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Chapter 157 In the Spotlight
Scientists, or highly educated people, are a very special group. They may not have a lot of wealth, but in a sense, a large part of the wealth growth of this society is based on the efforts of these people.

If we must make an analogy, they are like the engine of social wealth growth, doing the most tiring work in areas that people cannot see.

It’s like after a normal family buys a car, except for maintenance or repairs, no one will deliberately open the hood every day to check on the engine.

Yes, everyone knows that the engine is important, but when nothing is happening, no one is too lazy to take a look at it.

Because most ordinary people don't know how the engine works, nor do they understand its principles. They just need to know that this thing can still be used and not broken.

Mathematicians are like the engine of the academic world. They do the hardest and most exhausting work, and most of the time, people's attention to the mathematical world is limited to whether there are any good tools that can be used.

Even for the same scientific research funding application, the research funding for mathematics is less than that for other science subjects.

Such as physics, chemistry... After all, the latter requires various experiments. The investment in laboratories and various instruments requires money...

So in a sense, mathematicians don't have many highlight moments.

After all, only a few people can create the ultimate romance with just a pen and a piece of paper.

In fact, most people can make a name for themselves by making some improvements based on the research results of others.

Yes, in fact, Chen Zhuoyang has no need to feel ashamed.

Because the nature of mathematical research means that major breakthroughs are rare.

Ninety percent of mathematicians' work is to refine existing theories or solve local problems. Of course, this does not mean that these seemingly insignificant achievements are not important.

Because these accumulations may give rise to a sudden flash of inspiration in those geniuses at any time.

For various reasons, for most mathematicians, being able to give a 60-minute report at an important conference is already a highlight in their lives.

After all, this is not a branch venue, and the time given is very long. And there are really a lot of people here today, and it even seems that there are more people than the last World Algebraic Geometry Congress.

Fortunately, Qiao Yu has become accustomed to being an opinion leader among the crowd.

“The distribution of prime numbers is one of the core issues in number theory research, and its spacing problem has always been an unsolved mathematical problem. In practical research, mathematicians have proved that the upper bound of the prime number spacing can be limited to a specific range.

Professor Zhang Yuantang's pioneering work reduced the upper limit of this distance to 7000 million, and through the efforts of mathematicians around the world, it was reduced to 246. What I will report today is a new geometric method derived from the axiom system of generalized modal number theory to solve related problems.

By mapping the prime number distribution into the modal space and using geometric tools such as modal density functions, modal paths, and modal convolutions, we prove that the bounded distance between prime numbers can be further reduced to an upper bound of 6..."

The beginning is a brief introduction.

First of all, I want to let everyone know how this work is carried out. Without the cooperation of Lott Dugan, this area will be very troublesome.

Because the abstract "Based on the axiom system of generalized modal number theory, a new geometrization method is derived" is enough to confuse countless people in the audience.

But now, not all of them, but at least more than 80 percent of the participants will not be confused.

After Ann.Math was published yesterday at noon, the organizer, who had been prepared for this, had already started to take action.

More than 2,000 copies of the paper, which had been printed in advance, were distributed through the hosts of each branch venue before dinner.

At least every registered member of the Mathematical Society has a copy. If there are those who are not interested in this proposition, the paper will be given directly to those who are interested.

Some people also borrowed the paper directly to print a copy.

The hotel hosting this kind of academic conference will thoughtfully arrange printing services. Of course, if the hotel is too busy to handle it, there will be someone to send it out for printing.

Although one night may not be enough for all participants to fully understand the paper, at least most people already know the general concept and have a preliminary understanding.

At the same time, sixty minutes is the longest time for academic reports at top conferences, but it is not enough for Qiao Yu to popularize the generalized modal space framework. So after briefly discussing the abstract, Qiao Yu went straight into the state.

“…The modal path Γ is a continuous curve in the modal space, which is used to describe the distribution trajectory of prime numbers in the geometric space. In order to reduce the distance between modal points, the path needs to be optimized as follows:
As you can see in this formula on the big screen, T is the path period, which is used to ensure that the path has a periodic repeating structure in the modal space.”

“From the above, it can be seen that the curvature and distribution of the path Γk are driven by the local high value area of ​​the modal density function ρM(r). Γk passes through the local extreme point of the modal density function to ensure the path coverage of the high density area.

The modal path has geometric symmetry. If the symmetric mapping: M→M satisfies:
Through the above optimized construction, the high density, periodicity and symmetry of the modal path Γ can be guaranteed..."

……

"Do you understand?" Zhang Yuanling, who was deep in thought, was interrupted by Shen Zhongxing beside him.

He nodded slightly at first, then shook his head.

Well, actually it wasn’t that his train of thought was interrupted, it just interrupted his desire to explore further.

To be honest, I didn’t fully understand it!
But this cannot be blamed on him. In fact, Zhang Yuanling believed that at least 90 percent of the people at the meeting could not understand what Qiao Yu was saying at this time.

It's not that everyone's level is not good enough, or that their understanding ability is not good enough. It's mainly because the content of today's talk is too special. It's a brand new theoretical framework, and everyone has only been exposed to this framework for one night.

Before fully understanding the framework built by Qiao Yu himself, it is easy to imagine how difficult it would be to understand the content of this paper.

So while listening to the report, Zhang Yuanling kept recalling some conclusions and theorems from another paper.

For example, the definition of modal space, modal density function, construction of modal path, modal convolution formula and other knowledge points...

Then use these unfamiliar knowledge points to infer what Qiao Yu is talking about. These things have to go through a very complex transformation process in the human brain.

It's easy when you're young, but as people get older, their brains aren't as flexible as they were when they were young.

"I feel relieved since you don't understand. After all, I have examined his thoughts before." Shen Zhongxing said in a joking tone.

It's a joke indeed.

If Zhang Yuanling had known at that time that Qiao Yu could develop this axiomatic system to this level in more than two months, he would not have questioned anything at all and would have approved it directly.

But now I can only say that I miscalculated!
"Tian Yan's luck is so good that I don't know how to describe it." Zhang Yuanling said indifferently.

He knew Shen Zhongxing had no ill intentions. The two had a good relationship and had discussed it privately yesterday. If Shen Zhongxing were to review Qiao Yu's project proposal, he would definitely have doubts.

I can only say that Zhang Yuanling was very unlucky this time.

"Well...it's not just luck. After all, he is at Yanbei University." Shen Zhongxing sighed.

Zhang Yuanling was silent.

Yes, probably only Yuan Zhengxin has the qualifications to say that Tian Yanzhen is just lucky, even Yuan Zhengxin is a little worse.

The reason is naturally the siphon effect of famous schools.

When more than 80% of the competition students and candidates, as well as their parents, choose Yanbei and Huaqing as their first choice, it is indeed very difficult for other famous schools to compete with these two schools for the best students.

Especially a promising person like Qiao Yu who has already shown success at the age of sixteen.

Although Shuangdan University is also a famous university and its School of Mathematics is ranked among the best in the country, it is still somewhat inferior to Yanbei and Huaqing.

Seeing that Zhang Yuanling didn't say anything, Shen Zhongxing sighed and said, "Hey... yesterday those were two papers. For the next thirty years at least, I think we can expect China to have a say in the world mathematics community."

Zhang Yuanling smiled, but her smile was not that happy.

Listening only to the second half, it was obvious that this was a compliment, but since they were old colleagues, he could certainly understand the meaning of the whole thing:
At least in the next thirty years, there is no need to consider challenging Yanbei and Huaqing's status in the Chinese mathematics community...

Whatever ambitions you have, you can put them aside for now. These are all conceivable.

With this realization, Zhang Yuanling suddenly thought of a possibility and couldn't help but ask, "Old Shen, what do you think of next year's Fields Medal..."

Shen Zhongxing was stunned for a moment, then shook his head slightly and said with emotion: "This... shouldn't be possible? After all, he is still too young, he will only be seventeen next year.

We can look forward to the one in 2030. He will be only 21 years old then. But one thing I am sure of is that he will be considered for many awards next year. "

Zhang Yuanling nodded. Indeed... seventeen years old is too young.

This is definitely something that the International Mathematical Union jury needs to take into account.

If Qiao Yu really won the prize at the age of 40, how many years would he have dominated the mathematics world? Not to mention that every year there are many candidates who are stuck at years old and will never have a chance after that.

Moreover, the Fields Medal Selection Committee should also consider leaving some expectations for the future... If Qiao Yu really wins the award next year, the topic of the youngest Fields Medal winner will probably be completely ended.

This also made Zhang Yuanling somewhat emotional. Who could have imagined that one day, the reason preventing a mathematician from winning the Fields Medal was that he was too young? !
After all, this matter is too outrageous.

"So, Professor Zhang, after this meeting, I think you can pick a time to talk to Qiao Yu...Besides, he withdrew the project on his own last time, so it actually has nothing to do with you."

Shen Zhongxing looked at the young man who was still talking on the stage with a complicated expression and said something casually.

Zhang Yuanling thought about it, then nodded imperceptibly and said, "Let's first study the paper thoroughly. It's not a good idea to approach him rashly. We need to have a common topic."

Shen Zhongxing also nodded. He could understand Zhang Yuanling's concerns. They were all respectable people, so they couldn't completely lose face, right?

……

In the front row, Yuan Zhengxin didn't care too much about what Qiao Yu said. After all, he had read the paper countless times and had discussed it with Qiao Yu.

The presentation at the conference also followed the thesis, and he was clear about every step of Qiao Yu's thinking.

He might as well use this time to give more advice to his students.

"Yesterday you said Qiao Yu had already told you the idea of ​​this paper?"

"Yeah." Qiao Xi responded softly.

"Can you understand?" Yuan Zhengxin asked again.

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

Yuan Zhengxin nodded with satisfaction. Mathematics is like that. If you can understand it, you have surpassed 90% of ordinary people.

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

Moreover, if you want to know whether a high school student with good math grades has math talent, it is actually very simple. You can determine it by just asking him whether he feels tired studying math.

If a student has to work hard on solving questions in high school to get high scores, it is likely that he or she has no talent and it is best for him or her to stay away from mathematics when applying for a major.

After all, this is a subject that is useless if you just work hard once you reach a certain level. Yuan Zhengxin asked again, "Have you discussed with Qiao Yu what else needs to be done to further lower the upper bound or even completely solve this problem?"

Qiao Xi shook his head and said, "I haven't discussed it, but I think if we want to make further breakthroughs, we need to further optimize the structure of the modal path.

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

Yuan Zheng thought for a moment, then said, "Didn't he ask you to help with this work?"

Qiao Xi shook his head again and whispered, "He asked me to try to prove the modal existence of twin primes first."

"Oh? Any ideas?"

"I mentioned it briefly."

As he spoke, Qiao Xi took out a pen and paper and wrote down some concepts: "Qiao Yu said that if we want to introduce twin characteristics, we need to use a new mapping concept. For example, a high-order nonlinear operator is used to find core symmetries in modal space.

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

After writing this down, Qiao Xi shook his head again and explained, "To be honest, I think this is very difficult. Qiao Yu often has some ideas, um... I think the angles are very strange, and I can't keep up with his train of thought."

Yuan Zhengxin smiled and said, "It's normal that you can't keep up with his thinking. Look at the more than 3,000 people here today, at least 3,000 of them can't keep up with his thinking.

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

After solving this problem, he can still challenge higher peaks. So please 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 whose words were his bond would actually say these words to her in a pleading tone. She was stunned for a moment.

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

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

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

Looking at Qiao Yu, who was performing freely on the stage, he couldn't help feeling a little depressed.

……

In fact, many people in the back row had already quietly left by this time, mostly students and math enthusiasts, and of course a few professors.

There is nothing we can do about it.

If you don’t understand anything at a lecture... everyone can understand this feeling, it’s similar to the feeling of not understanding something in math class.

In short, once you don't understand, those complicated formulas are like incomprehensible books, not human language. Then you will feel bored, and even feel that the days are passing by like years.

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

For example, the mathematics I study and research seems to be different from others. Even if we are both studying number theory, it is really difficult to understand the geometric structure of number theory problems without a certain understanding of the previous framework...

All in all it was a very painful thing to do, and it was doubly painful if you consider that the mathematician giving the presentation was sixteen years old.

Fortunately, Qiao Yu, who was sitting on the podium, didn't actually notice these things. Even if he did, he didn't care too much.

If he felt excited when he made the report for the first time, this time, Qiao Yu was just completing the task, mainly because he started too high.

"…According to Lemma 5.7, modal convolution describes the distribution of modal points on the path Γ. The distribution of modal points in the local area is shown in the figure:"

"By controlling the maximum value of the wide basis, the spacing between modal points can be limited to no more than 6. At the same time, since the global structure of the modal path Γ is periodic, its local high-density characteristics are repeated globally. Therefore, the modal distance of any modal point r_p, r_q∈Γ on the path satisfies: d_M(r_p, r_q)≤6
...Finally, according to Theorem 2, Theorem 3, Theorem 4, and Theorem 5, we can know 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 numbers.

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

In summary, d_M(r_p, r_q)≤6 is equivalent to |pq|≤6, and the prime number pairs with prime spacing |pq|≤6 are infinite in the sense of number theory. From now on, the proof is complete. "

Qiao Yu has a strong ability to manage time, and he spent fifty-five minutes out of sixty.

In fact, if he spoke a little faster, he could finish the speech in 50 minutes, which is also a relatively suitable time.

Because usually at the end of a special invited report, about ten minutes of time will be reserved for answering questions.

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

This is also the reason why each report has a host. During the Q&A session, the host will select questioners to ask questions about the speaker's content.

However, today's lecture is rather special. Many people do not have enough time to fully digest the contents of the generalized modal axiom system, so they only listened to the 50-minute lecture on his paper and could not ask any valuable questions.

So we just left it for five minutes and let the host do whatever he wanted. If someone asked a question, he would just answer it casually. If no one asked a question, the host would say a few polite words, and then everyone could go to eat early.

Of course, if there is a problem, we can communicate with each other later.

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

A quick glance shows that few people in the front row have raised their hands... It will take some time to digest this new axiomatic framework.

Those who are chosen to be the report hosts are all smart and quick-witted people. Especially after seeing the expressions of some bigwigs in the front row, they naturally understand how to deal with this situation.

“Thank you very much for Qiao Yu’s wonderful report. The report has elaborated on the upper bound of prime number intervals, which is 6.

If you have any questions about the paper, I believe Qiao Yu will definitely take some time out of this meeting to discuss it with you in more detail. 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 giving the report on the stage, everyone else at the conference understood the significance of this article in the number theory community.

Back then, the whole world worked together to lower the upper limit of prime number intervals to 246. More than ten years later, someone finally lowered the number again, and reduced it to 6 in one go.

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

Even more than that.

With the publication of his and Chen Zhuoyang's papers in Ann.Math, anyone who has carefully read the two papers probably has mixed feelings at this moment.

A publication in one of the four top magazines, an honor that many people would only dream of, was just given away by that overly young guy on the stage...

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

Let’s forget about the framework of the generalized modal axiom system, but this entire set of proof logic is really not something that ordinary people can come up with.

But when it comes to the subsequent verification work, many people feel that they can probably do it too.

Even more than that...

There are always some invisible rules in the academic world, such as supervisors using students' research results. It sounds incredible, but this situation has always existed, and it can even be said that it is universal.

Incorporate students' research directly into your own framework, present the final results with the tutor as the protagonist, and use the data collected and analyzed by students directly to publish papers independently.

Even more shameless, there are cases where the supervisor directly signs the student as the first author in a paper completed independently.

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

The young man on the stage forcibly divided the content that could be covered in one paper into two papers, just to give his collaborator a first author title.

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

This makes many people feel so complicated that it is hard 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 happily. He was the second person to give a report today. Then it was time for lunch, and he would be free in the afternoon...

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

It wasn't for the lecture, but mainly because he wanted to listen to Brother Chen's flattery...

Everything is good about being with Qiao Xi, but it is still too difficult to get Qiao Xi to praise him to the sky.

Senior Brother Chen did a great job on this point. Unfortunately, Qiao Yu soon discovered that he had taken things too lightly.

Although the morning meeting was over, Qiao Yu found that he couldn't walk out of the banquet hall.

As soon as he stepped down from the podium, he was surrounded by a group of people.

It means to surround someone literally. Of course, the situation is not actually very chaotic because everyone is a mathematician and many of them are even professors at the doctoral level.

We are just doing academic discussion. It is just irrelevant to the content of today's report. All the questions we asked are about the generalized modal axiom system...

Although none of them were very humble, as long as someone squeezed next to Qiao Yu and started asking questions, most of the others would choose to listen quietly to Qiao Yu's explanation first.

"Qiao Yu, your paper, Lemma 1.3: The distribution of modal points on the modal path depends on the weighted modal density function, where the selection of the weight function w(α, β, γ) affects the geometric characteristics of the modal distance.

But I don’t quite understand the basis for choosing this weight function. Is it logarithmic density? Or other known number theory results or geometric properties? "

"This... well, it has been proven... is analogous to the logarithmic density 1/logp in prime number distribution. But it is not just a simple logarithmic density. There is an extension here to control geometric properties.

And we have to ensure symmetry and smoothness, for example, its definition parameters are symmetrical... Well, you see, if a periodic term sin(β) is introduced, the repeatability and global structure of the modal path will be weakened..."

……

Tian Yanzhen, Yuan Zhengxin and Qiao Xi stood at the side and watched from a distance. There was nothing they could do, as they couldn't even squeeze in.

Qiao Xi also roughly understood why Tian Yanzhen asked her to keep an eye on Qiao Yu and not let her go anywhere yesterday.

Once the enthusiasm of the mathematicians burst out, Qiao Xi felt terrified.

So he simply suggested: "Well...why don't we just ignore him for now?"

Well, out of sight, out of mind.

(End of this chapter)