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Chapter 182: Can't you see that we have proved the Riemann hypothesis?

Well, after finishing all this, Qiao Yu realized that whether the paper was published in April or July didn’t seem to have any impact on him.

I don’t know why Director Tian got so angry.

However, when he was scanning his mailbox, he unexpectedly found an invitation letter sent by the organizing committee of the World Mathematical Congress two months ago.

I clicked on it and saw that he was invited to attend the World Congress of Mathematicians in late July and give a report at the conference. Of course, it was not the opening report, but it was also a 60-minute plenary report.

The main content is naturally about the modal axiom system.

how to say……

Not checking your email is really fatal.

It's been three months and the invitation link is no longer valid.

Although Qiao Yu didn't have any obsession with whether to attend this meeting, he seemed to have heard Director Tian say that it would be best if he didn't go abroad after he developed an application.

So this time he still planned to see the world. It didn't matter whether he won the award or not, the key was to be able to do the report, which would be equal to the achievements of his mentor back then.

So after thinking for a moment, Qiao Yu picked up the phone and called Tian Yanzhen again.

The call was connected, and before the other party spoke, Qiao Yu stacked up the BUFF.

"Hey, Director Tian, ​​I'm reporting something to you, please don't mention me."

"What? Can there be problems when signing a copyright transfer agreement?"

"No, that's not it. I just checked my mailbox and found that the World Congress of Mathematicians sent me an invitation three months ago, but it has expired."

After Qiao Yu finished speaking, the other party fell silent. He did not urge them, but just waited quietly.

"Starting tomorrow, develop the habit of checking your mailbox every day. Or you can directly link it to your phone, so that at least you won't miss those important emails."

"Okay, Director Tian." Qiao Yu agreed quickly.

"As for the World Congress of Mathematicians, you don't have to worry about it. After discussing the invitation letter with Mr. Yuan, I have already confirmed it for you. As for whether you can go at that time, it depends on the situation."

"Huh? Director Tian, ​​can you get my approval without my permission?" Qiao Yu said in surprise.

"I have at least served as a member of the Executive Committee of IMU, and ICM is organized by IMU! And everyone knows that you are my student! In addition, the candidates for giving reports at the World Congress of Mathematicians are generally notified one year in advance.

The reason why you informed me later than others is that the paper on the generalized modal axiom system was only published in November and quickly became the most cutting-edge research direction. So when I sent you the invitation letter, I consulted my opinion. "

Qiao Yu roughly understood what was going on.

"Um, Director Tian, ​​how many people were invited to give 60-minute reports this year?"

"Including your game, the total is 23 games."

"23 games? So many?" Qiao Yu was surprised.

He originally thought that a 60-minute report was a very special treatment, and there should be very few mathematicians in the world who were qualified for it.

"23 are too many? The International Congress of Mathematicians is held only once every four years. There are only 23 plenary sessions in four years, which is already too few! If you think it's boring, try to give the opening speech directly after the opening ceremony."

"Isn't my generalized modal axiom system good enough for an opening report?" Qiao Yu couldn't help but argue.

"Almost. But you're not qualified enough. If you can solve the Riemann hypothesis by the way, it will definitely work."

Well, Qiao Yu felt that this answer was not very mathematical. What qualifications are required for mathematics? Why did Fields limit the age to under 40? Didn’t the big guys know this?
Of course, Qiao Yu was just thinking about this in his mind. In fact, he also knew that Director Tian must hope that he could shine at the World Congress of Mathematicians.

Otherwise, Professor Tian would not be more anxious than he was to publish the paper in a journal as soon as possible. To put it bluntly, it was just to meet the deadline of the Mathematicians' Congress three months later.

Of course, although he understood it, Qiao Yu still felt a little unconvinced.

According to previous statements, the opening report of the World Mathematical Congress will be presented by respected mathematicians on their views on the future development of mathematics...

Um, wait… highly respected.

Qiao Yu suddenly felt that everything was fine.

Perhaps the generalized modal axiom system can indeed represent the direction of mathematical development in the next few decades. However, the word "highly respected" is a bit of a stretch to describe him.

"Any thing else?"

"never mind."

"What did you promise me today?"

“Check your email every day, or log in to your email on your phone, so you don’t miss any important emails.”

"Well, just remember it, and don't forget it in the future. You just need to take care of your own affairs, and others will naturally arrange the rest for you."

From the tone, Director Tian seemed satisfied.

No matter what, a student who remembers things is always more likable than a forgetful student who forgets what he promised right after something is done.

However, Qiao Yu felt that his mentor still treated him as a child, but in fact, he was already able to have his own opinions.

However, considering the principle that you can't have your cake and eat it too, Qiao Yu still agreed obediently.

After all, it is better for him to be a child at this stage, as life has not yet reached the point where he needs to be independent.

"I see, Director Tian, ​​but it's still too fast! Is it because I met another great reviewer?"

Qiao Yu couldn't help but ask.

The other party was silent for a moment, but still answered the question very objectively: "Well, they are all very impressive. There are three Fields Medal winners, and two others who have not won the Fields Medal, but they are not far behind."

"Wow, five top reviewers didn't find any mistakes in my paper, nor did they ask me to explain the proofs of theorems and lemmas in the paper. Professor Tian, ​​does this mean that I have made great progress again?"

Hearing Tian Yanzhen's answer, Qiao Yu asked happily.

"Qiao Yu, last time everyone praised your paper with all kinds of flattering words, but this time no one praised your paper, so I think you have regressed!

Forget it! I won't talk to you anymore. You should prepare yourself. There will be two lectures during this period. You will be the main speaker. The content of the lecture is the prime number research techniques in the era of modal axiom system. It's late. You should go to bed early. I'm going to hang up first. "

……

Tian Yanzhen felt a headache when she saw the hung up phone.

Although he also felt that Qiao Yu should be given more praise and encouragement at his age - that's what the education experts on the Internet said.

Moreover, Qiao Yu's achievements are worthy of praise even in the eyes of a teacher like him.

But Qiao Yu's behavior always makes Tian Yanzhen feel that he is easily carried away and forgets everything else...

The main reason is that there are too many people praising him. Tian Yan really thinks that he is not a big deal. On the contrary, at present, there are fewer people warning him.

Really, speaking of it, Tian Yan really missed Zhang Shuwen. The first time he met Qiao Yu, he helped him teach Qiao Yu a lesson.

It's good to have more people like this. Unlike Yuan Zhengxin, Qiao Yu called him "Grandpa" twice, and then he lost his strict teacher style and played the bad guy, forcing him, the genuine mentor, to play the bad guy, which was very boring.

But what can he do?

When everyone was praising him, he was the only one who stood up as a mentor and kept Qiao Yu sober.

Oh, it’s hard to be a mentor!
……

Listening to the busy tone on the phone, Qiao Yu also felt that he was in a difficult situation.

If he doesn't work hard, he won't get any praise. If he works hard, he won't be praised either. Yet, he is still asked to prepare to give lectures and even the topic of the lectures is prepared for him. They are really becoming more and more strict with him.

Fortunately, Qiao Yu was not the type to hold grudges, and soon put the matter aside.

After all, I published another top journal paper. I will definitely get an award. And there are many happy things recently. If I calculate the scores, I will basically get enough credits to graduate successfully this year.

If his company can get on track, it means he can start making a fortune after he becomes an adult, which means everything is arranged just right.

As for the lecture, Qiao Yu didn't take it seriously. Even if he hadn't written the paper yet, as long as he had the derivation process in his mind, he could give a good lecture.

This is the ability that comes from being able to score 100 points in the Chinese language test. He not only knows how to do research, but also how to communicate with different types of people in a way that they can understand.

For example, telling other peers that they are not good enough. It is useless to tell them directly. The best way is to solve the problem while playing games.

Now, not only does no one of his peers compete with him in math, but he can't even find anyone willing to play games with him, even as a teammate. Everyone says that they are under too much pressure and want to learn from him when they see him.

After hanging up the phone, Qiao Yu also planned to read some more literature and then go to bed. Recently, he has also been studying the behavioral patterns of machine learning.

At present, AI is already very popular, but Qiao Yu believes that AGI is the real king.

Although we are still a long way from AGI, if we don’t consider universality, it would still be very promising if he could develop a PGI.

Of course, PGI is an abbreviation created by Qiao Yu. The full name is Professional General Intelligence. The definition is a system that has advanced general intelligence performance in a certain professional field.

At least it should be able to reach the level of experts in related fields. Although it does not have cross-domain capabilities, it is enough as long as it can reach the top in the professional field. It is similar to AlphaGo that can play chess. The difference is that AlphaGo does not actually create, but only learns, summarizes, and calculates.

However, within this field, PGI possesses certain capabilities of the human brain and can learn, think and even innovate independently, and has a certain degree of creativity.

Of course, this seems difficult at the moment.

It's as if Peter Schultz is still racking his brains to train an AI that can understand mathematical theorems.

However, Qiao Yu felt that he had an advantage in this field. After all, he now had a computer room, and his math skills were pretty good, at least at the level of a Fields Medal winner.

In addition, his model will undertake a large number of professional tasks in the future, which means that there will be a lot of multi-dimensional complex data for training.

However, just as Qiao Yu opened the paper and immersed himself in it, there was a knock on the door.

"Who is it?" Qiao Yu did not open the door directly, but asked.

The sudden "bang bang bang" sound in the middle of the night was really scary.

"I'm Xue Song."

Lao Xue's voice floated in from the corridor, and Qiao Yu quickly stood up and ran to open the door.

"Huh? Professor Xue, you haven't come home yet so late at night?"

"Where do I have a home in Beijing? I only have a dormitory, and I can only do research in the dormitory. It's better to stay in the office."

"Forehead……"

"Well, I came to you mainly to discuss a problem. I guess you haven't slept yet, and you don't want to wait until tomorrow."

Qiao Yu then noticed that Xue Song was holding a stack of manuscripts. He nodded and said, "Please come in."

There is no way. When a mathematics professor can’t wait until tomorrow to discuss a math problem, it means he is really interested in this problem, so it is best not to spoil his fun.

This was indeed the case. Following Qiao Yu into the small study, Xue Song handed the manuscript in his hand to Qiao Yu before he even sat down.

"Take a look at this first. Today, when I was studying the geometric mapping Ψ(Psi) (s), I found a very strange phenomenon. In most cases, Ψ(s) is a smooth geometric object on s.

For example, manifolds or hypersurfaces. But near the zero point, the properties of Ψ(s) show obvious anomalies. It can be understood as a break in some geometric structure or an enhancement of symmetry. "

Qiao Yu lowered his head and looked at the manuscript that Xue Song handed to him. Of course, he memorized every word Xue Song said.

He has always been very good at doing two things at the same time.

Based on the manuscript, Qiao Yu roughly knew Xue Song's research progress. The conclusion just now was discovered by Xue Song when he constructed the symmetry group of the modal space.

To sum up, the geometric mapping Ψ(s) is essentially controlled by a certain symmetry flow, and this flow can be explained by the action of the Lie group G.

Then Xue Song came up with a very bold hypothesis: the modal geometric mapping Ψ(s) is composed of the orbit of a modal Lie group Gs.

It’s really interesting!
Because he had been communicating with Xue Song the whole time, Qiao Yu quickly finished reading the manuscript.

After thinking for a while, he said: "I think there are two possibilities. The first is that the modal Lie group Gs acts on the modal hyperspace H, so that Ψ(s) is the fixed point set of Gs.

Second, does the symmetry enhancement of Ψ(s) at the zero point s mean that the group order of Gs has changed? Well, it is similar to the phase transition of symmetry enhancement?

Wait, let me think about it..."

Qiao Yu thought for a moment, then picked up a pen and added another formula to Xue Song's manuscript.

Xue Song leaned over to take a look, thought for a moment, and said, "Can we directly describe the generators of the modal group as Lie algebras?"

"Well, the geometric structure is controlled by the Laplace operator of modal geometry." Qiao Yu nodded, and his brain began to think rapidly.

Xue Song frowned, pointed to the position of λ(s) in the formula, and asked, "What is this?"

"Eigenvalues."

Qiao Yu explained casually, and then suddenly said, "Have you found a problem? The zero point condition of the modal zeta function is equivalent to the resonance condition of the modal Lie algebra?"

Then he added another formula: "λ(s)=0 s"

He muttered, "Look, s is the zero of the modal zeta function."

Xue Song frowned and looked at Qiao Yu. He felt it was a bit strange. Are they discussing the same issue?
"Um... what are you talking about? Wait, modal zeta function? You made a modal mapping of the Riemann zeta function?"

"Uh? Oh, I almost forgot. My latest paper hasn't been published yet. You should be able to see it in the latest issue of JAMS in two days."

Qiao Yu slapped his forehead and explained quickly.

"Oh..." Xue Song nodded silently.

Fortunately, he has gotten used to it.

Ever since Qiao Yu published his first article in the "Annals of Mathematics", it seemed that publishing in top journals was no longer a problem for this young man.

But he will be able to send it soon.

A lot of content has been accumulated on this topic. Xue Song is confident that he will publish one or two top journals this year, and at least one of them will be eligible to be published in the Big Four.

So I don’t envy you.

"Wait a minute, Professor Xue, I found a very interesting situation. Let me do the math first."

Qiao Yu said something to Xue Song, then picked up a blank piece of manuscript paper on the table and began to calculate quickly.

Xue Song took a stool and curiously moved to the table, watching Qiao Yu's derivation process. One was calculating, the other was frowning beside him, and before he knew it, Qiao Yu had already written seven or eight pages of manuscripts in a hurry, and the entire table began to become visibly messy.

Finally, Qiao Yu stopped calculating and finally got the following formula.

"Hmm, interesting, the topological invariants near the zero point actually exhibit strange behavior."

Qiao Yu muttered subconsciously.

"Well, it's like the Euler number, or the Euler number?"

"The description to be prepared should be that the modal manifold degenerates into a low-dimensional symmetric subspace at zero."

"You mean the classic Morse theory?"

"That's understandable. But Professor Xue, have you really not figured it out yet?"

Qiao Yu turned his head, looked at Xue Song, and asked seriously.

"What did you figure out?" Xue Song frowned and looked at Qiao Yu in confusion. He began to dislike the Riddler a little.

"Oh, by the way, you haven't read my paper yet. It's actually very simple. Well... we seem to have proved the Riemann hypothesis."

Xue Song laughed and said, "Haha...you just said that we proved the Riemann hypothesis. Qiao Yu, you really know how to joke. So should I act excited now?"

As Xue Song was laughing, he suddenly couldn't laugh anymore, because he found that Qiao Yu looked at him in a strange way, as if he was looking at a fool.

So Xue Song subconsciously restrained his smile, pondered for two seconds, and asked in a not-so-reserved manner: "Um...Qiao Yu, are you serious? Have you really done it?"

“I was very serious. I thought it would be a complicated process because there were many things that needed to be verified, but I didn’t expect it to be so simple.

The only regret is that we didn’t use any number theory methods. But I think the Riemann hypothesis has definitely been proved. So Professor Xue really hasn’t figured it out yet?”

Xue Song stopped talking.

He raised his hand and picked up the manuscript paper where Qiao Yu had just made all the calculations. He then read it line by line, thinking for a long time, and even went over the Riemann zeta function several times in his mind...

Finally, ten minutes later, Xue Song used all his strength to shake his head carefully.

"Although it's not in line with my identity, I really want to swear right now. Unfortunately, I have no research on the Riemann hypothesis, so I really don't understand why you said you proved the Riemann hypothesis!"

Really, after saying this, Xue Song suddenly felt a sense of relief.

If you don't understand, you don't understand. Even though you may miss out on great wealth, you can't always pretend that this is the case.

Although there was a moment just now when he really wanted to pretend like this.

After that, Xue Song took out his mobile phone, turned on the camera, entered the video mode, and pointed the lens at Qiao Yu: "Um, Qiao Yu, how about you write out the proof now?

Don't worry, I won't record your specific proof process, just keep some audio and video materials. If I don't have money to buy a house in the future, you can help me make a proof and I will auction this video."

Qiao Yu suddenly laughed and said, "In fact, it is very simple at this point. Use group action to construct a modal operator. Through spectral decomposition, you will find that the eigenvalues ​​of the modal operator are symmetrical.

Haha, Professor Xue, you didn't see it because you haven't read the paper I submitted to JAMS. If you have read it, as long as you combine the properties of the modal zeta function, you should be able to easily analyze that the zero modulus condition of the modal operator is equivalent to the Riemann hypothesis.

Finally, the problem was solved by combining the modal group with the modal operator. No need for those stupid methods to verify bit by bit, all the non-trivial zeros are on the 1/2 line! I am very sure of this now! "

(End of this chapter)