God of black technology

Chapter 165 About Interval Sieve

"I didn't want to come to the library at first." He shrugged his shoulders and said, "But when I thought about it, I have nothing to do with myself, not to mention you have already solved the Kakutani conjecture. After asking Yuan Chengde to solve the twin prime number conjecture , we are also in the same IMO competition anyway? One has already read a direct blog under the name of the well-known professor Professor Witten, and the other has solved the twin prime number conjecture. I can't bear it."

ummmmmmm...

You also know that you are now behind?Wang Yun was silent and did not speak. He pulled away the chair next to him and said, "Sit down, what are you going to watch?"

"Well, about the information about Hilbert space." Luo Zhendong smiled embarrassedly, scratching his head and said, "Speaking of which, I learned pure mathematics, but there is nothing wrong with Hilbert space recently. Pretty obsessed."

Obsessed with Hilbert spaces?Wang Yun thought for a while, "My professor Witten has been working on this recently, should I talk to the professor?"

"Farewell." Luo Zhendong shook his hand hastily and said, "I'm just looking around, I haven't even understood the functional analysis yet, I know you're talking about the Hilbert-Polya conjecture, Don't talk about it, it needs to be proved by quantum mechanics, and I can't keep up with Professor Witten's rhythm."

"That's all right, you study it carefully." Wang Yun smiled, and started to read again with his book.

Luo Zhendong looked curiously at the formula written by Wang Yun on the draft paper——

[Define β=λ+2μ.Initial conditions and boundary conditions——]

What is this thing?Why do I seem to be able to understand some of them separately, but I can't understand them together?Is it my pot or his pot?

Shaking his head, Luo Zhendong breathed a sigh of relief, fortunately he didn't regard this guy as an opponent, otherwise he must have collapsed now.

Is this someone who can be an opponent?He is simply a big guy to look up to!

The twilight was getting thicker, and there was some mist around, but the lights in the library were still a little bright.It was even bright enough to dazzle the eyes, squinting his eyes, Luo Zhendong moved his hands and feet.Two hours have passed now, and Wang Yun is still counting non-stop.

This guy is simply—can he take a break like a normal person?Sitting next to him, it makes people feel flustered for no reason.

This guy is so focused on his own business, I'm afraid he didn't notice this.But the person sitting next to him will realize that compared with this guy, he is really like a salted fish.This guy can count for hours without a break.While comparing the literature, he kept calculating.

Luo Zhendong looked forward blankly, and sure enough, the gap between himself and Wang Yun was still widening.

When Luo Zhendong looked forward, several sympathetic eyes also fell on Luo Zhendong.Sitting next to the king is simply suffering.Especially those students who often come to the library know that this king is simply a lunatic.There is often only a fine line between a genius and a lunatic.

If it is not a genius, sitting next to Wang, who is also quite legendary in Princeton, would seem too small.

There are many legendary characters in Princeton, and there are not many geniuses and monsters that everyone praises.But now in Princeton, the king is generally favored!

It took this guy half a year to solve the Kakutani conjecture, and it was generally recognized by the mathematics community. With this, he graduated from Princeton as an undergraduate, which is simply speechless.And then it was reported that his research subject was the NS equation, which was even more terrifying than Kakutani's conjecture. Although everyone knew that Wang Yun was indeed one of the people most likely to solve the NS equation, it was only possible.

There is still a long way to go before the real solution of the NS equation. At the beginning, the students who knew the news thought that Wang Piao was crazy.

It's like when they knew that Wang Yun's graduation subject was Kakutani's conjecture, they all felt that Wang Yun was drifting.As a result, in the blink of an eye, the students who were still waiting to laugh at Wang Yun could only study the topic given by Professor Witten were slapped by Wang Yun in the blink of an eye, and the whole person was stunned.

However, the Kakutani conjecture is different from the NS equation.There is no doubt that the NS equation, as one of the seven major mathematical conjectures, has a high degree of difficulty, and it is estimated that no one has successfully challenged it.

Seeing countless well-known mathematicians and physicists fall into the sand, what chance does Wang Yun have of winning?There are almost none, and the Euler coordinates are still being studied, and there is no chance of winning.It is not that no one has thought of solving NS equations from Euler coordinates and Lagrange coordinates, but all of them ended in failure.

Now it is generally believed that it may be better to use nonlinear partial differential equations. For example, Wang Yun used nonlinear partial differential equations to give the current optimal solution.

But it is still too far away from the complete solution of the NS equation.

Both the Lagrange coordinate system and the Euler coordinate system belong to the differential equation of particle motion in fluid mechanics, and Newton's second law is used to describe the differential equation of particle motion.

Whether it is the Euler coordinate system or the Lagrange coordinate system, they are all described under the description of Newton's second law.Although it is a physical problem, if you think about it from a mathematical point of view, wouldn't it be simpler?When Wang Yun wrote this, he paused, and Luo Zhendong, who was next to him, saw Wang Yun pause.

With a sigh of relief, if this guy continues to write, he will probably go crazy.

"I said, Wang Yun, have you eaten yet?" When Luo Zhendong asked, Wang Yun was resting his chin and thinking.After asking for a while, he found that Wang Yun didn't answer him at all.

ummmmmmm...

Sure enough, the world of geniuses cannot tolerate a normal person like myself.

Luo Zhendong used to think he was a genius, but he didn't realize what a genius he was until he saw Wang Yun.He is simply a scumbag, and there was a Yuan Chengde with him before.

But now, even Yuan Chengde has begun to exert his strength.To say that Yuan Chengde is indeed well-accumulated, he hardly took a break during his one-year stay in Princeton.Although not as strong as Wang Yun, it is almost the same.After studying Wang Yun's new Mersenne conjecture and the sieve method of Zhou's conjecture for a year, it seems to be a common thing to decide to start with the twin prime number conjecture.

Let alone whether Yuan Chengde can solve this ghost conjecture, being able to do it is enough to prove his self-confidence.

"Luo Zhendong." When Luo Zhendong turned his head, he found Wang Yun's dark eyes looking at him, which made him tremble from the soul.Those eyes seemed to see through unexpected stars, and he could even see countless formulas in Wang Yun's eyes.

Is he dazzled?

"You said that the differential equation of particle motion and the nonlinear partial differential equation can be expressed in another way?" Luo Zhendong was confused by Wang Yun's question.

What to change the way of expression, how to change the way of expression.What did Wang Yun mean by this?

Just looking straight at Luo Zhendong for several minutes, Luo Zhendong was also thinking about what Wang Yun meant by this sentence.But after thinking about it for a long time, I didn't come back to it.

"It seems that it should be possible." Wang Yun finally said to himself, it turned out that this guy wasn't looking at me just now, but just looking in a random direction and thinking about something.

ummmmmmm...

Sure enough, I was thinking too much. In the eyes of such a boss, there should be nothing else but formulas.

However, what the hell is the new method that the boss just mentioned?

Luo Zhendong tried to say, "Boss, what exactly do you mean by the new method you just mentioned?"

"It's nothing." Wang Yun showed a slight smile, "I just suddenly have some new ideas, but I'm not quite sure if I can succeed."

"Looks like I have to consult Professor Bourgain tomorrow." When Wang Yun said this, he closed the file and looked at Luo Zhendong. "By the way, didn't you say you were hungry?"

"En." Luo Zhendong rubbed his shriveled stomach, and said dumbfoundedly, "I've been hungry for a long time, seeing you thinking about something here, big brother, I dare not call you, am I?"

"If you want to eat, you can eat first." Wang Yun said dumbfounded, "There is no need to wait for me."

"Didn't I want the two of us to eat together?" When talking about this, Luo Zhendong looked at the sky outside the window, took a breath and said, "Wang Yun, why do I feel that the sky is getting darker and darker? Is there really anything in the cafeteria at that time?"

"There should be more." Wang Yun was silent for a while, "If not, I remember that the restaurant outside the school gate should still be open. We can go to the restaurant outside the school to eat."

"I'll go, get out of school." Luo Zhendong thought for a while, it seemed that there was no danger.Just opposite the Princeton school gate, there should be nothing to do, "Okay, then let's go have dinner there."

Walking out of the library, Wang Yun felt a chill, and looked at Luo Zhendong from the corner of his eye.I didn't expect this guy to be so tall and big, but he even wrapped his clothes tightly.

This somewhat surprised Wang Yun. He left the library and walked under the dim light.In Princeton at night, except for some running students and students who hurried back to the dormitory, there were almost no people.

Luo Zhendong's eyes were very sharp. Not long after they left the library area, he saw the figure in front of him and said, "Isn't that Yuan Chengde?"

"Are you sure?" Wang Yun was stunned for a moment, seeing that Luo Zhendong had already caught up, he shook his head and followed suit.

"Yuan Chengde." Luo Zhendong's figure is small, and he speaks Chinese. In a foreign country, he seems a bit eye-catching.Fortunately, no one was passing by at this time, and the figure slowly turned around, and it turned out to be Yuan Chengde.

This guy walked forward quickly, Luo Zhendong jokingly said, "Where are you going? So fast, it's just like...forget it. It's like going to meet your lover."

Yuan Chengde glared at Luo Zhendong, and found that Wang Yun was following behind Luo Zhendong, his eyes lit up, "Wang Yun, I'm going to find you."

"Looking for me?" Wang Yun was stunned for a moment, remembering what Luo Zhendong said just now, "Is it about the screening method?"

"Yes." Yuan Chengde nodded, "I have some questions about the interval screening method."

"Huh?" Wang Yun raised his eyebrows, "What's the problem?" He sized up Yuan Chengde when he said this, "Have you not eaten yet?"

"Yes." Yuan Chengde scratched his head, "I'm going to eat after I find you." When he said this, Yuan Chengde was stunned for a moment, looked at Wang Yun and said, "You haven't eaten yet, have you?"

Wang Yun spread his hands and shook his head and said, "As you can see, I haven't started eating yet. I was studying nonlinear partial differential equations just now. Let's go, let's go to dinner together."

"I was talking about the interval sieve method during the meal."

"Okay." Yuan Chengde nodded, and the three walked out of the school together.After a while, after ordering at the restaurant, Wang Yun looked at Yuan Chengde and asked, "I don't know where."

When he said this, Wang Yun was stunned for a moment, blinked his eyes and said, "Yuan Chengde, are you really solving the twin prime number conjecture?"

"En." Yuan Chengde nodded slightly, "That's right, this is my subject, I think you have started to set NS as a subject, obviously for the Fields Award, I can't be too far behind, right? .”

"What about you?" Luo Zhendong was stunned by Yuan Chengde's sudden question, and he said with a confused face, "I think it's pretty good now."

"It's not bad?" Yuan Chengde glared at him, "If you continue like this, you will be expelled from Princeton, do you believe it?"

"He failed the course?" As a Princeton student, cheating is definitely not cheating. The only thing that can make Yuan Chengde have a look of hatred is that this guy's credits are not passed.

"Basically, fly over at low altitude." Yuan Chengde sighed, "Luo Zhendong, weren't you quite capable before? Now you don't play middle two, are you decadent?"

"It can't be considered decadent." Luo Zhendong said dumbfounded, "I'm not interested in Hilbert space? You say my physics is not very good, and I dare not ask my tutors and professors. ,so……"

"Well..." Wang Yun was silent for a while, "It's really not possible, you can go to see Professor Witten with me. Hilbert Space, Professor Witten is doing research, and I will recommend you to him tomorrow. Prepare yourself , if the theory of Hilbert space can be passed, I believe that Professor Witten is still willing to be your tutor. If you can work out the Hilbert-Polya conjecture together with Professor Witten, maybe Fei You have booked the Woltz Award."

"Put it down, if you can solve the NS equation before the 18 International Mathematics Annual Conference, you will definitely have a place in the Fields Medal." Luo Zhendong shook his head, "As for studying Hilbert with Professor Witten— - Polya conjecture, do you think I understand the Riemann function or quantum mechanics?"

"No one is born with knowledge, this can be learned, don't worry." After Wang Yun finished speaking, he saw Yuan Chengde's eyes full of curiosity looking at himself, and he said with a wry smile, "I will give you this Talk about the interval sieve method."

[The set of prime numbers within √n can be obtained in advance through the traditional sieve method.Since the algorithmic principle of the linear sieve method is not applicable to the partitioned sieve method, the algorithmic principle of the Escher sieve method is used here for screening.For the interval [m, n], √n needs to use the prime numbers in it for screening, so the time complexity of the algorithm is O((nm)loglog√n), which is slightly lower than the complexity of the Esperanto sieve method①]

"Can you understand what I'm saying now?" Wang Yun looked at Yuan Chengde and found that Yuan Chengde was thinking with his head down.

After a while, Wei Wei nodded and said, "I understand a little bit." He smiled, and was about to say something, but unfortunately, at this time, the waiter just brought the dishes they ordered.

"Let's eat first, and we can continue talking after we have something to eat." Luo Zhendong looked at the two of them holding the draft paper and pen, and they were about to start counting.His stomach was rumbling non-stop, and he covered his forehead with his hand, and he sighed, how could he be so unlucky to meet these two?

These two people don't care about their studies at all, so can't they eat well first and then talk about other things?

"Okay." Wang Yun saw that Luo Zhendong was very hungry, nodded slightly and said, "Then let's eat first, and then study the sieving method." Having said this, he looked at Yuan Chengde ponderingly, "By the way, I remember that there are only you and Luo Zhendong in your dormitory, right?"

"Yes." Yuan Chengde nodded, "It was originally a dormitory for two people, what do you mean?"

"About the sieving method, I found that you may still not understand something, so tonight I am going to go to your dormitory to tell you about the sieving method." Wang Yun turned his head, looked at Luo Zhendong and said ,"You do not mind right?"

Luo Zhendong shrugged his shoulders, "Is there any good advice here?" His eyeballs rolled, "But, Wang Yun, when you go to Professor Witten's office tomorrow, will you really give me a suggestion?"

Originally, Luo Zhendong had no plans and was not qualified to participate in Professor Witten's research.As a sophomore, his grades are not outstanding, and Professor Witten probably won't let him participate.However, as Professor Witten's beloved student, Wang Yun promotes himself to Professor Witten, so the effect is naturally different.

Maybe, he really has the opportunity to participate in Professor Witten's research, even if it is only a part, it is enough for Luo Zhendong to submit it as a project when he graduates from university.

What's more, Luo Zhendong has been in Princeton for a year, so it is impossible not to think about staying in Princeton.

Although those great gods can often be seen, they are only able to see them.It may not be that people will really talk to you, after all, these great gods have their own subjects and their own disciples.

Luo Zhendong was naturally ecstatic to have such an opportunity.

"Don't worry, I will never forget you." Wang Yun thought it was a little funny, it seems that Luo Zhendong's thoughts changed quite quickly.As for talking to Professor Witten about this matter, he will definitely talk about it.We have to find a suitable opportunity tomorrow to talk about this matter.

As for whether it can be done, it depends on Luo Zhendong himself. He really dare not guarantee it.