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Chapter 189 I’m so worried!

“Princeton University and Annals of Mathematics would like to announce that Dr. Qiao Yu’s paper “Proof of the Riemann Hypothesis Based on the Generalized Modal Axiom System” has completed rigorous peer review and has been accepted for publication.

After two months of in-depth review, a review team consisting of 12 top international mathematicians and feedback from related academic networks confirmed that the proof proposed in the paper is completely correct and self-consistent.

This paper provides a solution to the Riemann hypothesis, a core problem in mathematics that has persisted for nearly two centuries, marking a milestone achievement in the history of mathematics.

Dr. Qiao Yu's paper proposed a new mathematical framework that transcends the boundaries of traditional number theory and logic. It constructed a formal semantics using the generalized modal axiom system and logically proved the symmetry and distribution law of the non-trivial zeros of the Riemann zeta function.

The following are the main contributions of the paper..."

That evening, the announcement was finally updated on Princeton University’s official website.

The title of the announcement is also very grand - "Official Statement on Dr. Qiao Yu's Paper Solving the Riemann Hypothesis."

This statement not only announced the official release and publication time of the paper, proposed a special issue plan, but also included evaluations from three reviewers.

Tao Xuanzhi: "Dr. Qiao Yu's work pioneered the introduction of modal logic into number theory. This is not only a proof of the Riemann hypothesis, but also a methodological revolution."

Peter Schultz: "This paper demonstrates a perfect combination of geometry, number theory and logic, opening up a brand new path for mathematical research."

Akushel Bates: "The proof of the Riemann hypothesis not only solves a century-old problem, but also adds an extremely important weapon to the number theory toolbox - generalized modal logic."

These are undoubtedly high praises, and this paper certainly deserves them.

In fact, no matter who solves the Riemann hypothesis, they will probably get similar evaluations - just brag about it.

As Princeton University commented in a statement on its official website, this is a difficult problem that has plagued the world's top mathematicians for nearly two centuries.

What's more, this conjecture is so important.

The zeta function formula is still essentially a sum of an infinite series, so there is a convergence problem. For any complex number with a real part greater than 1, the sum is convergent.

Then, mathematical techniques are used to extend the domain of the zeta function to the non-convergent region.

The zeta function has infinitely many nontrivial zeros, and no graph can represent all of them.

More than a hundred years ago, mathematician Riemann believed that the real parts of these non-trivial zeros are all on the straight line 1/2 of the complex plane.

In fact, up to now, mathematicians have verified through calculations more than 1 billion non-trivial zeros, and the real parts of these non-trivial zeros are indeed on the 2/ line, without exception.

But unfortunately, finite verification is not equal to proof at the mathematical level. After all, in view of the requirements of mathematical rigor, facing the concept of infinity, whether it is verified by 10 billion, 20 billion or more, it cannot replace the proof process of mathematical logic.

After all, theoretical mathematics is a subject in which just one counterexample can completely overturn the existing number theory framework.

Today this problem was finally proven!
Of course, proving the Riemann hypothesis is not just about verifying the correctness of the conclusion. The most important thing is to reveal why the hypothesis is correct. As the three reviewers commented, the most important significance of Qiao Yu's paper lies in the method it provides!

The applicability of the generalized modal axiom system has been verified once again. Even though these mathematicians do not yet know the application of this axiom system in computational mathematics, what can be confirmed now is that this will be a toolbox that cannot be avoided in future number theory research!
With this toolbox, a new path has been opened for everyone, and many number theory problems may be easily solved!

So, on that Chinese evening, when Princeton posted this statement on its official website, the world mathematics community exploded!

This time it really exploded!

Even those mathematicians who were not interested in the Riemann hypothesis before have read Qiao Yu's paper and are paying close attention to the opinions given by the reviewers.

After all, this reviewer lineup is already strong enough. If these people are sure that there is no problem with Qiao Yu's argumentation process, then there must be no problem.

Not to mention that this was an open community verification, and the results were officially announced by Princeton University.

Qiao Yu is still in his teens, not even an adult yet, so he still has more than 20 years of golden years in mathematical research. To be honest, this is scary...

Really, more than 20 years is a long time, God knows how much Qiao Yu can grow.

For a time, after Princeton issued an official statement, the phones of mathematicians around the world began to become busy.

Although 2026 is only halfway through, there is no doubt that this is already the hottest topic in the mathematics world this year.

……

"Pierre, do you really think that the child's certificate is flawless? So you gave it a pass?"

“No, Lucas, there was actually a tiny loophole that almost everyone analyzed word for word and found, but it only took him a week to fix that tiny loophole.

You will know when the official version of the paper is published. In addition, he proposed three continuation conjectures. Believe me, they are all very valuable conjectures. If they can all be solved, we will have a new understanding of the distribution of prime numbers. "

The other party was silent for a moment, and then continued: "Okay. It seems that we need one more candidate for the Fields Medal this year."

"Haha, this is inevitable! Anyone who solves the Riemann hypothesis will receive a Fields Medal. Even if he is over 40 years old, he will receive a silver medal, right? What's more, Qiao Yu is only 17 years old! Damn it, he is a genius that only appears once in a thousand years!"

"Yes, you are right! He is only seventeen! Oh, every time I think of his age, I feel very emotional. Pierre, we are all old. We don't have much time left."

"Okay, Lucas, stop sighing! Do you know why I'm in a good mood today? At least before we die, someone has proved the Riemann hypothesis! Don't you think this is our luck?
I just finished a phone call with Professor Yuan, and he told me an old Chinese saying, "If you hear the truth in the morning, you can die in the evening." It means that if you can understand the truth in the morning, then even if you die in the evening, you will be satisfied. That's what he thinks now!

So anyway, we are much luckier than Sir Atiyah, who held his last report three months before his death, but unfortunately his report was not recognized. "

Lucas Eisen sighed in his heart when he heard this.

From this point of view, Pierre is indeed much luckier than Atiyah. The British knight is still working hard to prove the Riemann hypothesis at the age of 89.

But it is a pity that the proof process he gave is difficult for many of his peers to evaluate. Indeed, many people, including his colleagues, refused to make public comments on this achievement.

There were even private comments that the old knight might have been really confused in the last part of his life, and was deceived by researchers who wanted to get resources from him, so that he talked nonsense in the last stage of his life.

This is really regrettable.

Lucas Eisen also knew why Pierre specifically mentioned Michael Atiyah.

After all, Pierre Delini was Alexander Grothendieck's most famous student, and Atiyah's early research was also greatly influenced by Grothendieck.

For example, Atiyah’s earliest achievement was the collaboration with others to create topological K theory.

From this point of view, Pierre is obviously much luckier than Atiyah. At least he witnessed the solution of the Riemann hypothesis with his own eyes, and he was even one of the reviewers of this paper.

Of course, this also means that Qiao Yu is certain to win the Fields Medal this year. Lucas originally thought that Qiao Yu should be allowed to run as a runner-up this year and win the award at the next World Congress of Mathematicians.

But now it seems impossible! After all, no one wants to offend those twelve reviewers, not even him.

After a few more brief conversations, Lucas Eisen hung up the phone. He sat in his office and thought for a few minutes, then suddenly thought of his grandson-in-law Frank.

Really, he originally thought that Frank was also a very talented guy.

When Frank was still dating his granddaughter, the paper he published, "From Modular Forms to Modular Spaces: Hecke Algebraic Actions on Algebraic Curves," also made him feel bright.

He then published "Properties and Applications of Hecke Algebra on Algebraic Curves".

After the two young people got married, Lucas Eisen really trained Frank as his successor. He hoped that Frank could take over his position and become the academic leader in the intersection of algebraic geometry and number theory at Berkeley in the future. So he introduced Frank to the research group of the geometric Langlands conjecture. At that time, Frank's performance was actually not bad. In 21 years, he also published "Analysis of Low-Dimensional Curves in the Geometric Langlands Framework".

This paper proposed a geometric Langlands correspondence method on low-dimensional curves, which simplified the processing of traditional high-dimensional moduli space. He also established himself at Berkeley and taught "Introduction to Algebraic Geometry".

But what made him unhappy was that since Qiao Yu pointed out problems in his paper, this guy's mathematical talent seemed to have suddenly disappeared.

It would have been fine if there had not been any significant results after such a long time, but he suggested that Frank contact Qiao Yu to conduct research on related topics together, but it ended up being a mess.

This reminded Lucas of the algebraic geometry conference, when he specifically called Frank over and told him in person that he should get along well with mathematical newcomers like Qiao Yu. It was really a waste of his efforts.

I have been in a daze day after day and still haven't found my research direction, which is really disappointing.

Well, Frank can’t be blamed for this, after all, there are so many people who want to work with Qiao Yu. And it’s actually quite difficult to find a new research direction in more than a year.

But what can I say? What people fear most is comparison.

After proving the geometric Langlands conjecture, Qiao Yu did a lot of things and proposed a generalized modal axiom system, reducing the interval between prime pairs to 6. Now he has directly proved the Riemann hypothesis.

Frank has achieved nothing so far, and can even be said to have no direction, which is a very obvious contrast. If you add that both of them are Chinese, the contrast is even more obvious.

There is no doubt that Frank has not shown any temperament or ability to become an academic leader during this period.

This also made Lucas feel very dissatisfied. After all, he had invested a lot of energy and resources in this guy.

After sulking for a while, Lucas Eisen did not calm down. Instead, he became angrier and angrier. He simply took out his cell phone and called Frank.

"Hey, Frank, you should have seen the statement just released by Princeton University, right?"

"Yes, Lucas, I saw it. It's incredible that he really solved the Riemann hypothesis. In fact, I have been studying his paper these days and have some insights."

Lucas Eisen felt that the other party's tone was very depressed, which made him even angrier. You have some experience reading papers now? What were you doing before? !

"I just spoke to Pierre on the phone. You know what? After two months of discussion, all twelve reviewers and the team behind them feel that there is no problem with Qiao Yu's final proof! You should understand what this means!"

Frank, who was on the other end of the phone, felt that everyone in the world could understand what this meant, especially since the World Congress of Mathematicians was to be held next month.

"Of course, Lucas, I understand. The Fields Medal judging committee cannot ignore the Riemann hypothesis. Oh, no, it should be the Riemann theorem now. So Qiao Yu will be able to win the Fields Medal this year, right?"

"Yes, it seems that you are still sober, so now you understand why I want you to try your best to cooperate with Joe? But look at what you did?
You wasted a golden opportunity. I told you to take advantage of the fact that both you and Joe are Chinese and get along well with him. I don't understand where your inexplicable sense of superiority comes from.

Is it because he is young that you feel embarrassed? If that is the reason, then you are so stupid! Really, I always thought you were a smart person who knew what was important and what was not! "

Lucas Eisen's lecture left Frank speechless.

He really wanted to say to Lucas Eisen, "Because I'm Qiao Yu's father! And he doesn't even know about this!" But in the end he didn't say it out loud.

Frank wasn't worried about Lucas finding out about his romantic affairs when he was young. In fact, at his current position, it wouldn't be a big problem if such things were exposed.

The main reason was that the way the matter was handled was not appropriate, and it was like abandoning his wife and children. Lucas was the kind of person who claimed to be very family-oriented.

Most importantly, from the perspective of Chinese culture, his behavior at that time was not right. If he rashly recognized Qiao Yu, he was afraid that he would become an enemy of Qiao Yu.

In fact, ever since Qiao Yu announced on arXiv that he had proved the Riemann hypothesis, he has been suffering every day recently.

And the mentality is particularly complicated.

On the one hand, he hoped that Qiao Yu was right. No matter what, he had already confirmed that Qiao Yu was his biological son.

On the other hand, he didn't want Qiao Yu to be so powerful. Frank was really afraid that Qiao Yu would know what happened that year and might take revenge on him.

After all, Qiao Yu has been living with his mother for all these years. Frank doesn't know what Qiao Xi said to Qiao Yu about him, but he thinks Qiao Xi wouldn't say anything good about him.

Blocked by a mathematical genius who solved the Riemann hypothesis at the age of seventeen, Frank felt that he would probably have no future in mathematics. After all, he really knew how much power the academic cliques had in this era.

Qiao Yu also happens to have all the elements needed to become a great scholar. Damn it, is this going to make people live?

At this time, I have to face Lucas's merciless questioning...

Frank regretted it! Very much!
If he had not chosen to go abroad, even if he had returned to China after graduating from MIT, found Qiao Xi, admitted his mistake, and assumed the responsibility of raising Qiao Yu himself...

Just thinking about how bright the future would be if he had made that choice, Frank wanted to slap himself twice!

God originally gave him a shortcut to heaven, but he chose the road behind the shortcut.

It's a pity that there is no "if" in life, so he is speechless when facing Lucas' questioning.

Of course, even if he had something to say, he wouldn't say it. Frank knew Lucas Eisen's character, he was a stubborn old man.

If he started to defend himself, it would only make the old man even angrier, and he would say even more nasty things. Unfortunately, he had no choice now and had to rely on Lucas to pave the way for him. So he could only endure this kind of scolding.

"I'm sorry, Lucas, to disappoint you. But you know, there are so many people who want to work with Qiao Yu. It's not that I didn't try, but he rejected me."

"Hmph... you better fend for yourself! How can I help you if you can't even use your own advantages?"

After saying that, Lucas Eisen hung up the phone angrily.

On the other side, Frank listened to the busy tone on the phone, his face uncertain.

There are many things to consider, such as what attitude should he take towards Qiao Yu at the upcoming World Congress of Mathematicians?
Especially since he had heard that Qiao Xi was now accepted as a disciple by Yuan Zhengxin. He didn't know if Qiao Xi would go to the World Congress of Mathematicians. If she did, what if she met him and recognized him...

But it was impossible for him not to attend this meeting. After all, although he was not qualified to give a full-time report at this conference, it had been confirmed that he would give a 30-minute report in the branch venue, and he could not give up this opportunity.

After all, even if he doesn't win the Fields Medal, he still has the Abel Prize and the Wolf Prize to look forward to in the future. He can't not show his face at such a top conference held every four years, right?

Worry!

……

In China, Lu Yanxiang from the Institute of Mathematics and Systems Science of the Chinese Academy of Sciences is also worried.

Of course, he wasn't as worried as Frank, but seeing Princeton's announcement still made him feel distressed...

It’s really recognized!

It can only be said that Zhang Yuanling has company. But Lu Yanxiang really wanted to find someone to talk to. Qiao Yu directly applied for a project to solve such a big problem as the Riemann hypothesis. Is there a problem with him rejecting it? !
Is there a problem with this?!

Before the Riemann hypothesis was solved, who would have dared to believe that a teenager could really solve this problem and leave an extremely luxurious review team speechless?
The most infuriating thing was that when he called Zhang Yuanling to complain, this guy actually said, "Hey... Academician Lu, our situations are completely different. They can't be confused.

After all, it was Qiao Yu who withdrew the project himself. I just raised a few questions and didn’t mean to deny it. But your situation is different. You directly rejected his project!"

Listen, is this Zhang guy talking like a human being?! Is there anyone in this world who can speak rationally?!
(End of this chapter)