Chapter 189 I’m so worried!
"Princeton University and the 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 composed of 12 top international mathematicians and feedback from relevant 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 lasted for nearly two centuries, marking a milestone achievement in the history of mathematics.
Dr. Qiao Yu's thesis proposed a new mathematical framework that spans the boundaries of traditional number theory and logic. It used the generalized modal axiom system to construct a formal semantics and logically proved the symmetry of the non-trivial zero points of the Riemann zeta function. and distribution rules.
The following are the main contributions of the paper..."
That night, the official website of Princeton University finally updated the announcement.
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 publication date of the paper and proposed a plan for a special issue, but also included the comments of 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 Schulz: "This paper shows the perfect combination of geometry, number theory and logic, opening up a new path for mathematical research."
Akushel Betes: "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."
There is no doubt that these are high praises. Of course, this paper also deserves this evaluation.
In fact, no matter who solves the Riemann Hypothesis, he will probably get similar evaluations - it's just a brainless boast.
As Princeton University commented in a statement on its official website, this is a problem that has troubled the world's top mathematicians for nearly two centuries.
What's more, this conjecture is still so important.
The ζ function formula is still essentially an infinite series summation, so there is a convergence problem. For any complex number whose real part is greater than 1, the sum converges.
Then the domain of the ζ function is extended to the non-convergent region through mathematical techniques.
The ζ function has infinite non-trivial zero points, and no graph can express all of these non-trivial zero points.
Riemann, a mathematician more than a hundred years ago, believed that the real parts of these non-trivial zero points are on the straight line 1/2 of the complex plane.
In fact, so far, mathematicians have verified more than 10 billion non-trivial zero points through calculations, and the real parts of these non-trivial zero points are indeed on the 1/2 straight line, without exception.
But unfortunately, limited verification does not equal proof at the mathematical level. After all, in response to the requirements of mathematical rigor, when faced with the concept of infinity, whether it is verified for 10 billion, 20 billion or more, it cannot replace the proof process of mathematical logic.
After all, theoretical mathematics is a subject that can completely overthrow the existing number theory framework with just one counterexample.
Today this problem has finally been proven!
Of course, proving the Riemann Hypothesis is never just about verifying the correctness of this conclusion. The most important thing is to reveal why this conjecture 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 again. Even if these mathematicians do not yet know the application of this axiom system in computational mathematics, what is certain now is that this will be an indispensable toolbox for future number theory research. !
Having this toolbox means opening up a path for everyone, and many number theory problems may be able to be solved!
Therefore, on this evening in China, when Princeton posted this statement on its official website, the world of mathematics exploded!
This time it was really explosive!
Even those mathematicians who were not interested in the Riemann Hypothesis before have mostly read Qiao Yu's paper and are paying attention to the opinions given by these 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 time it was an open community verification, and Princeton University officially announced the results.
Qiao Yu was still in his teens, not even an adult yet. He still had more than twenty years of prime time in mathematical research. To be honest, it's scary...
Really, after more than twenty years, God knows how far Qiao Yu can grow.
Suddenly, after Princeton issued the official announcement, the mobile 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 mathematics this year.
……
"Pierre, do you really think that child's certificate is flawless? So you gave it all a pass?"
"No, Lucas, there is actually a small loophole. Almost everyone found it by analyzing it word for word, but it only took him a week to fix that small loophole.
You will know when the official version of the paper is published. In addition, he also proposed three continuity conjectures. Believe me, these are 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 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 get a Fields Medal. Even if he is over forty years old, he will get a silver medal, right? What's more, Qiao Yu is only seventeen years old ! Damn it, he is a once-in-a-millennium genius!”
"Yes, you are right! He is only seventeen years old! Hey, every time I think about his age, I feel very emotional. Pierre, we are all old. There is not much time left for us."
"Okay, Lucas, stop feeling emotional! Do you know why I am 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 talking to Professor Yuan on the phone, and he told me an old Chinese saying, "If you hear the Tao in the morning, you will die in the evening." It means that if one can realize the truth in the morning, one will be satisfied even if one dies in the evening. That's what he thinks now!
So in any case, we are much luckier than Sir Atiyah. He held the last report meeting in his life three months before his death. Unfortunately, his report was not recognized. ”
Lucas Eisen sighed inwardly when he heard these words.
From this point of view, Pierre is indeed much luckier than Atiyah. This British knight is still working hard to prove the Riemann Hypothesis at the age of 89.
But it is really a pity. The proof process he gave can only be said to be difficult for many colleagues to evaluate. Indeed, many people, including his colleagues, refused to comment publicly on this achievement.
He even commented privately that the old Sir may have been really confused in the last part of his life, and was deceived by the 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 mentioned Michael Atiyah specifically.
After all, Pierre Delini was Alexander Grothendieck's most famous student, and Atiyah's early research was also greatly influenced by Grothendieck.
For example, Atiya's earliest achievement was to co-create topological K theory.
From this point of view, Pierre is obviously much luckier than Atiyah. At least he witnessed the Riemann Hypothesis being solved, and was even one of the reviewers of this paper.
Of course, this also means that it is certain that Qiao Yu will win the Fields Medal this year. Originally, Lucas thought that Qiao Yu should run with him this year and win the prize at the next World Congress of Mathematicians.
But now it seems impossible! After all, no one would want to offend the twelve reviewers, not even him.
After a few more brief conversations, Lucas Eisen hung up the phone. After he sat in his office and thought for a few minutes, he suddenly thought of his grandson-in-law Frank.
Really, he originally thought Frank was also a very talented guy.
When Frank was still in love with his granddaughter, the paper he published "From Modular Form to Modular Space: Hecke Algebraic Action on Algebraic Curves" once made his eyes light up.
Later, he published "Hecke Algebraic Properties and Applications on Algebraic Curves".
After the two young people got married, Lucas Eisen really trained Frank as his successor. He hoped that Frank could succeed him and become an academic leader in the intersection of algebraic geometry and number theory at Berkeley in the future. So he introduced Frank to the research group on the Geometric Langlands Conjecture. At that time, Frank's performance was actually not bad. In 2021, he also published "Low-Dimensional Curve Analysis in the Geometric Langlands Framework".
This paper proposes a geometric Langlands correspondence method on low-dimensional curves, which simplifies the processing of traditional high-dimensional module spaces. He also established a foothold at Berkeley, teaching "Introduction to Algebraic Geometry."
But what dissatisfied him was that since Qiao Yu found fault with his paper, this guy's mathematical spirituality seemed to have suddenly disappeared.
It's just that for such a long time, there has been no tangible results at all. He suggested that Frank contact Qiao Yu to conduct research on related topics together, but the result was also messed up.
This reminded Lucas of the algebraic geometry conference where he specially called Frank over and told him to have a good relationship with a rookie in mathematics like Qiao Yu. His efforts were in vain.
I have been confused day by day, and I still haven’t found a research direction yet, which is really disappointing.
Well, actually this can't be all Frank's fault. After all, there are so many people who want to cooperate with Qiao Yu. Moreover, it is actually quite difficult to find a new research direction in more than a year.
But how can I put it, what people fear most is comparison.
After Qiao Yu proved the geometric Langlands conjecture, he did a lot more to propose a generalized modal axiom system, reducing the interval between prime pairs to 6, and now he has directly proved the Riemann conjecture.
Frank has accomplished nothing so far, and it can even be said that he has no direction. The contrast is obvious. If you add that both of them are Chinese, the contrast becomes even more obvious.
6◇9◇Book◇Bar
There is no doubt that Frank did not show any temperament or ability to become an academic leader during this period.
This also made Lucas feel very dissatisfied, after all, he invested a lot of energy and resources in this guy.
After sulking for a while, Lucas Eisen did not calm down. Instead, he became more and more angry as he thought about it. Then 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. Unbelievable, he really solved the Riemann Hypothesis. In fact, I have been studying his papers these days, and I have some insights."
Lucas Eisen felt that the other party's tone was very depressed, which made him feel even more angry. Do you have any thoughts after reading the paper now? What were you doing earlier? !
"I just had a phone call with Pierre, you know? 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 that this means What!”
Looking at what he said, Frank on the other end of the phone felt that anyone in the world could understand what this meant. Especially when the World Congress of Mathematicians will be held next month.
"Of course, Lucas, I understand. It is impossible for the Fields Medal jury to ignore the Riemann Hypothesis. Oh, no, it should be the status of Riemann's 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 asked you to try to promote cooperation with Joe? But look what you did?
You wasted a once-in-a-lifetime opportunity. I told you to take advantage of the fact that both you and Qiao are Chinese and have a good relationship with him. I don't understand where your inexplicable sense of superiority comes from.
Is it because he is young that makes you feel embarrassed? If that's the reason, you're so stupid! Really, I always thought you were a smart person who knew what was important and what was light! ”
Lucas Eisen's sermon made Frank feel speechless.
He wanted to say something to Lucas Eisen, "Because I am Qiao Yu's father! And he doesn't even know about it yet!" But he still didn't say it out loud.
Frank wasn't worried about Lucas finding out about his love affairs when he was young. In fact, with his current status, it wouldn't be a big problem for this kind of thing to be exposed.
Mainly because the way it was handled at that time was not appropriate, and it felt a bit like abandoning one's wife and children. Lucas is the kind of person who prides himself on being family-oriented.
The most important thing is that from the perspective of Chinese culture, his behavior at that time was not right. If he recognized Qiao Yu rashly, he was afraid of turning against 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 extremely complex.
On the one hand, he hopes that Qiao Yu is right. No matter what, he has confirmed that Qiao Yu is his biological son.
On the other hand, he didn't want Qiao Yu to be so powerful. Frank was really afraid that Qiao Yu might take revenge on him if he knew what happened back then.
After all, Qiao Yu has been living with his mother these years. Frank doesn't know what Qiao Xi said about him to Qiao Yu, but he doesn't think Qiao Xi has anything good to say about him.
Being blocked by a mathematical genius who solved the Riemann Hypothesis at the age of seventeen, Frank felt that he would probably have a bleak future in mathematics. After all, he really knew how powerful academics could be in this era.
Qiao Yu happens to have all the elements needed to become a great scholar. Damn it, does this still allow people to live?
At this time, I have to face Lucas’s merciless questioning...
Frank regrets it! Very regretful!
If he had not chosen to go abroad, even after graduating from MIT, he would have returned to China to find Qiao Xi, admit his mistake, take on the responsibility of raising her, and train Qiao Yu by himself...
Just thinking about how bright the future would have been if he had chosen this way, Frank wanted to slap himself twice!
God originally gave him a shortcut to the sky, but in the end he chose the road behind the shortcut.
It's a pity that there are no what-ifs in life, so now he is speechless when faced with Lucas' question.
Of course, even if he had something to say, he wouldn't say it. Frank knew the character of Lucas Eisen, a headstrong old man.
If he opened his mouth to defend, it would only make the old man angrier, and then he would say a bunch of uglier words. But he has no choice now and has to rely on Lucas to help pave the way for him. So I can only endure this scolding.
"Sorry, Lucas, I'm disappointed. But you know, there are too many people who want to cooperate with Qiao Yu. It's not that I didn't try, but he rejected me."
"Hmph...you can do it for yourself! How can you ask me to help you if you don't even know how to 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 expression unclear.
There are many things to consider, such as how should he face Qiao Yu at the upcoming World Congress of Mathematicians?
Especially when he heard that Qiao Xi was still accepted by Yuan Zhengxin, and he didn't know if Qiao Xi would go to the World Congress of Mathematicians. If he went, if he met him and recognized him...
But it was impossible not to attend this meeting. After all, although he was not qualified to give a full report in this meeting, it was determined that he would give a thirty-minute report in a branch room. 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 help but go to such a top conference every four years to show his face, right?
Worry!
……
In China, Lu Yanxiang of 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 is still hard to avoid...
It’s really recognized!
It can only be said that Zhang Yuanling has company. It's just that Lu Yanxiang really wanted to find someone to talk to him. Qiao Yu directly applied for a project on solving such a big problem as the Riemann Hypothesis. Is there any problem with him rejecting it? !
What the hell is wrong with this? !
Before the Riemann Hypothesis was solved, who could believe that a teenage boy could really solve this problem and leave a super luxurious review team speechless?
The most annoying thing was that when he called Zhang Yuanling to complain, the guy actually said: "Hey... Academician Lu, our situations are completely different. We can't be confused.
After all, Qiao Yu withdrew the project on his own at that time. I just asked a few questions and did not mean to deny it. But your situation is different. You rejected his project directly! ”
Listen, is this guy named Zhang talking in human language? ! Is there anyone in this world who can be reasonable? !
(End of chapter)