was to talk less when outside.

Forget it, forget it.

However, Qiao Yu still followed Director Tian's instructions and sent a message to Mr. Yuan, telling him that he had returned to school and also mentioned that his mother would be coming to Beijing tomorrow.

But after returning to the room, before Mr. Yuan could reply, Qiao Yu rushed into the bathroom and started taking a shower.

After sitting on the plane for nearly a whole day, I feel smelly.

……

Huaqing, the old man is entertaining guests in Qiuzhai's office, but the way of entertaining guests is a little different.

The two of them held a magazine in their hands and read silently.

The tea beside it had obviously cooled down, and no more steam was coming out...

The magazine was a sample issue that Ann Math specially sent to Qiao Yu.

Lott Dugan mailed a total of five copies to Qiao Yu. Qiao Yu gave two copies to his tutor, two copies to Mr. Yuan, and kept one for himself as a souvenir.

It was obviously not the first time that Mr. Yuan watched it, but he still smiled when he saw the exciting parts.

Because it reminded me of what happened at the beginning of the year when Zhang Shuwen was invited to Yanbei to listen to Qiao Yu's lecture at Huaqing.

Afterwards, Zhang Shuwen even called him.

Neither of them expected that Zhang Shuwen was just giving the boy a lesson, but Qiao Yu actually wrote the paper.

The results given are still so concise and beautiful. Especially this unified set parameter constraint theorem, which is simply a stroke of genius.

This idea is not difficult, but the difficulty lies in being able to use this idea to unify four extremely complex parameters with different weights into a basic geometric structure.

Every time he saw this, Yuan Zhengxin couldn't help but applaud Qiao Yu's genius idea!
At this moment, he couldn't help but feel like showing off, and his eyes subconsciously looked at the junior next to him.

Although he is called a younger generation, he is actually nearly seventy years old, just like Tian Yanzhen.

"Lu Yuan, you have seen the unified geometric parameter constraint theorem, right? How is the proof?"

"What a genius idea! Oh... Yan Zhen is really lucky." Tan Luyuan broke away from his concentration and looked at Mr. Yuan next to him and sighed.

As a mathematician of the same generation as Tian Yanzhen, Tan Luyuan was indeed quite dissatisfied with Tian Yanzhen.

In fact, if we really want to talk about who has deeper knowledge between the two, history is really difficult to judge.

But there is nothing you can do about it, this is how life works. You spend decades working on a project, only to be overtaken by someone else.

The glory naturally belongs to others.

In recent years, Tan Luyuan, who found it difficult to make academic achievements, has put more energy into education, just like Yuan Lao. He has also trained a few students who are quite proud of him, but to be honest, they are still in the stage of scientific research accumulation.

Who would have thought that Tian Yanzhen discovered another sixteen-year-old monstrous genius without saying a word.

No, it is said that he was only 15 years old when he discovered it. How can others compare with him?
I can’t compare to him, and neither can my students... Maybe having just one student like him in a lifetime is enough for him.

"Apart from anything else, he has always had good luck." 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 let go of that grudge."

Yuan Zhengxin laughed at himself and said, "What else can I do? My grandson insists on calling him mentor and me grandpa. I can't let the child be caught in the middle, right?"

Tan Luyuan was stunned at first, then the corners of his mouth curled up involuntarily. He probably understood how Old Yuan's temper was changed.

Who could withstand being called Grandpa Master by a kid like this?

Was he going to reveal that the relationship between them was not good, and tell a sixteen-year-old child all the grievances of the previous generation?
I'm afraid neither Yuan Zhengxin nor Tian Yan would do such a thing. Or whoever does this to a child first will lose.

"This kid is really... interesting." Tan Luyuan sighed again.

“More than just fun.”

The old man shook his head and continued, "You don't know, he is not only talented, but also very self-disciplined. He would take 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 them solve a problem that had troubled them for half a year. He didn’t tell me, and I only found out when Lixing came to thank him.

Tan Luyuan asked intently, "Is there anything else? Could the topic you are talking about be the one that Professor Lixing applied for the Natural Science Foundation last year?"

Yuan Zhengxin smiled and nodded, saying, "That's right."

Tan Luyuan said 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, when I heard about this from Li Xing the other day, I suddenly had the urge to go see what this little guy would do after quietly achieving such outstanding results.

I didn't notify anyone and went to Yanbei's Mathematical Research Center. Guess what I saw my grandson doing when I got there?"

Tan Luyuan looked at the expression of Mr. Yuan opposite him and said with emotion: "Since you asked me this, I'm afraid you haven't slacked off at all and are still studying hard, right?"

Yuan Zhengxin laughed loudly and said, "Haha, that's right! Sixteen years old is the age when one is young and frivolous, full of vigor and vitality. After making achievements, one can immediately devote oneself to academic research."

After saying that, Mr. Yuan’s face changed, and he said in a muffled voice: “Look at the other students. They complain bitterly when the requirements are a little strict, and think that the teacher’s requirements are too high!

It's not just talent that's lacking. So this year, the requirements for Huaqing's elite class must be raised. Those who just want to get by can no longer be accepted!"

After hearing this, Tan Luyuan picked up the cup and drank a sip of tea to hide his embarrassment...

He understands the educational model of Huaqing Elite Program. Does he think the requirements of Huaqing Elite Program are too low? Then other schools should just stop running basic math classes...

Putting down the teacup, Tan Luyuan simply changed the subject: "Teacher Yuan, how do you think Qiao Yu compares to 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 clear about Qiao Yu's position 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 31 and is also one of the recognized geniuses in mathematics.

"Passed, passed...Qiao Yu is only sixteen years old, this will pass quickly." Tan Luyuan shook his head.

The old man smiled and said, "Passed? Lu Yuan, believe it or not, I can see Qiao Yu solve the Riemann hypothesis."

Tan Luyuan looked at Mr. Yuan in surprise, not knowing how to respond for a moment.

Can you just say that it depends on how long you can live?

Wait, the Riemann hypothesis?
"Do you plan to start working on the Riemann hypothesis now?" Tan Luyuan couldn't help asking.

"It's not our intention, but Qiao Yu is actually more interested in number theory. He once said that his research on the geometric Langlands conjecture, the Langlands program, quasi-complete space and other theories is all in the hope of creating more tools.

This is what he is interested in. Qiao Yu has great ambitions! When he talked to Tian Yanzhen about the future before, he said that he wanted to make this guess. Forget it, you will definitely not believe it if I tell you this. He just came back today and needs to rest.

Well, I'll send him a message and ask him to come to Huaqing to meet you tomorrow. You'll know after you talk to him. Lu Yuan, I dare say that you are not as bold as this guy in some research! He is not the kind of person who would kill his time by doing nothing. "

As he spoke, Yuan Zhengxin put on his glasses and picked up his mobile phone. He opened WeChat and saw that his beloved grandson had sent him a message.

After watching it, I laughed.

"What a coincidence! Qiao Yu's mother will also come to the capital tomorrow. They need to prepare a welcoming banquet. It's just right that I'll be the host, which can be regarded as a welcome banquet for you."

Tan Luyuan smiled bitterly.

Good fellow, he came today, but the welcoming banquet was scheduled for tomorrow? It seems that he was able to have this meal only because of the little guy's mother!
The old man is extremely biased.

A welcoming banquet was held for Qiao Yu's mother's arrival...

Tan Luyuan suspected that Yuan Lao regarded Qiao Yu as his own grandson...

……

Qiao Yu suddenly opened his eyes.

I woke up, but saw that it was still pitch black outside the window. Qiao Yu was lying in bed without moving.

His body didn't move, but his mind began to recall what Director Tian said to him after he came back yesterday.

The Riemann hypothesis was a topic that my master didn't want to touch before. This probably explains its difficulty, but it is also very interesting.

Of course, neither Director Tian nor the master across from him was that harsh.

At least he was not required to prove the Riemann hypothesis within a certain period of time.

But then again, even those premises are not so easy 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 Qiao Yu wanted to study prime numbers, he had already roughly understood the Riemann hypothesis, including 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 concentrated on techniques such as prime number theorem and sieve method.

Qiao Yu had actually read the paper written by Professor Zhang Yuantang that Professor Tian mentioned yesterday. The sieve method was one of the main mathematical tools.

To put it simply, it is to eliminate non-prime numbers through gradual screening and thus identify prime numbers.

However, Professor Zhang's method is indeed novel. If Qiao Yu were to evaluate it, it would be the use of a new application of the weighted sieve method to control the spacing between prime numbers.

But this is obviously not enough, otherwise Professor Zhang would have directly solved the twin prime conjecture.

In addition, Qiao Yu felt that the sieving method was too troublesome and lacked beauty.

The paper is more than 50 pages long. Moreover, the method cannot be expanded, for example, it cannot be applied to triplet primes or larger prime sets.

Moreover, Qiao Yu had a feeling that if he continued his research along this method, at most he would be able to limit the difference between the infinite number of prime numbers to a very small number, such as a single-digit number greater than 2.

But if you want to reduce it to 2, it is definitely impossible to do it by relying solely on the prime number theorem or the sieve method, as well as the known tools used by Professor Zhang, such as functional analysis and Fourier analysis, cumulative functions, smoothing weights, etc.

There is not much theoretical reasoning behind it, it is purely a feeling of Qiao Yu.

Then again, if existing tools can solve this conjecture, then are all those talented mathematicians just sitting there 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 in bed, then crawled out of the quilt.

Although it was still dark, Qiao Yu had gotten used to getting up as soon as he woke up, and it would be impossible for him to fall asleep if he continued to lie in bed.

Even if you really fall asleep, it is impossible for you to become more energetic due to the long sleep. On the contrary, you may become more lethargic.

He ran into the bathroom and washed up quickly. When he came 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 is so energetic.

I checked WeChat and saw that my master replied. Hmm...are you going to hold a welcoming banquet for Qiao Xi?
The private room was already booked, at the Jiasuo Restaurant in Huaqing Alumni Forest. Qiao Yu had heard of this restaurant, which was very famous within Huaqing, but she heard that it was difficult to book a private room.

I don’t know if it was because it was the holiday or because the old man had a lot of face, but he was able to book a private room even 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 this was just doting on him, what merits did Comrade Qiao Xi have...

One big-name academician went to pick up the car, and another big-name academician hosted a welcoming banquet...

This is a bit too much.

You should know that when he came to Beijing at the beginning of the year, he came alone with a backpack.

The only person who went to pick him up was Old Xue, and the first dinner they had after arriving at Yanbei University was just a casual meal shared by the two of them in an ordinary cafeteria at Yanbei University.

He didn't even get to see Director Tian on the day he arrived.

Well, this was indeed a bit unfair to Tian Yanzhen. In fact, the tutor wanted to meet him that night and had already arrived at the door of his dormitory.

I just saw Qiao Yu was too focused on his paper, so I didn't go in to disturb him...

Forget it...the two bosses gave my mother so much face, after all, it was because of him.

Thinking of this, Qiao Yu became proud again. He decided not to tell Qiao Xi the news for now, so as not to scare her.

Oh, thinking about it, Qiao Yu felt a little envious of his mother.

Qiao Xi was so lucky that she gave birth to such an outstanding son. She could easily have things that others could only dream of without any effort in life...

This seems to highlight how stupid that man is. He could have easily gotten something good, but he ran away. I guess he must be regretting it now, right?
I clearly recognized him, but I had to pretend not to know him. He got what was probably the most promising achievement in my life. I must feel very bitter, right?
It's really a pity.

Qiao Yu sighed in his heart and then picked up the book.

There is no other way. The fastest way to get into learning state every morning is to read a math book.

If you keep thinking about the happiness you have had during this period of time, you won’t have to do anything the whole day.

For example, his book "Analytical Number Theory" co-authored by Henryk Ivaniec 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 for clearing the mind.

Especially the content about Dirichlet L function.

Well, regarding the analytical extension of the Dirichlet L function, the derivation process is described in great detail, extending its domain directly to the entire complex plane.

I can only say that the two authors are really very patient.

Some of the special relationships, characteristic summation techniques, etc. are explained in great detail. It is simply a standard fool-proof textbook.

It is no exaggeration to say that Qiao Yu feels that even people who know nothing about analytic number theory can be considered to have gotten started after reading the derivation steps and application examples in this book.

He watched until the sky brightened, went out to eat breakfast, and returned to his study. After stretching, he picked up a pen and drew a frame on the manuscript paper...

Since we want to use a new method to solve the twin prime conjecture, we cannot follow other people’s old path.

Qiao Yu planned to start with the quasi-complete space and Langlands program, which he was most familiar with.

The Langlands Program aims to establish deep connections between different fields of mathematics, which is inseparable from the symmetries in number theory and representation theory.

So of course we can consider directly considering the properties of twin primes as symmetry and mapping problems in some kind of geometric or algebraic structure.

These are obvious.

The problem now is that if he wants to do this, he needs to construct a new category, whose objects are naturally twin prime pairs.

Then define appropriate morphisms to express the structural relationship between these pairs.

The next step is to build a topology.

Schultz's theory of quasi-complete spaces contains 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 establish 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 isometric sequence in the space.

Then we introduce topological tools to find possible topological invariants of the relationship between twin prime numbers.

Then directly define new algebraic and geometric objects to construct twin prime clusters. You can consider defining the relationship between twin number pairs through group structure or modular structure.

Alternatively, we can establish a twin prime moduli space to map all pairs of twin primes so that the geometric features in this space can reflect the properties of twin primes.

This way, we can use tools such as the Hodge structure to find the periodicity of the distribution of twin prime pairs...

Soon, the manuscript paper in front of Qiao Yu was filled with content, and the figures marked with arrows represented his thinking path.

Of course, this is just a rough idea. Qiao Yu himself doesn't know which ones are useful and which ones are just his imagination before he starts to deal with them.

However, there was no need to rush these tasks. Director Tian only asked him to submit the project before the start of the semester. In other words, he only needed to complete the feasibility report.

To be honest, Qiao Yu felt that his mentor looked down on him again.

As long as he is not asked to provide a complete proof, he can write and hand in a report on this purely misleading research idea in one day without any repetition.

Anyway, Qiao Yu feels that whether it is to solve 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 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 computable tool.

It would be best if we could not only verify the zero distribution of the L function, but also directly check whether the zero is on the critical line within a limited number of evolution steps, so as to maximize the utilization efficiency of the supercomputer...

There were so many thoughts at once that Qiao Yu wrote them all down.

When he was going to pick up Qiao Xi in the afternoon, he happened to chat with Director Tian in the car and showed his ambitions.

Since we are going to do it, we don't need to deduce it to a more precise position. Professor Zhang derived it to 7000 million digits, although this number is very large.

But what if his method could reduce the difference between infinite pairs of prime numbers to 6?
K can still only be equal to 3 instead of 2, so it doesn’t count as a complete proof of the conjecture. It’s meaningless!
Thinking of this, Qiao Yu suddenly had an epiphany - isn't mathematics just a game for creators?
It’s not that difficult!

Although this sentence may sound pretentious now, this is what Qiao Yu really thinks.

Yes, at this moment Qiao Yu felt that the twin prime conjecture and even the Riemann hypothesis were actually not difficult, but he just hadn't figured out how to create them.

Just like this, he was thinking and feeling proud. Soon the agreed time came and Director Tian called him out.

Director Tian actually prepared two cars, one in front and one behind, and parked them at the entrance of the Mathematical Research Center.

Director Tian sat in the back seat of the first car, rolled down the window, and waved at him: "What are you standing there for? Get in the car."

"Oh, here we come."

Qiao Yu responded, and quickly went around to the other side to open the door and got in. After the car started, he couldn't help but ask, "Director Tian: Why do we need two cars? Wouldn't one car with more seats be enough?"

"We are all in the same car, is it convenient to talk?" Tian Yanzhen glared at Qiao Yu and said.

"That's it."

Qiao Yu thought about it, and then said, "It's not really inconvenient. You can brag about me in front of my mother and let other people hear how good I am. There doesn't seem to be anything wrong with that, right?"

Before Tian Yanzhen could say anything, the driver in the front seat suddenly couldn't help laughing, but it was just one laugh and he stopped immediately.

Qiao Yu glanced at the driver. Why did this man seem both professional and unprofessional?
"Stop talking nonsense! My praise for you can only be based on reasons and evidence!" Tian Yanzhen glared at Qiao Yu and said.

"Oh, then I'm giving you some reason to praise me. I have completed what you asked me to think about during the summer vacation yesterday. It's about the twin prime conjecture, and I feel I can solve this problem directly." Qiao Yu said confidently.

Then he expressed his realization in a very arrogant tone: "Mathematics is actually very simple. It is nothing more than a game for creators!"

　Thanks to eugenehowel for the reward and encouragement!
　　The November 11-word update was completed on the 9th day.

　　
　
(End of this chapter)