Since Perelman invited Li Mu to his home, it was natural that he could not forget to tell Li Mu his address.
His house is located on the outskirts of St. Petersburg.
It was a small house that looked very quaint.
It has a dark brown roof and some yellowed walls. The roof is a very traditional triangle in Russia, and there is a small garden around the house, which looks very unique.
Li Mu took a taxi here.
"We've arrived. This is Perelman's home."
The taxi driver said to Li Mu.
Li Mu raised his eyebrows: "How do you know this is Perelman's home?"
The driver also had a big beard and said with a smile: "Most taxi drivers in St. Petersburg know that there are often reporters who have no news to cover, and then they want to try their luck with Perelman. .”
"Of course, they often get upset. Mr. Perelman is not a good-tempered person. In this case, we will often stay at the door, waiting for the reporter to come back, and we can make two trips back and forth. money."
"But later, when Perelman found out what we were doing, he asked us not to do it. This would only cause more trouble for him, so after that, we basically stopped accepting these requests to see Perel. Mr. Mann’s guest.”
"But you still brought me here today."
Li Mu said with a smile.
"Hey, you are Professor Li Mu, and you are the same person as Perelman. Of course I will not refuse."
"Huh? You know me too?"
"Hahaha, there have been too many guests going to the conference center recently. Of course, we have all known about the International Congress of Mathematicians for a long time. Of course, we also know that at this year's International Congress of Mathematicians, there will be a big show. Professor Li." The driver said with a smile: "What I admire most are scientists and intellectuals like you. You are the most important treasures of our mankind."
"Thank you." Li Mu nodded.
The driver smiled and said nothing more. Then he parked the car on the side of the road and said to Li Mu, "Your destination has been reached. The fare is 415 rubles."
Li Mu paid the fare readily. This price is considered normal in St. Petersburg. The starting fare in St. Petersburg is 250 rubles, equivalent to 2.5 yuan. It is much cheaper than in China, probably because the gas price here is very cheap.
"Thank you Mr. Li, and I wish you a pleasant communication with Mr. Perelman."
The driver waved to Li Mu who got out of the car, and Li Mu nodded to him. Then, he turned around and looked at the small house in front of him, and then walked over.
Came to the door and knocked on the door.
Then Li Mu heard a voice coming from inside the house: "Gerry, it should be the guest you mentioned before!"
"knew."
The voice speaking this time was Perelman's.
Soon, footsteps came from inside, and finally, the sound of the door handle turning was heard, the door was opened, and the iconic bearded man appeared in front of Li Mu.
"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, except that it is not as sloppy as Perelman himself, it is still relatively neat inside.
Arriving at the living room, Li Mu saw an old woman mopping the floor. After seeing Li Mu, a smile appeared on her face: "Hello, young man, Gregory hasn't brought anyone to the house for a long time. I heard that you are also a mathematician, I hope you have a pleasant chat."
"This is my mother." Perelman introduced Li Mu: "As people outside said, I also have a sister, but she is not at home recently."
Li Mu nodded and said to the old woman: "Hello."
The old woman nodded kindly.
Perelman's mother, named Liupov, was once a mathematics teacher. Later, in order to raise Perelman, who was still young but had already shown great talent, she quit her job, even though This is still the case to this day.
Looking at the mop in Liupov's hand, it was obvious that she was usually responsible for cleaning the room.
Then he didn't say anything more.
As a mathematician, when I go to other mathematicians’ homes, I am usually most interested in that mathematician’s study.
"Go to my study. I think you will be more interested there."
Perelman said.
Li Mu also nodded, and then followed.
When we arrived at Perelman's study, the decoration inside was normal.
Bookcases filled with various books, and a desk.
There are also a lot of scratch papers placed on the desk, which are messy. Of course, Li Mu thinks it is completely understandable that such a messy arrangement of scratch papers is because he is usually like this.
In addition, it is just a small blackboard.
For mathematicians, it is quite normal for everyone to have a small blackboard.
And Li Mu's eyes were directly attracted to this small blackboard.
Because there are rows of formulas listed above.
After Li Mu thought for a moment, he asked: "Are you studying the Riemann Hypothesis?"
"Can you tell?" Perelman asked.
"It's obvious." Li Mu said, "You should be trying to use the proof of Poincaré's conjecture to analyze the Riemann zeta function in the complex plane, but... you have omitted the process too much."
Then he smiled and said, "But this is quite in line with your habits."
When it comes to mathematical proofs, Perelman is often used to writing as little as possible. Writing one more word is considered a sign of mercy on his part.
So just like his proof of the soul conjecture, this problem in Riemannian geometry had stumped the entire mathematical community for more than 20 years. As a result, when the problem fell into his hands, he only spent four In just one page, the proof of this conjecture was completed - of course, the reason why this conjecture is called "soul" is just a naming. To a certain extent, it may be due to some kind of romance among mathematicians.
In addition to proving the soul conjecture, Perelman's proof of the Poincaré conjecture was also extremely simple, so much so that after he posted the paper on arxiv, mathematicians all over the world were stunned. I couldn't understand it for a while.
Because his proof process is full of "easy", "obvious" and other similar words.
Perhaps, for Perelman, his proof process is entirely for himself, so words such as "easy to obtain" and "obvious" are indeed true for him.
It's just that this kind of "customized proof" is not suitable for more people in the mathematics community, so that in the next two years, the mathematics community was dedicated to filling in some of the details that were lacking in his proof process.
Including Perelman, he had to go to major schools to give reports to explain his proof process.
It was not until finally that the mathematical community finally recognized his proof and announced that he had successfully proved the Poincaré conjecture.
Perhaps for Perelman, that trip to various parts of the world to give lectures was the longest time he had been away from home in his life, which may have made him feel very distressed.
"You're probably the first person who can tell at a glance what I'm proving."
Perelman said.
Li Mu smiled. It was actually quite simple for him to do this. Of course, he didn't say too much. He continued to look at the blackboard. After a moment of thinking, he said, "The problem you are encountering now is It’s...well, the algebraic expression of Σk cannot be integrated into the complex function...What you plan to use is the zero-point proportion method?"
"Yes." Perelman nodded, "I have increased this zero point ratio to 50 percent - if I am not wrong."
Li Mu was stunned for a moment, "Fifty percent?"
In the Riemann Hypothesis, it is judged that in the Riemann zeta function, the real part of all non-trivial zero points is 1/2, which means that these zero points all fall on the straight line 1/2+ti.
Currently, there are two main methods in mathematics to achieve this.
The first direction is to calculate the non-trivial zeros of the Riemann zeta function. In 1903, Danish mathematicians calculated for the first time the specific values of the first 15 non-trivial zeros. The real parts of these zeros were all 1/2. In 1925, Littlewood and Hardy - yes, this again Two of the most well-known collaborators in mathematics improved the calculation method and calculated the first 138 zero points; then, Hardy's students used Siegel's formula obtained by Siegel in 1932 to calculate the non-trivial zero points to 1041, artificial intelligence Turing, the father of the invention, advanced the number of non-trivial zero points to 1104.
After that, technology entered the scene and the birth of the computer allowed the number of non-trivial zero points to be verified to 3.5 million. Later, 200 million, 1.5 billion, 850 billion, and all the way to 10 trillion, no counterexamples could be found.
But obviously this mechanical verification method cannot complete the final proof, because the numbers are infinite, and even if the universe is exhausted, the numbers will never end.
Therefore, only general proof can prove this conjecture.
So the second direction was born, and its method was to prove the proportion of the number of zero points on the critical line.
It was Hardy who first proved that there are infinitely many zero points of the Riemann zeta function, all of which are located on the critical line where the real part is 1/2, but infinite numbers are not all, and people do not know whether there are zero points outside the critical line. Subsequently, Selberg proved that the proportion of the number of zero points on the critical line to the number of all non-trivial zero points is greater than zero, which means that the zero points on the critical line play an important role in the distribution of all zero points. Furthermore, Levinson introduced a unique algorithm and proved that the zero points on the critical line accounted for 34.74% of all zero points. After that, Kangrui pushed the proportion to 40% in 1989.
But then, the progress began to become extremely slow. The latest progress only pushed this ratio to 41.28% in 2012 - compared with the two-fifths ratio, it is almost equivalent to no improvement, so that the mathematics community I gradually lost hope in this method.
But what Li Mu didn't expect was that Perelman suddenly said that he had pushed this result to 60%.
"Can I see your paper?"
"certainly."
Perelman nodded, then he knelt down, opened a drawer of the desk, and took out a stack of papers.
At a glance, Li Mu recognized that the stack of paper only had about 9 pages.
"That's it. There's no layout, so it's probably not a paper," Perelman said.
Li Mu didn't pay attention and took the nine pieces of paper. As expected, they contained Perelman's proof on this issue.
He started reading from the beginning, and the content inside was omitted as always, almost reducing it to the point where it could no longer be reduced.
If it were anyone else, such a paper would probably give everyone a headache.
But for Li Mu, such a paper is particularly suitable for his mind.
Relying on the amazing analytical ability of the computer in his mind, he can easily fill in the detailed flaws in the proof. Those things that are "obvious" and "easy to obtain" are all real to him. "Obvious" and "accessible".
In this way, it only took him half an hour to read these 9 pages.
Then, he sighed: "It's a very good proof. If your proof can be published, it will probably rekindle the hope of proving the Riemann Hypothesis in the mathematical community."
Perelman shook his head and said, "I don't want to look like a monkey and be looked at by everyone."
"If you want to persuade me, forget it. Bolonnikov has tried it many times. I don't like this kind of thing."
Li Mu smiled: "Of course, I respect everyone's choice. Whether it is to integrate into the world or to alienate from the world, it is freedom."
"Thank you for your understanding." Perelman smiled for probably the first time.
Li Mu nodded.
In fact, judging from the exchanges with Perelman, he is not the kind of sociophobic person who is unwilling to communicate at all. I heard that when he was in school, he often helped those students who did not study well. It can be said that he was When he was a student, he was an excellent student with all-round moral, intellectual and aesthetic qualities - as for why he didn't have "physical", it was because he generally failed in physical education.
"However, you know so much, have you done some research on the Riemann Hypothesis?" Perelman asked at this time.
"After all, it is the Riemann Hypothesis, and I think any mathematician would try to understand this problem."
Li Mu replied.
With the help of the Bluetooth connection function of the brain computer, when he usually uses this function to read various papers, he has naturally also read various papers related to the Riemann Hypothesis.
Through these papers, his understanding of the Riemann Hypothesis has naturally become very profound, at least among the best in the world.
"So how is your research going? Do you think Kang Rui's method can lead to the final answer?"
Li Mu thought for a moment, and finally shook his head and said, "I don't think it's okay."
"The problems with Kang Rui's method are obvious, and this is also an important reason why the mathematics community has always been difficult to get closer."
"Although your paper has made up for that problem to a certain extent, the subsequent steps will become more and more difficult. I have this intuition."
"Your intuition is right." Perelman nodded, "I thought so too."
"Just like the twin prime conjecture you once proved, it also has limits."
Li Mu nodded slightly, "Of course, to be honest, I haven't done much research on the Riemann Hypothesis, 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 and expressed understanding.
For him, before he published his proofs on the soul conjecture and the Poincaré conjecture, in fact, the more purpose was to confirm whether his proofs were correct. This was his purpose.
And the fame that came from it were all "side effects" to him.
"I hope you can invite me when the time comes." Li Mu smiled.
Perelman smiled: "Of course."
"However, maybe you complete the proof first? Just like the NS equation problem."
Li Mu smiled and waved his hand: "It's still very early for this kind of thing."
"By the way, tomorrow, I will give a public class at St. Petersburg State University. This is what Dean Bolonnikov originally invited me to do. Maybe you can come and be my guest in this public class?"
Perelman waved his hand: "Forget it, I don't like to appear in places with too many people. If it weren't for your proof of the NS equation that day, I probably wouldn't have gone 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 stunned.
"Yes." Li Mu nodded: "Although the proof of this problem has been completed, the mathematical community has been hoping that I can add more details in the past few days, so I plan to report 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, in the many years since the proof of Poincaré's conjecture was completed, only the problem of the NS equation proved by Li Mu interests him the most.
Li Mu laughed: "Okay, then I'll wait for your special guest to arrive tomorrow."
…
(End of chapter)
