"Yeah." Qiao Xi responded softly.

"Can you understand?" Yuan Zhengxin asked again.

"I don't understand it just by reading the paper, but I probably understood it after Qiao Yu explained it." Qiao Xi replied.

Yuan Zhengxin nodded happily. Mathematics is like this. If you can understand it, you are already superior to 90% of ordinary people.

This has been the case even since junior high school, but it was not obvious at that time. In high school, math scores will gradually begin to show a polarization trend.

And if you want to know whether a high school student with good math scores has a talent for math, it's actually very simple. Just ask him if he is tired from studying math.

If students in high school have to work hard to get high scores by solving questions, there is a high probability that they have no talent. It is best to stay away from mathematics when applying for majors.

After all, this is a subject where after a certain level of study, hard work alone is of no use.

Yuan Zhengxin asked again: "Then have you discussed with Qiao Yu what work needs to be done to further lower the upper bound or even completely solve this proposition?"

Qiao Xi shook her head and said: "I haven't discussed it yet, but I think if there is to be a breakthrough, the structure of the modal path needs to be further optimized.

We also need to consider introducing some number theory methods, such as the sieve method, and verify the infinity of the prime numbers on the path again."

Yuan Zheng thought for a while and then said: "He didn't ask you to help with this work?"

Qiao Xi shook her head again and said softly: "He asked me to try to prove the modal existence of twin prime numbers first."

"Oh? Do you have any ideas?"

"I mentioned it briefly."

With that said, Qiao Xi took out a pen and paper and wrote down some concepts: "Qiao Yu said that if you want to introduce twin characteristics, you need to use a new mapping concept. For example, a high-order nonlinear operator, used in

Find core symmetries in modal space.

Since this type of modal mapping is nonlinear and irreversible, he designed an operator matrix structure called the supermodal operator matrix, or HOM for short. Then for any mode (α, β), there are specific elements that satisfy the following characteristics.

"

After writing this casually, Qiao Xi shook her head slightly and explained: "To be honest, I think this is very difficult. Qiao Yu often has some thoughts, well... I think the angles are very weird, and I can't keep up with him.

Ideas.”

Yuan Zhengxin smiled and said, "It's normal to not be able to keep up with his train of thought. Look at the more than 3,000 people present today, at least 3,000 of them can't keep up with his train of thought.

But you should be able to feel that Qiao Yu hopes that you can help him. So even if it is difficult, you have to think quickly and believe in yourself. Your work is very important in helping him completely solve the twin prime conjecture.

After solving this problem, he can still challenge to higher heights. So just do me a favor and don't let this kid slack off, okay? At least don't let him slack off when he is most creative!"

"Ah?" Qiao Xi found it hard to imagine that an old man who kept his word would actually say these words to her with a hint of pleading, and she was stunned for a moment.

But Qiao Xi soon came to his senses, nodded quickly and replied: "Don't worry, Teacher Yuan, I will definitely urge Qiao Yu to continue working hard."

"But it's not just that he has to work hard. Have you ever thought about the possibility that he is actually waiting for you?" Mr. Yuan asked.

"Well... I will work hard too." Qiao Xi, who had never felt that studying was a pressure, suddenly felt a mountain-like pressure falling on her slender shoulders...

Looking at Qiao Yu who was swaying freely on the stage, I couldn't help but feel a little depressed.

…

In fact, by this time the report was going on, many people in the back row had already begun to sneak away quietly. Most of them were students and mathematics enthusiasts, and of course there were a few professors.

This is actually something that can't be helped.

Listening to a lecture, if you don't understand it at all... This experience can actually be understood by everyone. It is similar to the feeling of not being able to understand it in a math class.

In short, once you don't understand it, those complicated formulas are almost like a heavenly book, not like the language of the human world. Then you will become bored, and even feel that your days are like years.

If you add in the fact that most of the students who can attend this meeting are graduate students majoring in mathematics, they may feel deeply affected, which may lead to a series of negative emotions.

For example, the mathematics I study and research seems to be different from other people's mathematics. Even if they are both studying number theory, without a certain understanding of the prerequisite framework, it is really difficult to understand the structure of the geometricalization of number theory problems...

…

All in all, this is a very painful thing. If you consider that the mathematician who gave the report is sixteen years old, this pain can easily be doubled.

Fortunately, Qiao Yu, who was sitting on the podium, didn't actually notice this. Even if he did, he didn't really care.

If he was still excited when he gave the report for the first time, then this time, Qiao Yu was completing the task, mainly because he started too high.

"...According to Lemma 7, modal convolution describes the distribution pattern of modal points on the path Γ. The pattern in the local area is as shown in the figure:"

"By controlling the maximum value of the wide basis, the distance between modal points can be limited to no more than 6. At the same time, because the global structure of the modal path Γ is periodic, its local high-density characteristics are repeated globally. Therefore, any

The modal distance of modal points r_p, r_q∈Γ satisfies: d_M(r_p,r_q)≤6

...Finally, according to Theorem 2, Theorem 3, Theorem 4, and Theorem 5, it can be seen that each modal point r_p∈M corresponds to a prime number p, and the modal path Γ describes the distribution trajectory of the prime number.

Modal distance d_M(r_pr_q) is the geometric distance between modal points, and its properties directly reflect the prime spacing ∣pq∣ in the sense of number theory...

To sum up, d_M(r_p,r_q)≤6 is equivalent to ∣pq∣≤6, and there are infinitely many pairs of prime numbers with a spacing between ∣pq∣≤6 in the sense of number theory. From now on, the proof is complete."

Qiao Yu's time control ability is very strong, and it took fifty-five minutes out of sixty minutes.

In fact, if he spoke a little faster, he could finish it in fifty minutes. This is also a more appropriate time.

Because generally invited reports require about ten minutes of Q&A time at the end.

Of course, in such a short time, you can probably answer three or five questions, so the quality of the questions is very important.

This is also the reason why various report conferences arrange a moderator. During the question and answer time, the moderator will select the questioner and ask questions about what the speaker said.

However, today's lecture will be quite special. Many people do not have that much time to fully digest the content of the generalized modal axiom system. Therefore, regarding his paper, I only listened to the fifty-minute lecture and could not find out anything valuable.

question.

So I just left it for five minutes and let the host take care of it. If anyone asked, just answer casually. If no one asked, the host would say a few words and everyone could go to eat early.

Of course, if there are any problems, you can wait until everyone can communicate with you later.

The fact was just as Qiao Yu imagined, it was obvious that the people in the audience were not very enthusiastic about asking questions.

At a casual glance, you can see that no one in the front row raised their hands... It is a brand new axiomatic framework, and it still takes some time to digest it.

Those who can be chosen to be the presenters of the report are all smart and flexible people. Especially after seeing the looks on the faces of some of the big guys in the front row, they naturally understand how to handle this situation.

"Thank you very much for Qiao Yu's wonderful report. Regarding the upper bound of 6 between prime numbers, this report has given a detailed explanation.

If you still have any questions about the paper, I believe that Qiao Yu will definitely take some time to communicate with you in more detail after this meeting. Let us thank Qiao Yu again for his wonderful discussion."

Soon there was extremely warm applause from the audience.

Although no one asked questions, except for the person who gave the report on the stage, everyone else at the meeting understood the significance of this article in the world of number theory.

At that time, all the efforts in the world only lowered the upper limit of the interval between prime numbers to 246. More than ten years later, someone finally lowered this number again, and lowered it to 6 all at once.

To be honest, 99% of the people in the audience looked at Qiao Yu with envy and a little bit of jealousy...

Even more than that.

With the publication of his and Chen Zhuoyang's papers on the Internet, anyone who has carefully read the two papers may have a rather complicated mood at the moment.

A work in one of the four top magazines, an honor so many people dream of, was given away by that ridiculously young guy on stage...

Yes, in the eyes of many people, the second paper is really just a gift.

Forget about the framework of the generalized modal axiom system, this whole set of proof logic is really not something that ordinary people can think of.

But when it comes to the follow-up verification work, it really gives many people the feeling that I can probably do it.

Even more than that...

There are always some invisible rules in academia. For example, it may sound unbelievable for tutors to use students' achievements, but this situation has always existed, and it can even be said that it does not distinguish between countries.

The students' research is directly incorporated into their own framework, and the final results are presented with the tutor as the protagonist. The data collected and analyzed by the students are directly used to publish independent papers.

Even more shamelessly, there are cases where the tutor directly names the first author on the paper that the student completed independently.

After all, not everyone in the academic world is a highly respected professor, and there are also those who are ignorant and unskilled...

The young man on the stage abruptly divided what could be done in one paper into two papers, just to give the collaborators one work at a time.

Yes, there is no need for Chen Zhuoyang to say anything. Everyone is in the academic circle. As long as they have read the paper, they probably know what is going on.

This makes many people's emotions so complicated that it is difficult to describe.

Of course, these feelings had nothing to do with Qiao Yu. He just stood up and bowed slightly to the audience. It still felt perfect.

Then he walked off the stage in a hurry. He was the second one to give a report today. Then it was time for dinner, and then he was free in the afternoon...

Qiao Yu planned to find Senior Brother Chen to accompany him around the venue and chat.

It was not because he wanted to listen to the report, but mainly because he wanted to listen to Senior Brother Chen’s rainbow farts...

Everything is fine with Qiao Xi, but it is still too difficult for Qiao Xi to praise him to the sky.

Senior Brother Chen did a good job in this regard. Unfortunately, Qiao Yu soon discovered that he had oversimplified things.

Although the morning meeting was over, Qiao Yu found that he could not walk out of the banquet hall.

As soon as I stepped off the podium, I was surrounded by a group of people.

It was literally surrounded. Of course, the situation was not very chaotic. Everyone was engaged in mathematics, and many were even doctoral-level professors.

Everyone is just doing academic discussions. But it has nothing to do with the content of today’s report. Everyone is asking questions about the generalized modal axiom system...
To be continued...