The same lecture hall was crowded.
Outside the gate, there were still a large number of people rushing inside.
Obviously, everyone can feel that there are more people attending the report today than at the previous opening ceremony.
In fact, all the seats were occupied, and people were standing behind and in the aisles on both sides.
There are far more media coming from various places than before.
In the past, there were very few media that came to record reports. They were basically relatively large and official media. However, the media that come now are all kinds of media, not only from Russia, but also from Coming from other countries.
Naturally, CCTV reporters from China also appeared here.
CCTV's reporter in Russia, Cao Yang, looked at the flow of people around him and couldn't help but sigh: "There are so many people."
On the side, his colleague Chen Xiaoming, who like him is also a reporter in Russia, nodded and said: "Yes, I have been here several times before, and I have never seen the seats here be full."
He looked around the entire venue and said with emotion: "There are all high-level intellectuals here, all math masters."
"This is the International Congress of Mathematicians, and of course all the people here are mathematicians."
Later, the webmaster of the correspondent station in Russia, Tu Chengyu, said, "Chen Xiaoming, I remember you got a bachelor's degree in mathematics when you were in college."
Chen Xiaoming suddenly felt embarrassed: "Hey, Boss Tu, don't mention this kind of thing. I haven't studied mathematics for many years."
"At the beginning, I thought I had some talent in mathematics. After all, I got full marks in mathematics in the college entrance examination. After studying it for four years, I thought it was better to give up as soon as possible. After that, I went to Russia to study abroad and changed to study Finance."
Hearing Chen Xiaoming's words, the other two people couldn't help but become curious: "Then how did you become a reporter?"
"Isn't this because I learned Russian while studying abroad in Russia?" Chen Xiaoming shrugged: "As for finance in Russia... I can only say that it is only theory."
Tu Chengyu and Cao Yang looked at each other, and couldn't help laughing in the end. Indeed, finance is something that can only be used in places with relatively developed economies, and the prerequisite is that there are enough connections in the family or assets.
Otherwise, it means that everyone understands it.
Chen Xiaoming immediately sighed: "So, the majors studied in university often have nothing to do with the final job."
"I really envy people like Li Mu."
Cao Yang and Tu Chengyu both nodded in agreement and expressed their approval.
People who can display their talents in college majors can indeed be envied.
The three people were chatting. At this time, a Russian reporter suddenly asked them: "Are you reporters from China?"
The three people turned to look, and then nodded: "Yeah, what's the matter?"
The Russian reporter gave them a thumbs up and said: "A truly great mathematician has appeared in your country."
"There used to be a lot of them in our country, especially in the last century, but now, they are becoming less and less."
The three reporters were stunned by the sudden compliment, but of course, they all smiled afterwards.
"Thank you for the compliment, but no matter what, your country's mathematics is still very strong. At least, you still have great mathematicians like Gregory Perelman."
"Perelman..." When the Russian reporter heard this name, he shook his head helplessly: "Although he is indeed our pride, but now he..."
Suddenly, the Russian reporter's eyes widened and he looked towards the entrance of the venue: "Wait... is that Perelman?"
Cao Yang and the other three were stunned. Following his gaze, they immediately noticed a bearded man walking in from the entrance.
As long as they are in the mathematics community, almost no one will be unfamiliar with this thick, somewhat slovenly beard.
This is the prover of the Poincaré Conjecture, Gregory Perelman!
For a moment, the entire venue became noisy because of Perelman's entry.
Of course, although people are talking about these mathematics masters who have claimed to have left the mathematics world, no one has taken the initiative to talk to him. After all, everyone can basically guess that Perelman probably does not want to talk to anyone. People have too much communication.
Therefore, people were just amazed that Li Mu's report could actually attract him.
In this way, the arrival of Perelman brought the atmosphere of this report to a new peak again.
"That is to say, no matter how much Perelman breaks away from the world of mathematics, he cannot remain indifferent to the proof of such an important conjecture."
Wiles, who was sitting in the front row, shook his head and said.
Seeing Perelman standing alone in a corner at the back, he sighed with emotion: "But, why is it like this?"
He should have been sitting in the same seat as them, not alone in the back.
Faltings just said expressionlessly: "It's all a personal choice. We don't need to comment too much. His willingness to come shows that he is still sincere about mathematics. This is enough."
Wiles smiled and nodded: "That's true."
"Then let's look forward to what kind of surprises Li Mu can bring us next."
They all looked towards the stage.
The PPT on the big screen has been opened.
Above, the theme of this report is displayed.
[Proof: Existence and smoothness of solutions to the Navier-Stokes equation]
Listed below this topic is the general form of the Navier-Stokes equation.
Today, will this mathematical problem that has been circulating in the mathematics and physics circles for many, many years come to an end?
…
The time came to half past nine.
According to the time plan, this time is the time when the report starts.
Footsteps sounded from the background.
The figure that appeared was none other than Li Mu.
There was no host who came on stage first to control the scene.
However, even if no one was controlling the scene, as Li Mu appeared on the stage, the originally noisy voice in the audience immediately fell silent.
More than four thousand, nearly five thousand pairs of eyes were looking at him closely.
It is he who will prove the problem of the century today.
"Hello everyone, my name is Li Mu."
Looking at the number of people in the audience, there were even more people than in his second report a few days ago.
He smiled and said: "First of all, I would like to thank the International Congress of Mathematicians and the International Mathematical Union for extending a day for me so that my third report can still appear at the conference."
"Of course, I am also very grateful to everyone who is willing to take the trouble and change their schedule to attend my report."
"Therefore, I will not disappoint everyone's expectations and repay everyone by revealing the truth."
Immediately, he turned around and walked to the big screen.
"Then let's stop talking nonsense and let this report officially begin."
"As I predicted before, in this report, I will prove to everyone the existence and smoothness of the solution to the Navier-Stokes equation."
PPT a little and go to the next page.
The content of this ppt page is like an outline, showing in detail the complete steps of his proof process.
This may be a bit incomprehensible to ordinary scholars, but for the real experts, it has an enlightening effect.
Experts can directly deduce the derivation process of the entire paper through the abstract of a paper, and this kind of thing is naturally not a problem.
"First use the integrated space after partial differentiation to spatially constrain the particles of the fluid, and then process the fluid viscosity coefficient of the Navier-Stokes equation to deal with the time explosion problem..."
Tao Zhexuan said in a daze.
Until finally, he suddenly reacted.
"Wait a minute...that's how he solved the problem of explosion time!"
Explosion time, of course, does not mean that time explodes, but that in the process of trying to prove the existence and smoothness of the solution to the NS equation, the time term often increases, resulting in the originally regular fluid, Suddenly it exploded at some point.
The simplest description is that without the influence of external forces, such as the huge impact caused by the sudden fall of a meteor, the originally calm sea surface suddenly exploded.
Just like all the particles in sea water, at a certain moment, the internal force will suddenly no longer be chaotic and uniform everywhere, but suddenly have a neat direction, so the uniform force everywhere becomes suddenly The huge pressure rises, causing the fluid to explode.
In this profession, this is also called blow-up time.
This problem has always existed in the study of NS equations, giving all researchers a headache. For example, Tao Zhexuan published a paper precisely to study this problem, but he also did not solve it well. question.
But now, there is no doubt that Li Mu has solved it.
In fact, after reading the outline he listed, Tao Zhexuan and others understood it.
"Yes... the integrated space is really perfect. It can perfectly eliminate internal pressure and balance the various interactive forces between particles."
Deligne also nodded deeply.
"Should have realized this a long time ago. "
…
These big guys couldn't help but cheer for Li Mu's step in their hearts.
And Li Mu on the stage could roughly guess what the audience was thinking.
When this biggest problem is solved, the subsequent problems will become very convenient.
But, what was the process before this?
"Integrating space can not only completely integrate an entire area of fluid, but in the same way, we must never forget the method of differentiation."
"We can also divide this entire area into countless small areas, and then integrate these small areas. This is also the idea reflected in the Boltzmann equation."
"Then, next, we start to substitute into the general form of the Navier-Stokes equation and start to use the method I just mentioned - I would like to call it global differential..."
Li Mu came to the blackboard and began to write the following steps on it.
Everyone in the audience was looking at what he wrote attentively, and they were also interested in what he just said, dividing the entire area into countless small areas, and then analyzing the overall space.
They could hear that this was obviously an application of integrated space.
This is exactly what they hope to learn.
However, as Li Mu started writing, everyone was amazed.
This integrated differential method is really a bit too impressive in terms of technical difficulty.
In terms of Go, it is a masterful move, in terms of piano music, it is Rachmaninov's Third Piano Concerto, and the violin music is Paganini's 24th Caprice.
Such technical difficulty...
They had to marvel, Li Mu was still the same Li Mu!
Just like several other conjectures he had proved.
Of course, the momentary exclamation did not affect them from following Li Mu's steps and continuing to think.
After completing this part, everything below seems to become clearer.
When the general form of the NS equation is described in the integrated space, the irregular problems of turbulence seem to become obvious.
What the NS equation attempts to describe is turbulence. Rapid rivers, rolling storm clouds or smoke from chimneys, etc., are all turbulent flows. This is also a problem that fascinates various scholars.
For example, Werner Heisenberg, the famous physicist who proposed the Heisenberg Uncertainty Principle, was once asked what question he would most like to ask God if he went to heaven after death. He replied: "When I meet God, I will ask Him two questions: Why relativity? Why turbulence? I believe He will only answer the first question."
This means that God probably cannot answer the second question.
So, can Li Mu take this issue a step further to a certain extent?
…
The blackboard was gradually filled with writing.
It was full of formulas that were like a book from heaven, making many listeners in the audience feel drowsy for a while.
Those who participated in Li Mu's first report and were surprised that they could actually understand his report could only smile bitterly, knowing that they were still too young.
It wasn't that they understood Li Mu's report, but that Li Mu made it possible for them to understand the report.
In this way, about forty minutes passed.
According to the previous normal one-hour report, the report was almost over in more than 40 minutes, but obviously everyone present knew that the current report was only half over, maybe not yet——
When Li Mu completed the finishing touches on the blackboard, he turned around and said, "Now, I have completely controlled every part of the fluid within the integrated space."
"When we process the timeline here, we can find that no matter how the timeline changes, blow-up time will no longer appear."
"In other words, in the past, the explosion time problem we faced was completely solved."
"So--"
As Li Mu's voice fell, the PPT page moved again, and a statement appeared on it.
People in the mathematical community are very familiar with this statement.
[In three-dimensional space and time, given an initial velocity field, there is a vector velocity field and a scalar pressure field, which are the solutions to the Navier-Stokes equation, where the velocity field and pressure field need to satisfy Smooth and globally defined properties. 】
"This statement, I think everyone knows, is the Clay Institute's complete statement on the existence and smoothness of solutions to the Navier-Stokes equation in the seven millennium problems."
"Then, return to equation 3.3."
Li Mu pointed to the blackboard. He was talking about the combination of NS equations and integrated space.
"From here, I will prove the existence of this velocity field and pressure field."
"Of course -" Li Mu smiled slightly: "I think everyone can basically see the next steps."
Ninety-nine percent of everyone: "?"
They saw a ghost!
They haven't seen anything since probably dozens of minutes ago.
In the end, they could only acquiesce that the people Li Mu mentioned were actually the "mathematical experts" sitting in the front rows.
Of course, the big guys in the front rows were indeed relieved at this time.
The next steps are indeed obvious.
"In the integrated space, NS equations become so simple."
"That is to say, we still cannot avoid the second-order derivative term, and we cannot obtain an exact solution."
"What are you thinking about... As long as we can prove the existence of the solution, we should wait until we die to ask God about the precise solution."
"Whether God knows or not is hard to say."
Deligne and others shook their heads and sighed.
It was exactly as they thought. Li Mu didn't even give much explanation on the next steps and just started writing them without any hindrance.
There may still be some problems that ordinary people cannot understand, but for Li Mu, these problems are not problems.
Until the blackboard is erased and filled with writing again——
"...It has been verified that the velocity field and pressure field are both smooth."
"So, I think the final result has come out. In three-dimensional space and time, there is indeed a smooth vector velocity field and a scalar pressure field that satisfies the global definition, which is the Navier-Stokes Solution of the equation."
Having said this, Li Mu also put down the pen in his hand and walked to the front of the podium.
"The undulating waves follow our boat as it meanders across the lake, and the turbulent air follows the flight of our modern jet aircraft."
"Both mathematicians and physicists are convinced that both breezes and turbulence can be explained and predicted by understanding the solutions to the Navier-Stokes equations."
"And now."
"If my proof process is rigorous enough and there are no possible contradictions or errors in theory before and after."
"So I think what we know now is that there is indeed a smooth solution to the Navier-Stokes equation."
"With this, we are one step closer to understanding turbulence."
"Some people say that God may not know why there is turbulence."
"But I think we mathematicians and physicists will eventually know!"
Lean your upper body slightly forward.
Applause then burst out like an explosion.
The Blow-up time of the NS equation is over, but the Blow-up time belonging to Li Mu has begun again!
(End of chapter)
