Ultimate Scholar

Since Perelman invited Li Mu to his house, it is naturally impossible to forget to tell Li Mu the address.

His house is located on the outskirts of St. Petersburg.

It was a very quaint little house.

The dark brown roof and some yellowed walls, the roof is a very traditional triangle on the Russian side, and there is a small garden around the house, which looks very chic.

Li Mu took a taxi here.

"It's already here, this is Perelman's home."

The taxi driver said to Li Mu.

Li Mu frowned: "How do you know this is Perelman's home?"

The driver also had a beard on his face, and said with a smile: "Most taxi drivers in St. Petersburg know that, after all, there are often some reporters who have no news interviews, and then they want to come to Perelman to try their luck. .”

"Of course, they often touch the ashes of the nose. Mr. Perelman is not a good temper. In this case, we will often guard the door, waiting for the reporter to come back, and we can make a trip or two money."

"But after Perelman found out what we were doing, he told us not to do it. This would only cause him more trouble, so after that, we basically didn't take these things and wanted to see Perel. Mr. Man's guest."

"But you still brought me here today."

Li Mu said with a smile.

"Hey, you are Professor Li Mu, the same person as Perelman, of course I will not refuse."

"Huh? You know me too?"

"Hahaha, there are too many guests going to the conference center recently. Of course, we all know about the International Congress of Mathematicians, and of course we know it. At this year's International Congress of Mathematicians, we will show off our limelight." Professor Li." The driver said with a smile: "I admire scientists and intellectuals like you the most, and you are the most important treasures of our human beings."

"Thank you." Li Mu nodded. \b

The driver smiled, didn't say anything more, then parked the car on the side of the road, and said to Li Mu: "Your destination has arrived, and the fare is 415 rubles."

Li Mu paid the fare readily. This price is considered normal in St. Petersburg. The starting price in St. Petersburg is 250 rubles, which is equivalent to 2.5 yuan, which is much cheaper than in China, probably because the gas price here is very cheap.

"Thank you Mr. Li, I wish you a pleasant exchange with Mr. Perelman."

The driver waved to Li Mu who got out of the car, Li Mu also nodded to him, then he turned to look at the small house in front of him, and then walked over.

Came to the door, knocked on the door.

Then Li Mu heard a voice from inside the house: "Gerry, it should be the guest you mentioned earlier!"

"knew."

This time the speaking voice was Perelman's.

Soon, footsteps came from inside, and finally, the sound of the doorknob being turned, the door was opened, and the iconic beard appeared in front of Li Mu's eyes.

"Lee, come in quickly."

Perelman stepped aside and said to Li Mu.

Li Mu nodded and walked in.

Looking at the environment in the room, apart from not being as sloppy as Perelman himself, the inside is relatively tidy.

When he came to the living room, Li Mu saw another old woman mopping the floor. After seeing Li Mu, a smile appeared on her face: "Young man, hello, Gregory hasn't brought anyone home for a long time. I heard that you are also a mathematician, I hope you have a good chat."

"This is my mother." Perelman introduced Li Mu: "As people outside said, I also have a younger sister, but she is not at home recently."

Li Mu nodded, and nodded to the old woman: "Hello."

The old woman nodded kindly.

Perelman's mother is called Liubov. She used to be a mathematics teacher. Later, she quit her job in order to raise Perelman, who was still young but had already shown great talent. Until now, it is still the case.

Looking at the mop in Lyubov's hand, it was obvious that she was usually responsible for cleaning the room.

He didn't say anything more after that.

Also as a mathematician, when visiting the homes of other mathematicians, the study of that mathematician is generally the most interesting thing.

"Go to my study, I think you are more interested in it."

Perelman said.

Li Mu also nodded, and then followed. \b

When I came to Perelman's study, the decoration inside was normal.

A bookcase filled with various books, and a desk.

There are a lot of draft papers placed on the desk, which are in a mess—of course, Li Mu thinks that the mess of draft papers is completely understandable, because he is also like this in normal times.

In addition, it is a small blackboard.

For mathematicians, it is quite normal to have a small blackboard in hand.

And Li Mu's eyes were directly attracted by this small blackboard.

Because there are rows of formulas listed above.

After thinking for a moment, Li Mu asked, "Are you studying the Riemann Hypothesis?"

"You can see it?" Perelman asked back.

"Obviously." Li Mu said, "You should be trying to use the proof of the Poincaré conjecture to analyze the Riemann ζ function in the complex plane, but...you omitted the process too much."

Then he smiled, "But this is quite in line with your habits."

Perelman’s mathematical proofs are often used to write as little as possible, and writing one more word is considered an outpouring of mercy.

So just like his proof of the soul conjecture, this problem in Riemannian geometry has stumped the entire mathematical community for more than 20 years. As a result, when this problem fell into his hands, he only used four One page of paper completes the proof of this conjecture—of course, the reason why this conjecture is called "soul" is simply a naming, and to some extent it may be because of a certain romance of mathematicians.

In addition to the proof of the soul conjecture, Perelman's proof of the Poincaré conjecture is also extremely simple, so that after he put the paper on arxiv, mathematicians all over the world temporarily I couldn't figure it out for a while.

Because his proof process is full of words like "easy to get" and "obvious".

Perhaps, for Perelman, his proof process is entirely in his own service, so words like "easy to get" and "obvious" are true for him.

It's just that such a "customized proof" is not suitable for more people in the mathematics community, so that in the next two years, the mathematics community has been working on filling in some details that he lacked in the proof process.

Including Perelman also had to go to various schools to give reports to explain his proof process.

It was not until the end that the mathematics community finally recognized his proof and announced that he had successfully proved the Poincaré conjecture.

Probably for Perelman, that trip to the world to give lectures was the longest time he had been away from home in his life, which probably made him feel very distressed.

"You're probably the first person who can see at a glance what I'm proving."

Perelman said.

Li Mu smiled. For him, it is actually quite simple to do this. Of course, he did not say too much. He continued to look at the blackboard. After thinking for a while, he said: "The problem you are encountering now It's... um, it's impossible to integrate the algebraic expression of ∑k into a complex function... what you plan to use is the zero-point ratio method?"

"Yes." Perelman nodded, "I have increased this zero percentage to 50%—if there is nothing wrong."

Li Mu was taken aback for a moment, "Fifty percent?"

In the Riemann conjecture, the judgment is that in the Riemann ζ function, the real part of all non-trivial zeros is 1/2, that is to say, these zeros all fall on the straight line 1/2+ti.

Currently, there are two main approaches in the mathematical community to achieve this.

The first direction is to compute the nontrivial zeros of the Riemann zeta function. In 1903, Danish mathematicians calculated the specific values ​​of the first 15 non-trivial zeros for the first time. The real parts of these zeros are all 1/2. In 1925, Littlewood and Hardy—yes, this again One of the most famous collaborators in mathematics, improved the calculation method and calculated the first 138 zeros; then, Hardy's students used the Siegel formula obtained by Siegel in 1932 to calculate non-trivial zeros to 1041, artificial intelligence Turing, the father, advanced the number of non-trivial zeros to 1104.

After that, the entry of technology and the birth of the computer verified the number of non-trivial zeros to 3.5 million. Later, 200 million, 1.5 billion, 850 billion, and up to 10 trillion, no counterexample was found.

But obviously this kind of mechanical verification method cannot complete the final proof, because the number is infinite, even if the universe is exhausted, the number will never end.

Therefore, only a general proof can confirm this conjecture.

Then the second direction was born, the method is to prove the ratio of the number of zeros on the critical line.

It was Hardy who first proved that there are infinitely many zero points of the Riemann zeta function located on the critical line where the real part is 1/2, but not all of them are infinite, and people do not know whether there are zero points outside the critical line. Then, Selberg proved that the proportion of the number of zeros on the critical line to the total number of non-trivial zeros is greater than zero, which means that the zeros on the critical line play an important role in the distribution of all zeros. Further, Levinson introduced a unique algorithm, which proved that the zero points on the critical line accounted for 34.74% of all zero points. After that, Kang Rui advanced the proportion to 40% in 1989.

But after that, the progress began to become extremely slow, and the latest progress was only to increase this ratio to 41.28% in 2012-compared with the ratio of two-fifths, it was almost equivalent to no improvement, so that the mathematical community Hope for this method is also gradually lost.

But to Li Mu's surprise, Perelman suddenly said that he had pushed the result to 60%.

"Can I have a look at your paper?"

"certainly."

Perelman nodded, then he squatted down, opened a drawer of the desk, and took out a stack of papers from it.

At a glance, Li Mu recognized that the stack of paper was only about 9 pages.

"That's it, no typesetting, probably not a thesis," Perelman said.

Li Mu didn't pay attention, and took the nine pieces of paper, which indeed contained Perelman's proof on this issue.

He started to look at it from the beginning, and the content inside was omitted as often as possible, and it was almost reduced to the point where it could not be reduced any more.

Had anyone else come over, such a thesis would probably be a headache for anyone.

But for Li Mu, such a thesis is particularly in line with his mind.

Relying on the amazing analysis ability of the computer in his mind, he can easily fill in the detailed defects in the proof, and things like "obvious" and "easy to get" are also true for him "obvious" and "easy to get".

Just like that, he finished reading these 9 pages in just half an hour.

Then, he sighed with emotion: "It's a very good proof. If your proof can be published, it will probably rekindle the hope of the mathematical community for the proof of the Riemann Hypothesis."

Perelman shook his head and said, "I don't want to be looked at like a monkey."

"If you want to persuade me, forget it. Bolonikov has tried many times. I don't like this kind of thing."

Li Mu smiled: "Of course, I respect anyone's choice, whether it is to integrate into the world or alienate from the world, it is freedom."

"Thank you for your understanding." Perelman probably smiled for the first time.

Li Mu nodded.

In fact, just judging from the communication with Perelman, he is not the kind of social phobia who is unwilling to communicate at all. I heard that he often helped those students who were not good at learning when he was in school. It can be said that he was When he was a student, he was an excellent student with morality, intelligence and beauty-as for why he didn't have "body", because he generally failed in sports.

"However, you know so much, do you have some research on Riemann's conjecture?" Perelman asked at this time.

"After all, it is the Riemann conjecture. I think any mathematician will try to understand this problem."

Li Mu replied.

With the Bluetooth connection function of the brain computer, when he usually uses this function to read various papers, he has naturally read various papers related to the Riemann Hypothesis.

Through these papers, his understanding of Riemann's conjecture has naturally become very profound, at least among the first-rate in the world. \b

"Then how is your research? Do you think Kang Rui's method can point to the final answer?"

Li Mu thought for a moment, then finally shook his head and said, "I don't think so."

"The problems with Kang Rui's method are obvious, and this is also an important reason why the mathematical community has always been difficult to approach."

"Although your thesis has made up for that problem to a certain extent, the next steps will become more and more difficult. I have such an intuition."

"Your intuition is right." Perelman nodded, "I think so too."

"Just like the twin prime number conjecture you once proved, it also has a limit."

Li Mu nodded slightly, "Of course, to be honest, I haven't done much research on Riemann's conjecture, so I can't give too many meaningful suggestions."

"Then, I wish you success, but I don't know, if you really complete the proof, will you announce it?"

Perelman shook his head: "I won't announce it, but I will invite my friends over."

"Because sometimes I don't know whether my proof is correct, just like the Poincaré conjecture."

Li Mu nodded, expressing his understanding.

For him, the purpose of announcing his proofs of the soul conjecture and the Poincaré conjecture before was to confirm whether his proofs were correct, which was his purpose.

And the fame that comes from this is all "side effects" for him.

"I hope you can invite me when the time comes." Li Mu smiled.

Perelman smiled: "Of course."

"However, maybe you completed the proof first? It's like the NS equation."

Li Mu smiled and waved his hands: "This kind of thing is still very early."

"By the way, tomorrow, I will hold an open class at St. Petersburg State University. This was invited by Dean Bolonikov. Perhaps, you can come to be my guest in this open class?"

Perelman waved his hand: "Forget it, I don't like to appear in places with too many people. That day, if it weren't for your proof of the NS equation, I probably wouldn't go to the conference center."

"Okay." Li Mu shook his head helplessly: "I originally thought that the open class on NS equations would attract you."

"About the NS equation?" Perelman was taken aback for a moment.

"Yes." Li Mu nodded: "Although the proof of this problem has been completed, the mathematics community has been hoping that I can add more details to the problem these days, so I plan to make this matter , put it in tomorrow's open class."

Perelman was silent for a moment: "If that's the case, I'll go."

For him, since the proof of the Poincaré conjecture was completed for so many years, only the NS equation proved by Li Mu interested him the most.

Li Mu laughed: "Okay, then tomorrow, I will wait for the arrival of your special guest."

...