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Chapter 186 Do you need to reflect on yourself?

Liu Zhaoyuan from the Institute of Computing Technology learned the news about an hour later than Lu Yanxiang.

It's not that Liu Zhaoyuan is not well-informed. It's mainly because the work at the Institute of Computing Technology has been very busy recently.

In fact, the work at the Institute of Computing Technology has always been busier than that at the Academy of Sciences. There is no way around it. All the work here is more practical computing-related.

If you encounter an impatient party A, he will call you several times a week to urge you to do something.

This was also the reason why Professor Liu from the Institute of Computing Technology had an unpleasant experience with Ma Botao from the Institute of Materials.

There is no way. Those engaged in scientific research all think that their own projects are the most important, and other people’s projects are wasting the country’s limited research funds.

Well, no matter what you think in your heart, you must say this to others. Over time, you will believe it.

The specific manifestation is that when I have nothing to do, I will find out that the Institute of Computing Technology is helping others with things, and if it doesn't help me with things, I will think that they are not doing their job properly.

Obviously, this would indeed make many mathematicians who do auxiliary calculations feel annoyed. When receiving a call from someone like Ma Botao who is engaged in material research, naturally, they would not have a very good attitude.

Moreover, those who engage in computational mathematics are not that concerned about mathematical theory.

After all, computational mathematics is more concerned with the application of mathematics in practical problems and the implementation of algorithms. After all, they face real problems every day.

As for theoretical completeness or abstract logical beauty, those are things that only those who engage in theory like to pay attention to.

So no one called Liu Zhaoyuan specifically to tell him about this.

But now, all the elite soldiers and generals have become Qiao Yu's "fans".

Every profession has its own specialization, and there is a difference in the order in which one learns something. It is a tradition for front-line technical people to admire talented people.

He only heard about this incident after dinner when he called the technical backbone who was still working overtime to the office to inquire about the progress of the moon landing plan calculations.

"Qiao Yu claims to have solved the Riemann hypothesis?"

"Yeah, you don't know yet? It's almost spread all over the Internet!"

Okay, this statement is actually a bit exaggerated.

It can only be said that it has spread in a small range. After all, it has only been two or three hours since the paper was published on arXiv.

But it's not too exaggerated. After all, even they already know the news.

Many mathematics leaders posted this news on their social media accounts. For example, Tao Xuanzhi posted relevant content on his blog and announced that he had agreed to become a member of the joint review panel for the paper.

Although in most cases, well-known journals use double-blind or single-blind review methods, this is obviously not applicable to papers that prove the Riemann hypothesis.

In addition, Qiao Yu has already published the paper on arXiv, so this time we will directly use a method that combines public review with international discussion, or verification by the mathematical community.

Just like what Lott Dugan is doing, he directly invited twelve top experts in the field to conduct an open joint review.

Under this model, there is no anonymity between authors and jury members, because as Lott Dugan and Qiao Yu said, frequent and direct academic communication is needed between the two parties.

Qiao Yu kept communication open at all times, answering any questions from the jury members regarding the details of the paper's proof, ensuring that every detail was explained clearly.

This review mode naturally does not require reviewers to keep their identities secret. The advantage of this is that it can not only greatly shorten the time of paper review, but also ensure that there are no problems in the judgment of paper details.

Whether it is Perelman's proof of the Poincare conjecture or Wiles' proof of Fermat's Last Theorem, they actually use similar verification models.

The former's proof was verified by multiple international research teams over a three-year period, while Wiles' proof also went through a long period of community review and revision.

Of course, there is a reason why it took a long time to verify these two papers.

The proof process of the former can be said to be full of twists and turns. Many people, including Mr. Yuan, believe that Perelman's early work was not detailed and too simple to be accepted.

Many key steps were briefly mentioned or skipped, and the details were not fully developed. These international research teams did a lot to supplement Perelman's work.

As for Wiles' proof, he used an obvious one, but apparently the one he used was not so obvious.

And that apparently was a crucial step, requiring a completely new technique to derive the structure of what came to be known as the Euler system.

The review team discovered a logical loophole in this step, so Wiles spent a year and a half dealing with this "obvious" problem, but fortunately he succeeded in the end.

Obviously, in a sense, this review mode is much more rigorous than double-blind or single-blind review. Countless eyes around the world are watching the paper and the reviewers, ensuring that no logical loopholes in the paper will be missed.

In addition, researchers can access this information more easily than ordinary people. So it is not surprising that people in the Institute of Computing Technology who follow Qiao Yu can learn about this news.

Of course, after Liu Zhaoyuan heard these, he really didn't know how to comment.

Although he was not a theorist, he was naturally aware of the importance of the Riemann hypothesis.

So he couldn't help but ask, I promised to contribute to computational mathematics and build a cross-century computing platform to solve problems for everyone. Now that I have received the money, what is the point of proving the Riemann hypothesis?
What is this? !
Damn, can't I just use the money from the National Natural Science Foundation to complete this certification just because my application for the project was not approved?

Well, Liu Zhaoyuan sent away the guy who was called to report on his work, and then logged into arXiv on his computer.

There is no way around it. Computational mathematics is also mathematics. Anyone who studies mathematics will probably be interested in this paper. They want to see if this paper is serious or not.

After all, this is not the first time someone has claimed to have proved the Riemann hypothesis. Previously, a knight claimed to have proved this century-old problem, but it turned out to be a huge joke to the whole world.

I downloaded and studied the papers, and before I knew it, it was evening.

After finally reading the paper, Liu Zhaoyuan felt his mind was empty... To be honest, he didn't quite understand it.

If Qiao Yu knew Liu Zhaoyuan's method of reading papers, he would probably sneer at it and then teach him some tips.

When reading a paper, you can't just read the paper. You will definitely not understand it.

Instead, when you find that you don’t understand the first lemma, you should proactively turn to the last page to find the references. Then read all the references first, and after you understand them all, you can work on this paper.

If you can't even understand the literature cited in this paper, then go and read the literature cited in the cited literature first...

As long as you keep doing this, you will be able to understand no matter how obscure the paper is in the end!

In fact, Qiao Yu has always done this when reading papers. If he doesn't understand something, he will go to the superior literature until he understands the original paper. This often means that he has directly understood the entire research direction.

Just like when Qiao Yu was studying the Langlands conjecture and P-geometry, he read almost all of Langlands and Peter Schultz's early papers and works...

Unfortunately, Liu Zhaoyuan obviously did not have the patience or time. Although Qiao Yu's paper did not cite many references, it did include some works.

And they were all pure number theory. If he had really been interested in this area, he would not have chosen to do computing.

But to be honest, Liu Zhaoyuan was not optimistic about Qiao Yu's paper because even including the page of thanks and literature citations, it only had 38 pages.

It is not surprising that a mathematics paper has 38 pages, but Liu Zhaoyuan thinks it is unrealistic that a paper solving the Riemann hypothesis has only 38 pages.

Even if the paper is truly valuable, it probably doesn't contain enough details.

His doctoral dissertation was over 70 pages long, twice as long as this paper!
After reading the paper, Liu Zhaoyuan rubbed his eyes and checked the time. Before he knew it, it was already ten o'clock in the evening.

In other words, even though he didn't understand much of it, he spent three hours on the paper.

Then he sat at his desk and thought for a moment, considering whether to call Yu Yanjiang. You, the boss, took the lead in the task of building a computing platform, but others are doing theoretical research. You should at least say a few words, right?
It's not that Qiao Yu can't study these things, but things always have priorities. It's okay to build the computing platform first and then do these fancy research.

Anyway, it doesn’t matter whether the Riemann hypothesis is proved earlier or later. So many top mathematicians in the world have been working on this problem for years, but there is still no result, right?

I picked up the phone and was about to make a call to complain, but then I noticed a lot of WeChat messages flashing in the notification bar.

I opened a WeChat group and took a look, and sure enough, everyone was discussing Qiao Yu's paper.

However, what was being discussed did catch Liu Zhaoyuan's attention.

"It has been confirmed that the article has been submitted to the Annals of Mathematics. You can go and take a look. Princeton has officially announced the reviewers of Qiao Yu's paper. They are twelve gods!"

"See, I told you I was not kidding this time. The review team is announced at this time, and many reviewers must have already read the paper. If they really think the paper is not completed well, they will definitely not accept the review."

"No way? Could it be that this paper really solves the Riemann hypothesis? Doesn't that mean Qiao Yu is qualified to win the Fields Medal this year?"

"It depends on how long the review takes and the final review result, right? A cursory review does not represent the final result."

“It took three years just to review Perelman’s paper!”

"But Perelman uploaded three papers to arXiv alone, and they were more than 38 pages long. Qiao Yu's paper is only pages long. It shouldn't take that long to review, right?"

……

Seeing a group of people who didn't even study the Riemann hypothesis arguing so fiercely, Liu Zhaoyuan couldn't help but roll his eyes.

However, the reviewer lineup published on Princeton's official website still attracted him, and he subconsciously opened Princeton's official website.

After all, this situation is very rare. After all, whether the reviewers of a paper are made public requires the consent of the reviewers.

This can only be done if the reviewers are willing to be transparent to the public. Of course, this is only possible if the paper involves major mathematical events. Otherwise, it is impossible to do this.

Even among the seven problems of the millennium, Liu Zhaoyuan feels that perhaps only the Riemann hypothesis, the NP problem and the mass gap hypothesis can receive such treatment.

Although Perelman's review process was not officially announced, the identities of all verification teams were also made public.

So it can only be said that this is a rare special case.

Soon, Liu Zhaoyuan saw the content of the official announcement.

"Princeton University and the Annals of Mathematics are pleased to announce that Dr. Qiao Yu's paper on the Riemann hypothesis has passed preliminary screening and is currently undergoing rigorous peer review.

This paper aims to solve the Riemann hypothesis, which is considered to be the core problem of number theory and the entire mathematical community. Due to the historical importance of the problem and the potential impact of the paper, the review process will strictly follow the most rigorous academic standards.

We are pleased to announce that the following 12 mathematicians from the world’s top academic institutions are conducting an in-depth review and verification of the paper. These reviewers have outstanding achievements in related fields such as analytic number theory, complex analysis, algebraic geometry, spectral theory, and modular forms…”

Following this are the twelve names and their brief introductions.

Among them, there are eight Fields Medal winners, eleven Wolf Prize winners, seven Abel Prize winners, five Clay Prize winners, all Steele Prize winners, and ICM invited speakers...

This list also means that although the review team consists of only twelve people, there are definitely more than twelve reviewers.

After all, each of these names represents a top mathematical research team. Rather than saying that these listed names are reviewers, it is better to say that most of them are symbolic persons in charge.

Behind these top mathematicians are many PhDs, postdocs, and collaborators. When reviewing this manuscript, some people will definitely be selected from the team to work together.

That is to say, the review team consists of twelve mathematicians, but the actual reviewers may exceed fifty or even more.

Don’t ask Liu Zhaoyuan how he knew this. After all, if he really encountered an important paper to review, he would definitely arrange it this way.

Liu Zhaoyuan probably also understood why the Annals of Princeton Mathematics did this. The official announcement of the reviewer list means that the entire related academic network may become reviewers.

After all, Qiao Yu's paper has been posted on arXiv, which means that every colleague who has studied the Riemann hypothesis can become an invisible reviewer.

If these uninvited mathematicians find any problems in the paper, they will definitely send their ideas to the reviewers they know via email.

There is no shortage of skeptics in academia. Any paper claiming to have solved a world problem will attract these people, who will then use their most critical eyes to look for possible logical loopholes in it.

Of course, there is a disclaimer at the end:
“Princeton University and Annals of Mathematics would like to reiterate that the review and verification process of the paper has not yet been completed, and the participation of the review team does not constitute an approval or endorsement of the correctness of the paper.

Any further updates will be officially released through the Princeton University website and the Annals of Mathematics website.

Well, after reading this passage, Liu Zhaoyuan felt that Princeton might have done this to promote the "Annals of Mathematics".

It seems that the four major mathematics journals are no longer enough for the editorial department of Annals of Mathematics. Perhaps they hope that the four major mathematics journals will be changed to one super four...

But no matter what, the release of this statement at this time is enough to show that at least a dozen top experts, after reading Qiao Yu's paper roughly, do not think there are obvious loopholes in Qiao Yu's paper.

In other words, is it possible for a 38-page paper to prove the Riemann hypothesis?
Being able to solve such a difficult mathematical problem at the age of seventeen, is he the reincarnation of Gauss?

It is said that when Gauss was ten years old, he discovered the common formula for the sum of the first N terms of an arbitrary arithmetic sequence, proposed the prototype of the prime number theorem at the age of sixteen, proved the quadratic reciprocity law at the age of eighteen, and solved the problem of constructing a polygon with a normal period at the age of nineteen...

Qiao Yu is not far behind. At the age of 6, he found the error in the geometric Langlands conjecture and proved it, proposed the generalized modal axiom system, and reduced the interval between prime pairs to . At the age of , he developed an efficient calculation system and proved the Riemann hypothesis...

Once again, it proves to the world that mathematics is a subject that requires talent and has no logic at all.

Diligence and hard work may help you learn most of the knowledge in this world, except mathematics...

Otherwise, there is no way to explain why some people in their teens can solve a problem that a group of legendary mathematicians have been unable to solve in their entire lives.

Liu Zhaoyuan was feeling a lot of emotions in his mind when the phone suddenly rang.

I picked it up and saw that it was from Yu Yanjiang.

He was just about to call this big boss, but he didn't expect the other party couldn't hold it in anymore.

Well, he decided to follow the boss's words and criticize Qiao Yu for not doing his job!

So what if they claimed to have solved the Riemann hypothesis and caused a collective shock in the mathematical community? Now they are the first party!
As soon as the call was connected, the boss on the other end started to question me.

"Liu Zhaoyuan, I want to ask you whether your Institute of Computing Technology is capable of doing this or not?!"

This sentence made Liu Zhaoyuan stunned for a long while.

"No, Chief Engineer Yu? I don't quite understand what you mean. What do you mean by whether our computing institute is OK or not?"

"Don't you understand this? You know that Qiao Yu claimed to have proved the Riemann hypothesis, right?"

"Yes, I just found out that I was..."

"Don't say so much. I just called Tian Yanzhen. I asked him whether Qiao Yu really cared about our project. Guess what he said?"

"Hmm? What else can he say?"

"He said that because your computing department is not good enough, the verification is too slow and the progress of the project has been delayed. Qiao Yu had nothing to do when he was free, so he just verified the previous work. It's not that they don't care about our project, it's that your efficiency is too low!
I think what Tian Yanzhen said makes sense. After all, they have almost finished the computing software, and they are just waiting for your quick testing and feedback. But you are so inefficient that they have no time to think about this world-class problem? Liu Zhaoyuan, should your Institute of Computing Technology reflect on this?"

Liu Zhaoyuan: “???”

(End of this chapter)