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Chapter 180: The legendary story of mathematics

Qiao Yu ignored all those intrigues. From a child's perspective, sincerity is the eternal killer skill.

Qiao Yu did not include Senior Brother Chen in the research group he applied for because he was very sure that his application to the Natural Science Foundation of China would not be approved this time.

Unless the auditing expert is really out of his mind.

If he could get his application for a proof of the Riemann hypothesis approved today, with the current strength of the Chinese scientific research community, tomorrow, the NS equation, NP-complete problems, Hodge conjecture, Yang-Mills theory...

These high-sounding propositions are likely to appear on the desks of the review team of the National Natural Science Foundation of China. Who wouldn’t be annoyed?

Therefore, as long as the teacher responsible for reviewing his project is still rational, he or she will probably throw his application aside after reading it.

The only thing that Qiao Yu did not expect was that submitting a project application to National Natural Science Foundation of China would also trigger heated discussions in the Chinese academic community.

All I can say is that there are still many people in the Chinese academic community who have nothing to do after having their fill every day.

If he had known this would be the case, he should have plunged into the academic field earlier.

If he had come to the fore two years earlier... No, Qiao Yu recalled the past and suddenly realized that he might not have been able to come to the fore even earlier.

Because when he was in the first grade of junior high school, he found the content of Riemannian geometry very obscure and difficult to understand. When he looked back at those contents in the third grade of junior high school, he could understand them easily.

This probably shows that his brain was still in the development stage during his first and second year of junior high school, and his brain at that time was not strong enough to handle such advanced knowledge.

But now it’s different. After all, the more you use your brain, the more flexible it becomes.

……

After giving Brother Chen some encouragement, Qiao Yu felt at ease handing over part of the verification task to Chen Zhuoyang.

The reason why Qiao Yu felt that the proof method he thought of was stupid was that the proof process required patient analysis and trial and error.

For example, the modal path and symmetry verification is to verify the symmetry of the zero point by verifying whether all modal points are concentrated on the modal path Γ.

If it has been found that all points are strictly distributed on the path Γ* and the symmetry conditions are satisfied, the conclusion of the Riemann hypothesis can be directly drawn.

Of course, if there are local deviations in the verification results, it may be found that the modal points cannot be concentrated, but it does not matter, and you can still use methods such as modal convolution and modal density to analyze from a global perspective.

In short, as long as the Riemann hypothesis is correct, there is always one way to verify the result.

After all, if we can solve those nonlinear data problems in the laboratory, there is no reason why such a simple number theory problem cannot be solved.

What he needs to do is to give a precise definition of the mapping between number theory and modal space. For example, if the modal density is used to solve the problem, then the equivalence relationship between the modal density function ρM and the prime number counting function π(x) must be precisely established.

Although it sounds troublesome, Qiao Yu has already completed the first step. The next step is just to see which method is useful in the end and then deduce a few more theorems.

Math problems are like this. If you don’t have a method, you will just feel that they are extremely difficult and you have no idea what to do.

But as long as you can find the right method, it will probably feel so easy. This so easy feeling is exactly what mathematicians all over the world are pursuing.

In the blink of an eye, it was mid-March, and the weather in Beijing began to warm up. I also received a response to my project application from National Natural Science Foundation of China.

As expected, I failed.

This time, it was not discussed at the conference. As for the Riemann hypothesis, everyone knows what it is.

However, this time the review committee also gave Qiao Yu some thoughtful tips, such as when applying for the National Natural Science Foundation of China project, there is no need to come up with such a big proposition at once.

It might be helpful to narrow down the scope of the topic, such as the study of new solutions to the Riemann hypothesis. This might help you pass the exam. It feels somewhat explicit.

But Qiao Yu didn't take this application seriously. In theory, he didn't need these funding projects to prove himself. He was only seventeen years old, so it didn't matter whether he wore a hat or not.

Anyway, the money from the fund application is very troublesome to use. It is better to take more bonuses from the school.

Of course, a new semester means a new atmosphere, and naturally I have to publish a paper. However, this time I did not submit the paper to the Annals of Mathematics at Princeton, but to JAMS.

It is also one of the four top mathematics journals in the world. It is the flagship journal of the American Mathematical Society. The journals accepted also cover pure mathematics and applied mathematics.

The reason why I chose JAMS is that when I joined the American Mathematical Society last year, I promised to write a paper and submit it. Qiao Yu always keeps his word on such simple things.

After all, even breaking one's word should be applied to major events. If one cannot keep one's word even in small matters, then one's character is really poor.

Of course, there is a little-known fact. Although the American Mathematical Society has the word "American" in its name, its essence can be said to be an international mathematics organization.

After all, the members of the American Mathematical Society actually come from all over the world. People from Europe, Asia, and other regions can apply.

Similarly, activities organized by the American Mathematical Society also include IMO, ICM, and other well-known competitions and conferences.

Qiao Yu is now an international member of AMS. He can access the AMS mathematical literature database and buy publications or attend conferences more cheaply.

The former can directly access the database, which is still useful. As for purchasing journals and attending conferences, Qiao Yu feels as if he has never spent any money.

Of course, it is possible that he has spent it, but it was his supervisor who paid for it. But it doesn’t matter, because many mathematics projects get research funds for this purpose.

It's always good to save some for later.

This time when publishing the paper, Qiao Yu learned from the last lesson and greeted Tian Yanzhen in advance.

After reading it roughly, Tian Yanzhen asked, "You sent out this paper before the proof is complete? Aren't you afraid that someone else will prove the Riemann hypothesis first using your method?"

"How is that possible! I am the one who knows this axiomatic system best. I know exactly what difficulties will arise next, but others may not know!" Qiao Yu answered nonchalantly.

So after Tian Yanzhen changed the correspondent's name to Qiao Yu, he said, "Okay, go submit the paper yourself. You don't need to put my name as the corresponding author in your future papers.

Just use your own name. You are already well-known in the mathematics community anyway. It might be more useful than my name, and it will save me from having to be a mouthpiece between you and the editor.

"Okay, Director Tian!" Qiao Yu nodded in agreement. His own mentor was still good.

Another good news is that AMS's centralized manuscript processing system is quite easy to use...

……

For Tian Yanzhen's genius student, the impact of suddenly having to study the Riemann hypothesis gradually faded with the passage of time.

There was no way. The news was so popular at the time that the issue everyone was most concerned about was whether the National Natural Science Foundation expert group would approve Qiao Yu's application.

Unfortunately, the review team could not withstand the pressure and directly killed Qiao Yu's project.

In fact, from the perspective of watching the fun, there is indeed a small group of people who hope to see Qiao Yu's application approved.

As for whether Qiao Yu can really solve the Riemann hypothesis...well, most people are still not optimistic.

After all, the Riemann hypothesis, as an important problem in number theory, is different from other mathematical problems. Top mathematicians from all over the world have almost torn this problem to pieces.

……

On the other side of the ocean, at XXX Charles Street in Providence, Rhode Island, the headquarters of the American Mathematical Society.

John Henry walked into his office with a cup of coffee.

In fact, the organization of JAMS is somewhat different from that of the editorial boards of some journals and some traditional journals.

With the huge influence of AMS, its editorial board is composed of well-known mathematicians from all over the world who have a significant impact in their respective research fields.

The headquarters is responsible for handling all editorial matters.

With this organizational structure and the efficient communication mechanism among reviewers, if we only compare the four major mathematics journals in the world, JAMS actually has the fastest review speed compared to the other three.

On average it only takes about 6-9 months.

Don’t think this time is too long. Ann.Math and Acta Mathematica nearby often take nine months or even more than a year to review papers. And JAMS’s acceptance rate is also the highest compared to the other three.

Probably more than 20%.

Of course, this does not mean that JAMS's review standards are lower.

In fact, it is precisely because the editorial board of JAMS is composed of a group of high-level mathematicians that it is extremely attractive in the academic community and has attracted submissions from many top mathematicians.

Of course, in such a high-level academic circle, there may be subjective tendencies caused by personal connections, but this does not affect the overall academic rigor of JAMS.

After exchanging a few brief greetings with his colleagues in the office, John Henry sat down in front of his computer and skillfully entered his login information. Soon the JAMS backend submission management system was loaded.

This is the starting point of his daily work and the core link of JAMS editorial process.

Unlike others who like to relax during breakfast, John Henry prefers to take a quick look at the backstage in the early morning to see if there are any new submitted papers that catch his attention.

Especially those manuscripts that involve areas he is familiar with or seem to have potential academic value always cheer him up.

Finding the most suitable reviewer for a high-quality paper was an interesting task for John Henry.

Well, he likes those mathematicians he often collaborates with to complain to him: "Damn it! Why do you ask me to review this kind of paper?"

I also like the mathematician who complained to him: "Damn it! Why didn't you ask me to review this paper?"

In short, John Henry is an editor who loves life and mathematics.

It seemed that there was no paper that could catch his eye until suddenly a paper was refreshed in the submission system.

John Henry was attracted when he first saw the title of the paper!
"The Geometrization of the Riemann Hypothesis under the Generalized Modal Axiom System".

I have to say that when Riemann Hypothesis is combined with the Generalized Modal Axiom System, it is really eye-catching.

One is a well-known unsolved problem in mathematics, and the other is the most cutting-edge and hottest research direction in mathematics.

The combination of the two makes this paper have the potential to become a hit. Of course, the premise is that the paper is really meaningful.

The number of citations for Qiao Yu's paper in the Princeton Annals of Mathematics officially exceeded 1,000 the day before yesterday.

In four months, the number of citations exceeded a thousand. At the level of pure mathematical articles, the popularity represented by this number is probably not much different from the popularity of a certain popular celebrity officially announcing his relationship, which caused Weibo to shut down.

They are all phenomenal in popularity.

This time GMAS can be combined with the Riemann hypothesis, and John Henry couldn't even imagine how popular it would be.

Especially when he saw the corresponding author at the end of the paper: "Qiao Yu*", John Henry's eyes lit up.

The founder of GMAS popped up, and I submitted a paper to JAMS for the first time, and I was bumped into by him.

So John Henry clicked the "Claim Paper" button immediately.

According to the internal allocation rules, when the paper is initially reviewed, if the editor is on duty and finds that the paper is related to the subject area for which he is responsible, he can "grab" the paper first.

After grabbing it, I left a note: "This document involves number theory and generalized modal systems, which happens to be in line with my relevant expertise. I will be responsible for the initial review and editing."

For a senior editor within a journal, it is also a very meaningful thing to grab a paper that can become a hit and follow the entire process of review, editing and final publication.

For example, he can not only learn the content of the paper and the comments of industry leaders on the paper at the first time, but also communicate directly with the corresponding author, Qiao Yu himself, regarding the paper through email.

Isn't this a rare opportunity for in-depth academic exchange? It would be even better if we could establish personal friendships.

After all, it is difficult to find suitable reviewers for so many manuscripts on generalized axiomatic systems. Qiao Yu is undoubtedly one of the most suitable reviewers.

But the entire journal community knows that if you send this kind of review request to Qiao Yu, it will basically be rejected. Or it’s a template rejection.

"Thank you for your kindness, but I am still young and still learning. I am not suitable for the role of reviewer for the time being, and it is difficult for me to give a fair and effective evaluation."

In addition, publishing such a paper is equivalent to being personally responsible for the publication process of a top-level paper, which is also a highlight in one's career.

If he leaves JAMS and changes to a journal, he can use this as an excuse.

Finally, after all his operations, a prompt box popped up on the computer: “This paper is now assigned to John Henry.”

John Henry felt satisfied.

But before he could download the paper and read it carefully, the phone next to him rang.

As soon as I answered the phone, I heard a strong voice coming from the other end.

"John, did you steal Qiao Yu's paper?"

John Henry could certainly recognize the voice as that of his mentor at MIT, Larry Guth.

As a former student of Professor Guth, he knew better that Larry Guth had been studying the Riemann hypothesis with Professor James Maynard of his alma mater over the years.

In the past two years, the two professors have made some breakthroughs in their research on the Riemann hypothesis. More specifically, they have used more precise methods to improve their understanding of zero-point distribution and large value behavior.

This is a theoretically crucial result because, from the perspective of number theory, it provides a more powerful basic tool for further studying the core properties of the Riemann zeta function, verifying the Riemann hypothesis, and studying broader number theory problems.

John Henry even went back to listen to the lecture. The two big guys did cite new methods, including more accurate Taylor expansion technology, estimation of higher-order derivatives, and improved analytical continuation technology...

But it is obviously still a long way from completely solving the Riemann hypothesis. But then again, their work has also been extended to other Dirichlet series.

At the same time, it seemed that his mentor was also a member of the editorial committee, so John Henry was not surprised at all to receive the call.

"Yes, Professor Gus, I just saw this paper and claimed it immediately. You know, I am definitely not the only one watching the background at this time."

John Henry said excitedly.

"Yes, I was just about to claim this article, but it disappeared when I refreshed it. You have very fast hands! But you'd better be quick in the initial review. James and I can be the reviewers of this paper."

Well, John Henry was quite proud of having snatched the right to review the paper from his supervisor. He even felt that he was definitely more qualified than his supervisor to review Qiao Yu's paper.

Although his mentor and Professor James Maynard have been conducting research on the Riemann hypothesis in recent years, their research on the generalized modal axiom system may not be as in-depth as his.

For this kind of interdisciplinary article that combines the two, the initial review requires someone like him who has some knowledge of both sides.

"Don't worry, Professor Gus. In fact, the first two reviewers I thought of after I snatched the article were you and Professor James. I will do it as soon as possible."

Sure enough, hard-working birds are always rewarded.

After hanging up the phone with his supervisor, John Henry downloaded the paper directly. He had no choice, his supervisor asked him to be faster, so he had to give him some face.

Soon John Henry was immersed in the wonderful world of thesis. Qiao Yu's thesis reminded him of a legendary story in the mathematical world about the Riemann hypothesis.

The story is probably about an accidental exchange between Hugh Montgomery and the famous physicist Dyson, and the discovery that the same universal laws that govern random matrices and atomic spectra also apply to the zeta function.

This point is also supported by a lot of numerical work since the 20s.

The two people came up with the same formula in different ways. Physicist Dyson came up with this company by studying the energy levels in matrix mathematics, while Hugh Montgomery studied the prime number image of the correlation function...

Of course, this doesn’t mean anything. At most, it can only show that some rules are indeed universal, and extend the related conjecture - Gaussian unitary set conjecture:

The distribution of nontrivial zeros of the Riemann zeta function has the same statistical properties as the eigenvalue distribution of Gaussian unitary matrices in random matrix theory.

Qiao Yu started with two formulas with similar structures and gradually verified a certain isomorphism between the distribution of modal points and the distribution of zero points of the Riemann zeta function.

This constructive geometric method, although different from the statistical law research of Montgomery and Dyson, essentially reveals some universal laws.

I have to say, this is really interesting!
(End of this chapter)