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Chapter 213 This is a magnificent era with many talented people
After rejecting Chen Zhuoyang's invitation, Qiao Yu still ate boxed lunches at night. When a person has gained enough honors, this aspect is indeed much more convenient.

After he just said hello, someone would pack his meal and deliver it to his dormitory while it was still hot.

After quickly finishing his dinner, Qiao Yu went back to work.

With Chen Zhuoyang's answers as a reference, Qiao Yu also had some experience in how to grasp the difficulty of the questions.

The difficulty should be lowered a little bit. After all, he didn't set up an exam specifically for someone. It was for the project!

He continued to work attentively until the knock on the door sounded again. Qiao Yu turned his head and glanced at the lonely figure outside the door, which surprised him.

He really didn't expect Yu Wei to come to see him at this time. Although the three of them would come to his place to sit in the past, they would usually notify him in advance via WeChat.

He got up and opened the door, glanced at Yu Wei, then stuck his head out of the door, looked around for a few times before asking, "Why are you alone? Where are the other two?"

"I came to see you for something." Yu Wei said, and to Qiao Yu's surprise, this guy actually forced a smile at him.

Although this smile is quite ugly, it is rare. They have known each other for such a long time, and although they often meet each other, this is the first time Qiao Yu has seen a smile on this guy's face.

Qiao Yu said bluntly: "No, if you don't know how to laugh, don't laugh. It's quite creepy."

This sentence earned a roll of Yu Wei's eyes, and then he stopped smiling and looked much more normal.

"Well, please come in."

Qiao Yu then welcomed Yu Wei into the study, and then asked directly out of curiosity: "Well, excuse me, you came to see me secretly and smiled at me for the first time. Could it be that you want my help with something?"

Yu Wei was silent for two seconds, didn't say anything, but nodded.

Qiao Yu laughed. This was really like that. The second generation of rich people were indeed different. They couldn't even show the attitude of asking for help.

"Let me guess, Yu Wei, you didn't fail a course last semester and asked me to help you get a favor from the professor, right? I can help you with other things, but I can't help you with this. After all, everyone in Yanbei University knows that I, Qiao Yu, am the most rigorous when it comes to academic matters."

Qiao Yu looked at Yu Wei seriously, but in fact, he was almost laughing...

After all, it's rare to make a rich second-generation lose face. Even when he won the Fields Medal, this guy just sent a congratulatory message in the group.

"I'm sorry, I got A+ in all subjects last semester!" Yu Wei glanced at Qiao Yu and said in a muffled voice.

"Hmm?" After hearing this answer, Qiao Yu was a little unsure of Yu Wei's purpose in looking for him.

He didn't know about other places, but he got A+ in all his subjects after one semester at Yanbei University, so he knew how great he was.

After all, there are not only professional courses but also general courses in daily study. The difficulty is quite high.

Anyway, he didn't get an A+ in many of his general education classes, so of course he didn't go to class.

"No, then what do you want me to do for you? You can't ask me to borrow money, right? How much? Just tell me an amount. If it's too much, forget it. It has to be consistent with our friendship." Qiao Yu began to talk nonsense seriously.

Yu Wei curled his lips, then silently took off the backpack on his back, took out a stack of printouts from the bag and handed them to Qiao Yu.

"What is this?" Qiao Yu asked.

"I recently completed a paper with Professor Chen. He thought it was pretty good, but he still suggested that I ask you for help to see if there is room for improvement."

Yu Wei explained.

Qiao Yu curiously took the paper handed over by Yu Wei and took a look at the title at the first time - "Using modal spectral manifold and sparse mapping technology to reduce the upper bound of prime numbers to 4"

After reading it, Qiao Yu looked up at Yu Wei and subconsciously asked, "You spent a whole summer researching this?"

Yu Wei shook his head and replied: “No, I had already started studying it when you published the generalized modal axiom system.

Last year you published the paper that reduced the upper bound of prime numbers to 6. Professor Chen used your method to derive some propositions in the algebraic geometry class.

I started discussing this with him. Then we worked together and it took about eight months to complete the paper. ”

Qiao Yu nodded. Although he still found it magical, he could accept it after hearing this.

Although he had narrowed the upper bound of prime numbers to 6, and there was a way to narrow it to 4, he was too lazy to do it at the time. After all, there was more important work to do.

Later, the Riemann hypothesis was directly proved, so there was no need to continue writing papers on this topic. Unexpectedly, Yu Wei proved this problem with the help of a professor from Yanbei University.

Qiao Yu also had an impression of Professor Chen mentioned by Yu Wei. His name seemed to be Chen Zhelun. He had come to discuss related academic issues with him before. After all, they were all at Yanbei University, so they would see each other every day.

"Professor Chen used my method to explain the questions to you during class? What were you explaining?"

Qiao Yu asked as he quickly looked at the paper.

For someone who can solve problems and play games at the same time, it is not a problem at all to read the paper and learn about things that he is interested in from Yu Wei.

He was actually very curious about the professor using his theories directly in lectures.

"At that time, we were talking about algebraic clusters. After finishing the material in the textbook, Professor Chen used your modal density function ρM(p) to characterize the density of the algebraic cluster V in the modal space.

It is proved that if the modal path corresponding to ρM(p)>0 coincides with a part of the algebraic variety V, then the geometric properties of V can be determined by the analytical behavior of the modal density distribution. For example, the curvature and the distribution of singular points. "

Yu Wei answered quickly, and it was obvious that he still remembered the content of that lesson clearly.

"Oh, that should be to analyze the embedding behavior of algebraic clusters in modal space. Is there anything else after that?" Qiao Yu continued to ask.

"Yes, there are isomorphisms between modal paths and torus mappings, and the intersection properties between modal paths and algebraic curves. But he only mentioned some of these in passing during class, without going into detail, and the exams didn't cover such questions. He said that if we want to study this in the future, we have to wait until graduate school."

Qiao Yu nodded. In just a few words, he had finished reading the review and abstract of the paper and started reading the main text.

After understanding the situation, he became serious. After all, Lao Yu was actually a good person, with a cold appearance but a warm heart.

Although continuing to satisfy his curiosity would not slow down his reading of the paper, Yu Wei was an extremely meticulous guy and might think that he did not read the paper carefully.

Qiao Yu stopped asking questions. Yu Wei was a taciturn person, so naturally he would not speak any more.

His good upbringing also prevented him from touching Qiao Yu's things. He simply sat there and watched Qiao Yu flipping through the paper... Just like that, half an hour later, Qiao Yu had read the entire paper.

The time taken was short because Qiao Yu had already thought about this problem for a long time.

When he reduced the upper bound of prime numbers, he did not reduce it to 4 because he was too lazy to prove some related tools.

But now the other party's thoughts are actually similar to what he had at that time.

Simply put, he used the theorem he derived before to construct a modal spectral manifold by embedding the point set of the modal path of this problem, that is, the prime number distribution, into a space with higher-dimensional geometric symmetry and using it to capture local regularities in sparse distributions.

The modal spectral manifold M (moda) is a high-dimensional topological space, where the coordinates are generated by the correlation values ​​between prime numbers in the modal space.

The geometric properties of the manifold are directly used to characterize the microstructure of prime number distribution. Then a sparsity mapping S operator is introduced to characterize the symmetry of the local sparse distribution on the modal spectral manifold.

And got an expression:

Then comes the proof process.

"There is indeed nothing wrong with the paper. You should have revised it several times, right? But why did you only prove up to 4? The tools have been developed, why don't you just go straight to 2? You are not short of money, do you want to write more papers?"

After reading the paper, Qiao Yu looked at Yu Wei and asked.

Yu Wei withdrew his dazed gaze and looked at Qiao Yu in silence. After a while, he said indignantly: "Who doesn't want to get it done in one step? But the distribution resolution of the density function is not enough and is limited by smoothness.

This results in the gradient being too small in high-density areas, smaller intervals cannot be handled, and the flexibility is not enough... and I wrote all of this at the end! "

"How do I know if what you wrote at the end is true? Maybe you deliberately exaggerated the difficulties in this paper, and then directly solved the problems in the next paper, so that you can appear very capable. To be honest, I often think about doing this."

Qiao Yu retorted confidently.

Yu Wei opened his mouth, but found that he couldn't reason with Qiao Yu on this point, so he simply asked directly: "So do you think this paper can be published directly?"

Qiao Yu did not answer directly, but asked: "Why are you in such a hurry? How do you plan to allocate the first and second author roles for this paper? Or what are your and Professor Chen's respective contributions?"

“I proposed the local isometry property of modal spectral manifolds, but I couldn’t prove its continuity under embedding mapping. Then I started to discuss it with Professor Chen.

Professor Chen’s ideas include reconstructing the modal density function and using the kernel integral characteristics of the modal path to verify the convergence of the isometric relationship.

So Professor Chen meant that we could be co-authors on this paper. But I think Professor Chen probably suggested this because he thought I had a good relationship with you. Strictly speaking, my contribution was not that great.”

Qiao Yu nodded, and then asked curiously, "Why didn't Professor Chen come with you?"

Yu Wei answered honestly: "Professor Chen said he had a guess, but asked me not to tell you."

Qiao Yu rolled his eyes at Yu Wei...

Yu Wei thought for a moment and said, "Well, he said he had some discussions with you before. A lot of inspiration for this paper came from discussions with you. He thinks you can complete this proof independently, so he is embarrassed to come."

As expected, Qiao Yu realized that there was no good person among mathematicians, they were all cunning.

But to be honest, Yu Wei was impressed that he could work with the professor to perfect the paper to such an extent. This guy didn't seem to be as stupid as he showed during the IMO.

"Taking the initiative to propose to be a co-first author shows that Lao Chen is quite conscientious. Okay, but since the paper has reached this stage, it is better to push it to 2nd issue than to publish it directly, and then submit it directly to Ann.Math. To be honest, I am quite familiar with the editor-in-chief of Ann.Math, Lotte Dugan."

Qiao Yu gave direct advice.

Yu Wei took a deep breath and said, "This is difficult. We have tried many methods and have been discussing it all summer. If we didn't want to achieve 2, we would have published it last semester."

"That's because you didn't come to me earlier. Actually, there are only two problems. The one you just mentioned is a problem, and the other is that the local analytical properties of the modal spectrum manifold of your method are insufficient.

The curvature of the manifold is limited, so it can be slightly modified. Redefining the regularity conditions of the modal density function and introducing an embedding mapping with variable curvature adjustment can increase the local resolution capability.

Then you will find that you can also optimize the modal path kernel function, and then you will find that the problem begins to become simple. Wait a moment..."

After saying that, Qiao Yu picked up the pen and began to revise the paper quickly.

Yes, the general direction of their proof is correct. It's just that some details are not thought deeply enough.

In Qiao Yu's opinion, it is not worthwhile to publish the paper directly, because once the paper is published, someone with a keen eye will read it and may be able to quickly reduce the upper bound to 2.

Maybe we can also prove the twin prime conjecture by the way. Because proving that the upper bound interval is 2, we can further prove the twin prime conjecture through mathematical induction, or by proving that the path generated by the modal density function under certain conditions always contains point pairs with an interval of 2.

We can't let outsiders take advantage of this.

Qiao Yu, who already had an idea in mind, spent about half an hour on it and then put down his pen.

The clean printout of the paper just now has been modified into pieces.

"Go back and study it with Professor Chen. If you push it according to what I said, you should be able to figure it out. You are so lucky to have a friend like me.

By the way, let me tell Professor Chen. Ask him if he has signed up for my project at the Academy of Sciences. If not, hurry up. If you miss this opportunity, you will miss it.

As for you, keep working hard. After you graduate, you can apply for my postgraduate program directly. By the way, don’t tell Gong Jiatao and Yu Yongjun about this. They are too stupid!

If they knew about this and kept begging me, and I softened my heart and accepted them, then our sect's reputation of a hundred years would be ruined by the two of them!"

Yu Wei didn't care about Qiao Yu's weird words. He just took the revised paper blankly. After a while, he asked, "I'll give you this... that one?"

"Heh... who are you looking down on? I'm helping you revise your paper just to steal your first authorship? Do you think I'm the one who needs this crappy paper?!"

Qiao Yu said with a sneer.

Seeing Yu Wei's rare awkwardness, he softened his tone and said, "Hey, if you really feel bad about it, if this paper is published, you can double the reward the school gives you and give it to me as a fee for revising the paper!"

Although Qiao Yu was no longer short of money, he was still unhappy that there was a rich second-generation guy around him. However, when he felt that he was short of money, he had never been able to make a penny from this guy, which made him very unhappy.

After all, being able to get money out of an extremely stingy guy is a happy thing in itself.

Long live happiness!
(End of this chapter)