Chapter 157 In the Spotlight
Scientists, or intellectuals, are a very special group. They may not have a lot of wealth, but in a sense, a large part of this society's wealth growth is based on the efforts of these people.
If we must make an analogy, they seem to be the engine of social wealth growth. Doing the most tiring work in areas that people don't see.
Just like after a normal family buys a car, except for maintenance or repairs, no one will deliberately open the car hood every day to see what the engine looks like.
Yes, everyone knows that the engine is important, but no one bothers to take a look at it when nothing happens.
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 still works and is not broken.
Mathematicians are like the engines of academia. Doing the hardest and most tiring work, most of the time people's attention to the mathematical community is limited to whether there are any good tools that can be used.
Even for the same scientific research funding application, the research funds for mathematics are less than those for other sciences.
Such as physics, chemistry... after all, the latter requires various experiments. Investment in laboratories and various instruments require money...
So in a sense, mathematicians don't have many bright moments.
After all, only a few people can create the ultimate romance with a pen and a piece of paper.
The vast majority of people can actually become famous by making some improvements based on other people's research results.
Yes, in fact, Chen Zhuoyang has no need to feel ashamed.
Because the nature of mathematical research determines that major breakthroughs are uncommon.
Ninety percent of mathematicians’ jobs are to refine existing theories or solve local problems. Of course, this does not mean that these seemingly inconspicuous results are not important.
Because these accumulations may give those geniuses a sudden flash of inspiration.
Various reasons also determine that for most mathematicians, being able to give a sixty-minute report at an important meeting is already the highlight of life.
After all, this is not a branch venue, and the time given is very long. And there are really many people here today, and it even seems to be more people than at the last World Congress on Algebraic Geometry.
Fortunately, Qiao Yu is used 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 actual research, mathematicians have proven that the upper bound of the spacing of prime numbers can be limited to Within a specific range
Professor Zhang Yuantang's pioneering work reduced the upper bound of this distance to 70 million, and through the efforts of mathematicians around the world, it was reduced to 246. What I want to 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 distribution into modal space and using geometric tools such as modal density functions, modal paths, and modal convolution, it is demonstrated that the bounded distance between primes can be further reduced to 6 The upper bound..."
The beginning is a simple introduction.
First of all Let everyone know how this work unfolds. Without the cooperation of Lot Dugan, this part will be very troublesome.
Because as the abstract, "According to the axiom system of general modal number theory, it is derived." "Inventing a new geometric method" can make countless people in the audience confused.
But let’s not talk about everything now, at least more than 80% of the participants will not be confused.
Because after Ann.Math was published at noon yesterday, the organizers who had prepared for it had already started to move.
More than two thousand papers that had been printed out in advance were distributed through the hosts of each session before dinner.
At least one copy is available to all registered members of the Mathematical Society. For those who are not interested in this topic, the paper will be given directly to those who are interested.
Some people directly borrowed the paper and printed a copy.
Hotels hosting such academic conferences will thoughtfully arrange printing services. Of course, the interior is too busy, and someone will send it outside for printing.
Although one night may not be enough for all participants to fully understand the paper. But at least most people already know the general concept and have a preliminary understanding.
At the same time, sixty minutes is already the longest time for an academic report at a top conference, but it is actually not enough for Qiao Yu to popularize the generalized modal space framework. So after briefly talking about the summary, Qiao Yu got into the mood directly.
“…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 modal point spacing, the following optimization construction of the path is required:
As you can see 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. ”
"It can be seen from the above that the curvature and distribution of the path Γk are driven by the local high-value area of the modal density function ρM(r), and Γk passes through the local extreme point of the modal density function, ensuring path coverage in high-density areas.
The modal path has geometric symmetry, assuming symmetric mapping :M→M satisfies:
Through the above optimization structure, 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 a heavy line beside him.
First he nodded slightly, then shook his head.
Well, it doesn’t actually interrupt his train of thought, it can only be said to interrupt his idea of further exploration.
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% of the people at the meeting could not understand what Qiao Yu was talking about at this time.
It’s not that everyone is not good enough or has poor understanding. The main reason is that what I’m talking about today is too special. It’s a brand new theoretical framework, and everyone has only been exposed to this framework for one night.
Before you fully understand the framework built by Qiao Yu, you can imagine how difficult it is to understand the content of this paper.
So while listening to the report, Zhang Yuanling kept recalling some conclusions and theorems in another paper.
For example, knowledge points such as the definition of modal space, modal density function, construction of modal paths, modal convolution formulas, etc...
Reuse these knowledge points that are not very familiar to you. To deduce what Qiao Yu is talking about. These go through a very complex transformation process in the human brain.
It was easy to say when you were young, but as you get older, your brain is not as flexible as when you were young.
"You don't understand either, so I feel relieved. After all, I have reviewed his ideas before." Zhong Xing said in a joking tone.
It is indeed a joke.
If Zhang Yuanling knew at that time that Qiao Yu could complete this axiom system to this extent in more than two months, he would not have questioned anything at all and directly approved it.
But now it can only be said that it was a miscalculation!
"Tian Yan is so lucky that I don't know how to describe it." Zhang Yuanling said nonchalantly.
He knew there was no harm in the heavy line. The relationship between the two is good, and they discussed it in private yesterday. If Zhong Xing came to review Qiao Yu's project document, there would definitely be doubts.
It can only be said that Zhang Yuanling was quite unlucky this time.
"Hey...it's not just good luck. After all, he is at Yanbei University." Zhongxing sighed.
Zhang Yuanling was silent.
Yes, probably only Yuan Zhengxin has the qualifications to say that Tian Yanzhen is lucky, and even Yuan Zhengxin is a little bit worse.
The reason is naturally the siphon effect of prestigious schools.
When more than 80% of the competition students and candidates in the society, as well as the parents, regard Yanbei and Huaqing as their first choices, other prestigious schools want to compete with these two schools. The best seedlings are indeed too difficult.
Especially for a youngster like Qiao Yu who is already in his prime at the age of sixteen.
Although Shuangdan University is also a famous school, and the School of Mathematics is also ranked high in the country, it is still a little behind compared to Yanbei and Huaqing.
Seeing that Zhang Yuanling did not speak, Zhenxing sighed and said: "Hey... those were two papers yesterday. In the next at least thirty years, I think we can look forward to China's success in the world of mathematics. The right to speak.”
Zhang Yuanling smiled, but the smile was not so cheerful.
Only listening to the second half, it is obvious that this is a compliment, but since he is an old colleague, of course he can understand the meaning of the connection:
At least in the next thirty years In the year, there is no need to consider challenging the status of Yanbei and Huaqing in the Chinese mathematics community...
Any ambitions can be put aside for now. These are all conceivable.
With this realization, Zhang Yuanling suddenly thought of a possibility and couldn't help but said: "Old Shen, what do you think about next year's Fields Medal..."
Zhongxing was startled, then shook his head slightly, and said with emotion: "This...should be impossible, right? After all, he is still too young, he will only be seventeen next year.
But we can look forward to that time in 2030 He was only 21 years old at that time. But one thing I am sure of is that he will be considered for many awards next year. Indeed... seventeen years old is too young. .
This is definitely one of the situations that the International Mathematical Union jury needs to take into consideration.
Qiao Yu really won a prize at the age of seventeen. How many years will he rule the world of mathematics? Not to mention that every year there are many candidates who are stuck at 40 years old, and will never have a chance after that.
And the Fields Medal judging committee should 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 that prevents a mathematician from winning the Fields Medal is that he is too young? !
After all, this matter is too outrageous.
"So, Professor Zhang, after this meeting, I think you can choose a time to chat with Qiao Yu... Besides, it was a project he withdrew on his own last time, so it actually has little to do with you. "
Zhong Xing looked at the young man who was still talking on the stage with a complicated expression and said casually.
Zhang Yuanling thought for a while, then nodded inconspicuously, and said: "Let's finish the paper first. It's always a bad idea to rush into it. There must always be a common topic."
Zhong Zhongxing also nodded. He could understand Zhang Yuanling's concerns. They are all decent people, so they can't completely lose face, right?
......
In the front row, Yuan Zhengxin didn't care much about what Qiao Yu said. After all, he had read the paper countless times and had communicated with Qiao Yu.
The narration at the report meeting also followed the paper. He knew Qiao Yu's thinking at every step.
If you have this time, why not mention more of his students.
"Yesterday you said that Qiao Yu had already told you the idea of this paper?"
"Yes." 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.
It has been like this even since junior high school, but it was just not obvious at that time. By the time you reach high school, your math scores will gradually begin to become polarized.
And if you want to know whether a high school student with good math scores has a talent for math, it is 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 in order to get high scores, 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 that requires a certain level of study and 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 still a breakthrough, the structure of the modal path needs to be further optimized.
And we should also consider adding some Number theory methods are also introduced, such as the sieve method again for primes on the path. Verify the infinity of numbers."
Yuan Zheng thought for a moment, 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 primes first."
"Oh? Do you have any ideas?"
"I just mentioned a little bit."
As she said that, Qiao Xi took out a pen and paper and wrote down some concepts: "Qiao Yu said if To introduce twin properties, a new mapping concept is needed, such as a high-order nonlinear operator to find core symmetries in the modal space.
Given that this type of modal mapping is non-linear. Linear and irreversible, he designed An operator matrix structure is created, 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 jotting down these, Qiao. Xi shook her head slightly again and explained: "To be honest, I find this very difficult. Qiao Yu often has some ideas, well... I think the angles are very weird, and I can't keep up with his thoughts."
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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 it , Qiao Yu hopes that you can help him. So even if it is difficult, you must believe in yourself and your work is important to help him completely solve the twin prime conjecture. >
After solving this problem, he can challenge to a higher level, 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. !”
“Huh?” Qiao Xi was stunned for a moment as it was hard to imagine that an old man who kept his word would say this to her with a hint of pleading.
But Qiao Xi soon reacted, nodded quickly and replied: "Don't worry, Teacher Yuan, I will definitely urge Qiao Yu to continue working hard."
"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 of heavy pressure falling on her slender shoulders...
Looking at Qiao Yu who was swaying freely on the stage, he couldn't help but feel a little depressed.
......
In fact, by this time the report meeting was going on, many people in the back row had already begun to sneak away quietly. Most of them are students and mathematics enthusiasts, but of course there are also a few professors.
This is actually something that can't be helped.
Listening to a report meeting, if you don’t understand it at all... This experience can actually be understood by everyone, just like 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 human language. What follows is boredom, and it even feels like every day seems like a year.
If you add in the fact that most of the students who can attend this conference 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 other people’s mathematics. Even if you are studying number theory, without a certain understanding of the pre-framework, it is really difficult to understand the structure of the geometricization of number theory problems...
All in all, this is a very painful thing. This pain is easily doubled when one considers that the mathematician giving the presentation is sixteen years old.
Fortunately, Qiao Yu, who was sitting on the rostrum, didn't actually notice this. Even if he did, he didn't care too much.
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 5.7, 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:"
"And By controlling the maximum value of the wide basis, the spacing between modal points can be limited to not exceed 6. At the same time, because the global structure of the modal path Γ is periodic, its local high-density characteristics appear 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, 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. 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 there are infinitely many pairs of prime numbers with spacing ∣pq∣≤6 in the sense of number theory. Since then, the proof has been completed. ”
Qiao Yu’s time control ability is very strong, and it took fifty-five minutes to complete sixty minutes.
In fact, if he spoke a little faster, he could have used fifty-five minutes. Finished in minutes. This is also a more appropriate time.
Because in general, 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 reports will be assigned a host. During the question and answer time, the host will select the questioner and ask questions about the speaker's content.
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, so for his paper, I will only listen to the fifty-minute lecture and ask questions. No valuable questions asked.
So I just left it for five minutes and let the host figure it out. If anyone asks, just answer casually. If no one asks, the host will say a few words and everyone can go to dinner early.
Of course, if there are any problems, you can wait until everyone can communicate with you later.
The fact is 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.
Those who can be selected as report moderators are all smart and flexible people. Especially after seeing the expressions of some big guys in the front row, they naturally understand how to handle this situation.
“Thank you very much Qiao Yu for your 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 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 that this article was What is the significance of the world of number theory?
At that time, it was just a matter of strength. The upper limit of the interval between prime numbers has been lowered to 246. After more than ten years, someone has finally lowered this number again, and it has been lowered to 6 at once.
To be honest, 99% of the people in the audience are watching at this moment. Qiao Yu's eyes were filled with envy and a little bit of jealousy...
Even more than that.
With the publication of his and Chen Zhuoyang's papers on Ann.Math, anyone who has carefully read the two papers may have a rather complicated mood at the moment.
A work for one of the four top magazines, an honor so many people dream of, was given away by that young guy on stage...
Yes, in the eyes of many people , the second paper is really 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, such as tutors using students’ results. It may sound incredible, but this situation has always existed, and it can even be It doesn’t matter what country it is.
Integrate students' research directly 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 some who are uneducated and unskilled...
The young man on the stage abruptly divided the content of one paper into two papers. Just to give collaborators one piece of work.
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 feels pretty perfect.
Then he stumbled off the stage. He was the second one to give a report today. It was time for dinner, and then he would be free in the afternoon...
Qiao Yu planned to go find Senior Brother Chen to accompany him. He wandered around the venue and chatted.
It was not because he wanted to listen to the report, but mainly because he wanted to listen to Senior Brother Chen’s rainbow fart...
Everything is good with Qiao Xi, but he wanted Qiao Xi to praise him so much Going up to the sky is still too difficult.
Senior Brother Chen has done this very well. 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 is literally surrounded. Of course, the situation is not very chaotic. Everyone is engaged in mathematics, and many are even doctoral level professors.
We are just doing academic discussions. But it has nothing to do with the content of today's report meeting. Everyone is asking questions about the generalized modal axiom system...
Although they are not very humble, as long as someone squeezes in next to Qiao Yu and starts to ask questions, other questions will be answered. Most people would choose to listen quietly to Qiao Yu's explanation first.
"Qiao Yu, in your paper, Lemma 1.3: The distribution of modal points on the modal path depends on the weighted modal density function, in which the selection of the weight function w (α, β, γ) affects the geometry of the modal distance. Characteristics.
But I don’t quite understand the basis for selecting this weight function. Is it logarithmic density? Or other known number theory results or geometric properties?”
“This... well, It has been proven...kind of Compared with the logarithmic density 1/logp in the prime distribution, it is not a simple logarithmic density. There is an extension to control the geometric properties, such as symmetry and smoothness. The defining parameter is symmetry... Well, you see, if a periodic term sin(β) appears, the repeatability and global structure of the modal path will be weakened..."
...
Tian Yanzhen, Yuan Zhengxin and Qiao Xi stood watching from a distance. There's no way, I can't even squeeze in now.
Qiao Xi also probably understood why Tian Yanzhen asked her to keep looking at Qiao Yu yesterday and not let him go anywhere.
Once the enthusiasm of mathematicians bursts out, Qiao Xi feels quite scary.
So I simply suggested: "Well... why don't you just ignore him for now?"
Well, out of sight, out of mind.
(End of this chapter)