Chapter 154 Proof of infinity of pairs of prime numbers with an interval of 6
Tian Yanzhen told Qiao Yu to get out of here. After Qiao Yu walked out of the office honestly, he started to make calculations in his head.
The benefits of giving a report at the annual mathematics meeting are obvious. Qiao Yu thought that probably the tutor and Mr. Yuan felt that it was shameful that they had not been able to apply for the previous project, so they fought for this opportunity.
Let him speak out this idea in front of everyone, which somewhat means letting the entire mathematical community comment on it.
It can be understood as a shout out to the Chinese mathematics community: "Everyone, come and see if we are selfish in giving Qiao Yu the opportunity to work on a major project!"
But of course this is under the premise that he has not contributed to Ann.Math. Qiao Yu can analyze from the instructor's attitude that giving a report at a conference is not as useful as publishing a paper in a top journal.
After all, the former is only speaking to the Chinese mathematics community, while the latter is speaking to the world mathematics community.
But now there are only 17 or 18 days left on the 25th. Prepare a paper that can be delivered as a one-hour report at the annual mathematics meeting, and you can’t lose the instructor’s face...
It does seem a bit difficult.
This is the disadvantage of being too good. The instructor thinks he can do anything!
So on the way back to the dormitory, Qiao Yu felt what he should have felt at his age - melancholy!
I am completely unprepared!
During this period, he has been concentrating on completing the proof of the multi-modal space system, and is working on the proof of generalization from two dimensions to three dimensions. This work will take at least one or two months. can be completed.
Okay, Qiao Yu must admit that without any direction, it must be a joke to ask him to spend half a month to come up with a paper out of thin air?
This is a bit troublesome...
Soon Qiao Yu sat in front of his computer and began to think hard.
The main reason is that the meeting time is too long. It happens to be the beginning of November, the month Ann.Math is published every year, and it happens to be the single month every year.
This is why Qiao Yu feels that his and Senior Brother Chen's papers may not be published this year.
Submitted in October, no matter how quickly the review is, it will probably be November. Adding to the typesetting time, the fastest publication time will be January next year, or even March.
This is assuming everything goes well. If the reviewer has any questions about the paper, discuss it back and forth, and maybe push it back.
This is also the reason why many university teachers who have signed 3+3 employment agreements with universities are under great pressure.
Generally, this kind of agreement has clear requirements for the number of papers to be published during the assessment period, such as three papers to be published in journals of a certain level in three years.
It doesn’t sound difficult. But for young teachers who have just entered universities, they not only have to complete the most arduous teaching tasks, but also do research and go back and forth with reviewers.
Projects always have more monks than meat. It is difficult to publish the article on time without the recommendation of a big boss. Universities can only offer so many academic positions.
Most people are unwilling to compromise. After all, going to teach in a certain three or even junior college basically means severing oneself from the mainstream academic world, and they will stay like that for the rest of their lives.
Thinking of this, Qiao Yu suddenly felt that he was not in such a difficult situation after all. After all, it is impossible for him to encounter the above situation.
It is nothing more than writing a paper that will make Director Tian and Mr. Yuan feel that they will not lose face. Although the time is shorter, as long as there is a general direction, it should not be a big problem.
The key is direction.
Then Qiao Yu set his sights on prime numbers...
Just as he told big guys like Zhang Yuantang, Tao Xuanzhi, Lot Dugan, etc., he planned to construct a generalized model The original intention of the axiom system of state number theory is to solve the prime number problem.
So apart from this axiom system, he thinks about prime numbers the most in his daily life.
I even tried to use this axiom system to solve some prime number problems. And there's a lot of progress.
For example, regarding the twin prime conjecture, Qiao Yu felt that he could use the method he constructed to reduce the bounded distance between prime numbers to two digits, or even a single digit greater than 2.
Since Zhang Yuantang proved that the interval is less than 60 million, the collective efforts of the mathematical community have only pushed this value to 246.
This number has not changed since 2014, because with the method given by Zhang Yuantang, it is already the limit to prove it. It is basically recognized in the mathematics community that new mathematical ideas and tools will be needed to complete the next step.
For Qiao Yu, he had never thought of writing a paper on this issue before. The main reason was that he could not make this value equal to 2 for the time being.
Because we want to be equal to 2 and completely solve the twin prime conjecture, there are still some technical problems that remain unresolved.
After all, tools such as modal density and modal path have not yet been fully proven, and once they get to that point, accuracy must be considered.
For example, can the local oscillation of the modal density function satisfy the twin prime trajectory? Only after these are proven can we start to formally discuss this issue.
However, as long as it is not equal to 2, the accuracy requirements are actually not that high, and it can be proved using the existing tools of the axiom system of generalized modal number theory.
And a paper like this is definitely enough to handle a conference. Not to mention that this was a report given on the morning of the third day of the meeting, not an opening report.
The most important thing is that if it is such a paper, he will not need eighteen days, but ten days at most. After all, the proof ideas are already in his mind.
The only problem is that such a paper still needs to use many concepts from the first stage of his axiom system of generalized modal number theory. But this paper has not been published yet...
Quoting the results of his unpublished paper at the conference to demonstrate a result, Qiao Yu could imagine how many mathematicians in the audience could do it with his buttocks. I wonder how much controversy it will cause.
But with only such a short time, it is almost impossible for him to choose a proposition again.
So Qiao Yu decided to leave this issue to Director Tian for decision-making.
Although he did not communicate with Director Tian and Mr. Yuan when he sent the paper to Ann.Math, it was indeed his fault.
But Director Tian and Mr. Yuan asked him to give a report at the Chinese Mathematics Annual Conference without explaining it to him in advance, so it can be said that both parties are responsible for this matter.
If he had to make a report anyway, then it would be this paper. If this paper doesn't work, then quickly find someone else.
After all, half a month starting from the topic selection to write a mathematics paper that is qualified to attend the top domestic conferences, in Qiao Yu's opinion, is as outrageous as giving him a pile of sand and asking him to pinch out a chip.
Not even a god can do it!
Of course, you can’t say that after the phone call is made.
“Hey, Director Tian, I have a very bold idea about the conference paper you just mentioned!”
After hearing this sentence, the other person didn’t know if it was because of I was reading a paper and was silent for more than ten seconds before my voice came through.
“You think it’s bold? Okay, let’s talk about it.”
"What do you think of my paper, which focuses on reducing the upper bound interval of prime numbers to single digits greater than 2? But I'm not sure how far it can be reduced, but I think single digits should be no problem." Qiao Yu immediately said.
The silence lasted longer this time. Director Tian's voice came again for more than twenty seconds, but this time it was much more serious and had a hint of inquiry.
"Single digits? Are you sure you can do it?"
Qiao Yu immediately replied affirmatively: "Of course, I can definitely do it, but I have to use my new set of Theory. So the question is, I can use a new method to reduce this gap, but this new method has not been published in the mathematics community. Do you think?"
Generally speaking, as a graduate student, you should not make your supervisor feel entangled. of. Otherwise, there is a high probability that your postgraduate career will not be perfect.
But there are always a small number of people who have this power and are lawless. Obviously Qiao Yu falls into this category.
Three sentences, making the instructor silent three times, and the silence time continued to extend... If it weren't for the slight sound of breathing, Qiao Yu would have suspected that the phone was disconnected.
Finally, when Qiao Yu felt a little nervous, the mentor's voice finally came again.
“You write first, and then we’ll talk after you finish.”
“Okay, Director Tian, please wait a minute! I’ll write the paper as soon as possible.”
When the busy signal came from the phone, Qiao Yu also let out a sigh of relief.
At least his problem is solved.
As long as he writes this paper, it doesn't matter whether he gives a report at this meeting or not.
Anyway, Director Tian asked him to write out the paper first. If it couldn’t be used, he couldn’t be blamed.
You can’t give him half a month to write two papers that can give a 60-minute report at such a top domestic conference, right?
Unless someone doesn't understand mathematics at all, no one would make such an outrageous request.
After feeling relaxed, Qiao Yu opened WeChat with a smile, and then clicked on Senior Brother Chen's chat interface.
"Hey, Senior Brother Chen, you have caused me so much trouble..."
As the project leader and an oppressed junior brother, he can definitely channel the pressure away. . Based on the principle that whoever benefits should bear greater pressure, we can only say that Senior Brother Chen is blessed again.
……
United States, Princeton.
Lot Dugan has always believed that a good paper is like an excellent work of art. Therefore, the better the paper, the more it needs an excellent reviewer.
So after reading Qiao Yu's paper, he directly found five of the world's top reviewers. One of them was also his friend.
Coincidentally, his friend also recommended a top reviewer. Then we gathered six people.
Some of them have no intention of taking over the paper at all.
Like Andrew Wiles.
After he received the call from Lot Dugan, he refused directly. The excuse used was that he was very busy recently...
Lot Dugan did not give up and suggested that the other party carefully read the introduction of this paper before making a decision.
Andrew Wiles gave Lott this face, read the introduction, and then commented: "Are you sure the author is not talking nonsense?"
Then Lott Dugan Before Pierre Delini had even read the paper, he helped the Fields Medalist evaluate the paper.
"Of course, do you know what Pierre said about this paper? He said that this will be the greatest milestone work of this century, bar none. This is also the reason why I chose you as a reviewer... Andrew! < br>
After all, you have made history. There is no doubt that your work is the greatest in the world. One of the great milestones of mathematics, so I want to believe that you must be interested in this world's relay work. "
As a journal editor, he is as skillful as a salesman, just for the sake of success. Finding matching reviewers for Qiao Yu's paper is enough to prove how responsible Lot Dugan is for his work.
It was this sentence that made Andrew Wiles no longer refuse and readily agreed to become a reviewer of this paper.
Then Andrew Wiles began to send emails to Lot Dugan continuously.
The first email was to the effect: This article does have some interesting ideas.
Second letter, this article contains many creative ideas that should not be said to be subversive, which may be correct.
In the third letter, he seemed to be right. I tried hard to find the loopholes but couldn't. Maybe I need to find the faults word for word.
The fourth letter, I have to admit that Pierre Delini seems to be right. This paper can start an era, because I can't seem to find faults. I can’t wait to find out who the author of the paper is! So this paper passes!
Lot Dugan replied to Andrew Wiles' email and sent Qiao Yu's current results.
Then he forwarded the four emails sent to him by Andrew Wiles to Pierre Delini.
After all, these contents actually have nothing to do with privacy, and he also directly asked Andrew Wiles for his opinion in one sentence.
“Thank you very much, Professor Wiles. I will inform Professor Delini of your comments on this paper and Pierre’s evaluation. He will definitely feel that you understand each other again. Soulmate."
Soon, Pierre Delini gave him feedback.
“My opinion is basically the same as Andrew’s, so you can publicize my comment to more people.”
…Generally speaking, the higher the ranking, the longer the review cycle. Especially for mathematics papers, it is nothing new that the review cycle is calculated in years.
Of course, the reviewers did not deliberately delay for so long. The key issue is that generally the articles that can be published in such journals either solve major problems or contribute new ones. The proof process is often cumbersome.
Especially from the perspective of the editorial office, the more important the paper, the more cautious the editor will be when selecting reviewers.
After all, it is difficult to establish academic credibility, but easy to destroy it. A few times is enough.
It’s like some journals have become recognized as water journals in the industry as long as they give people the impression that they can publish them by paying page fees. As long as you look at the name of the journal, you can know what is going on.
However, as Andrew Wiles and Pierre Delini responded almost at the same time that the paper was approved, Lot Dugan felt that Qiao Yu and Chen Zhuoyang’s paper should be published in November. .
After all, these two papers are not very long, only twenty-five pages in total.
The elderly Professor Wiles can pass the review so quickly, and other reviewers should have less problems.
Of course, he didn’t want to push too hard, but in order to ensure that if the other four reviewers could complete the review this month, it would be published in November, he simply called the editor in charge of typesetting directly. A phone number...
"Hi, John, I hope you can do a favor...that is, do two copies of the typesetting work for the next issue. I sent you an email, and the two attached papers will be proofread first.
Yes, put the front page If these two papers can be reviewed and approved before this month passes, then these two papers will be published in the November magazine."
Well, actually, this is not too exaggerated. Qiao Yu has not yet broken Zhang Yuantang's record.
His paper on bounded intervals of prime numbers was accepted in just three weeks. At that time, it set a record for the fastest acceptance of papers in Ann.Math's 130-year history.
If Qiao Yu's paper can be published in November, it will probably rank among the top three in terms of the speed of publication.
Of course, doing this is not free.
Journals have always achieved mutual success with high-quality papers. After Qiao Yu told Lott Dugan about his ambitions, Lott Dugan naturally hoped that all papers on the axiom system of generalized modal number theory could be published in Ann.Math.
After all, there are four top journals in mathematics, not just one top journal. A luxurious and efficient review team is also a reflection of competitiveness for top journals.
Qiao Yu is a very smart man, and Lot Dugan believes that this future star of mathematics can feel his painstaking efforts.
……
At this time, Qiao Yu had no time to think about this, and he did not communicate with Lot Dugan.
Anyway, according to the previous publication time of Ann.Math, even if his paper is really published in November, it will be at least mid-term.
The Chinese Mathematics Annual Conference will be held in early November. It would be impossible to make it in time anyway, so he never considered when the paper would be published.
His whole mind was on quickly writing the paper and submitting it to Director Tian, and settling the matters related to the report first.
After all, having confidence and completing the thesis are two different things. The paper mainly includes three key points.
The first is the modal geometrization of prime spacing. The original prime spacing problem is that among the pairs of prime numbers (p, p′), there are infinitely many pairs of prime numbers that satisfy p′p=d, where d is a fixed value.
After conversion, in the modal space M, whether there are infinite pairs of modal points (r_p, r_p') that satisfy the modal distance d_M (r_p, r_p') = d.
First of all, we need to prove that this transformation is reasonable. This part can be directly borrowed from a small part of the paper he submitted to Ann.Math...
He directly quoted this part and sent it to Ann. Some theorems in the Math paper.
The second part is to prove a key theorem. In the modal space M, there is a modal path Γ, so that the upper bound of the modal distance d_M(r_p, r_q) can be reduced to a single digit. At the same time, density analysis is performed on the points on the modal path and verification results are given.
The third part is the final homomorphic transformation. Through these mapping relationships, the characteristics of the geometric model are re-transformed into the language of number theory...
It sounds simple, but in fact it is still very hard to get started with Qiao Yu and it costs a lot of money. It took ten days to complete the first draft. In the end, Qiao Yu lowered 246 to 6.
That is, Qiao Yu proved that there are infinite pairs of prime numbers with an interval of 6. It is not far away from completing the proof of the twin prime conjecture.
Actually, Qiao Yu felt that he could narrow the scope down a bit, but he didn't think it was necessary. Further narrowing the scope will add more technical details. Even to 4, Qiao Yu feels that it will take more than ten pages, which will obviously make the proof lengthy.
It’s just a conference paper, that’s about it.
Then I spent another five days carefully checking whether there were any problems with the article, almost step by step.
This has become Qiao Yu's obsession. After reviewing the manuscript of Senior Brother Qin from Yujiang University, Qiao Yu felt that he really did not allow operations that would make people laugh out loud because of a little carelessness.
The final paper was twenty-one pages long, and the title was also very simple: "Proof of the Infinity of Prime Number Pairs with an Interval of 6."
After checking it, Qiao Yu sent it to Director Tian and Mr. Yuan via email on October 25th on time. In short, we must not make any mistakes this time.
After the paper was sent out, there was no news. But Qiao Yu didn't care anymore. He had already completed the thesis. As for whether he could present it at the Mathematics Society, that was a matter decided by the tutors.
As for him, he can relax for another two days.
……
October 30th, Huaqing, Qiuzhai, multi-functional conference room.
If someone breaks in here today, they will find that there are many bigwigs gathered in the conference room.
A bunch of academicians gathered together sitting at the conference table.
Yuan Zhengxin, Tian Yanzhen, Pan Yuedong, Li Luhe...
Not only Yanbei and Huaqing University, but also those from the Chinese Academy of Sciences, Nanjin University in the nearby satellite city, and Beijing Normal University...
Really, the dozen or so professors sitting in the conference room can basically represent half of the Chinese mathematics community.
Not only that, there are also three internationally renowned Chinese mathematicians who participated in this conference via remote video, Zhang Yuantang, Zhang Shuwen and Tao Xuanzhi.
Each person will receive a copy of Qiao Yu’s latest paper.
There was no way, the situation this time was indeed very special, so five days ago, after Qiao Yu sent the paper to Tian Yanzhen and Yuan Zhengxin, the two bosses met to discuss it.
During this period, I also made a phone call to Lot Dugan.
Then the two big guys made a list, selected Chinese and Chinese mathematicians who were qualified to review Qiao Yu's paper, and then started making phone calls one by one.
After the paper was sent out, today’s meeting took place.
However, after Tian Yanzhen discussed with Yuan Zhengxin, Qiao Yu was not allowed to attend the meeting today.
Mainly because some things are not easy to explain. For example, Qiao Yu posted two Ann.Math articles without telling his tutor.
As a result, the tutor wanted him to give a report at the annual mathematics meeting, but he couldn't give it, so he rushed out a paper at the last minute.
The whole thing was so shocking that the cause and effect could be written into their memoirs later, but both of them felt that it was not necessary for their colleagues to understand it so clearly for the time being.
Of course, even if Qiao Yu did not come, it would be difficult for many academicians present to evaluate this paper.
After all, many people in the mathematical community have not heard of a series of brand-new concepts such as the modal axiom system in the paper.
But the proof process looks like that. This feeling is very strange.
However, Tao Xuanzhi’s speech solved many people’s doubts.
"I have read this paper carefully in the past five days and found no mistakes. Of course... he cited some new theories that have not been released to the public..."
Speaking of this , Tao Xuanzhi was silent for a moment, because he also felt that this matter was a bit difficult to comment on, and then continued: "Coincidentally, I I was invited by Ann.Math to review two papers about this modal axiom system framework.
As far as I know, the six reviewers of these two papers gave their approval for publication. Opinions. Therefore, there is a high probability that these two papers will be published in the last issue of Ann.Math this year.
So I personally don’t think there’s much problem with the argumentation process of this paper. Including the modal space, path existence theorem, and modal density function mapping theorem that he cited. and related transformation processes. ”
Everyone in the conference room had different expressions.
Tian Yanzhen and Yuan Zhengxin behaved very calmly, and they have been able to accept this accident for so long.
As for the others People are confused , I was surprised...
After a while, Academician Pan from the Academy of Sciences asked: "Well, although it may be a bit presumptuous, Professor Tao, can I ask, do you know the two papers you mentioned? Is there anyone other than you who is the reviewer? ”
Tao Xuanzhi nodded and replied: "Besides me, there are Professor Pierre Delini, Professor Andrew Wiles, Professor Richard Taylor, Professor Andrew Granville and Peter Schu. Professor Ertz.”
Sometimes reviewers are reluctant to let people know that they have reviewed certain manuscripts.
But obviously this case is not included.
In fact, when these reviewers are willing to comment on a paper, it usually means that they really don’t mind letting the outside world know that they are reviewers.
So, the big guys in the conference room were speechless again.
Good guy, there are five Fields Medal winners. Although the other one did not win the Fields Medal, he did win a Fields Silver Medal, which is the only one in history.
This team of reviewers all thought that the other two papers were fine, which made those who originally wanted to question them simply shut their mouths.
After another long while of silence, Yuan Zhengxin coughed twice and said, "Professor Zhang Yuantang, do you think there are any flaws in Qiao Yu's paper?"
This is a very polite statement. question.
After all, one of the earliest important issues regarding the twin prime conjecture was whether the minimum interval between prime numbers is limited.
You must know that in 2008, a group of the world's top number theory experts held a meeting at the National Institute of Mathematical Sciences to discuss this issue.
But the meeting ended in failure.
Zhang Yuantang was the first mathematician to answer this question. Even though his result was that the bounded distance between prime numbers is 70 million...
But his proof directly answered this important question. It can be said that it is progress from scratch on the milestone of number theory. It was later reduced to 246, all based on the tools provided by his paper. It is no exaggeration to say that he is the founder of this issue.
“I went to Yanbei University to give lectures in August this year and met Qiao Yu. He told me that in order to solve a series of prime number problems, he planned to design a new axiom framework.
At the time I thought this was a very amazing idea. But what's even more amazing is that in October he did it, not just actually constructed a new axiomatic framework.
More importantly, when I tried to find the unreasonable part of the proof, I failed... I couldn't believe that this was done by a sixteen-year-old boy.
But one thing I am sure of is that a new number theory track is about to open. In the modal space, we are no longer studying specific numbers, but elements that contain all possible states.
Give every number a geometric meaning... I don't even know how to evaluate this framework, but it is obvious that he is on the road to success.
So if I were to simply evaluate this paper, I think it is right. As I said earlier, I tried very hard to find fault, but failed.
Of course, all this is based on the premise that the definition given by modal space can be logically self-consistent. As for whether the definition of modal space is reasonable, I think Professor Tao Xuanzhi has already given the answer. I'm done. "
After carefully listening to Zhang Yuantang's evaluation, Tian Yanzhen waited for a moment to give everyone enough time to think before officially speaking.
"Ahem, that... It's better for everyone to vote directly, because Qiao Yu is the joint training target of Yanbei and Huaqing, so Mr. Yuan and I abstained.
If you think this paper is suitable for presentation at this year's annual meeting, please raise your hand. ”
There was no long hesitation, and soon everyone in the conference room raised their hands.
Thanks to the Chinese treasure, the little squid with sore balls for the reward and encouragement
(End of this chapter)