The blackboard in this large conference room is large enough for any mathematician to write down enough equations on it.
I heard that this was also specially prepared by the St. Petersburg International Conference Center for this International Congress of Mathematicians.
For Li Mu, this huge blackboard is just what he wants.
As time passed, he had written nearly three-quarters of this huge blackboard.
The rigorous derivation process made it impossible for any mathematical expert in the field to find any points to question, or even to find fault with the eggs.
【f/t+P/m·▽f+F……】
When the last equation filled the last blank space on the blackboard, Li Mu turned around, faced the audience present, and said, "At this point, we can integrate the collision terms."
"And collision is the most critical element in fluid mechanics."
"All the complexity of a fluid is based on the various collisions of particles within it."
"Like a chaos model, what we want to do is to trace the changes in the fluid through these collisions."
"This is extremely important for the internalization of external force sources into space."
"The shortcoming of the internalization of external force sources is the integration of internal forces. Using the Boltzmann equation, we can make up for this problem."
"But obviously, it is impossible to directly integrate the Boltzmann equation, an integral and differential equation, into it. So how do we deal with the Boltzmann equation?"
Li Mu smiled slightly, and under the gaze of everyone, he first began to erase the front part of the blackboard, and then began to write.
"Wait...is this a Fourier transform?"
After seeing what Li Mu wrote next, the people below all showed incredible expressions. They could never imagine that Fourier transform could be used here!
However, this is the case with mathematics. Before the method is revealed, those who cannot imagine it will never be able to imagine it anyway.
And once the method is revealed, it will bring about a sudden enlightenment.
Now, except for Li Mu, all the other mathematicians in this venue suddenly realized.
As Li Mu continued to write, his thoughts gradually emerged.
Faltings in the audience squinted his eyes. With each step of Li Mu's writing, he nodded his head from time to time, obviously expressing his approval.
On the side, Terence Tao began to serve as the official commentator: "This is... number theory thinking."
"He actually used number theory methods to deal with the Boltzmann equation..."
"Incredible, unimaginable. Although it is true that the method of number theory can be used to deal with some problems in statistical physics, I never imagined that it can also be used to change the Boltzmann equation!"
"I can't believe it."
He couldn't stop shaking his head.
Wiles, who was separated by a Faltings from him, said with a smile: "After all, Li Mu is now known as the Emperor of Number Theory. It is not surprising for him to use number theory ideas to solve problems."
Tao Zhexuan sighed: "Sometimes I really can't imagine how his mind is made. Is there a quantum computer hidden in it?"
"Maybe?" Wiles also joked.
Of course, it's just a joke.
After all, who has a computer inside their head?
Do you believe it?
I do not believe.
…
Time passed quickly as the report was told.
Until the blackboard was filled up for the second time, Li Mu's hand stopped again - of course, he was able to fill the blackboard exactly every time, basically because he could use the computer in his mind to follow the layout of the blackboard. And estimate the content he wants to write to control the size of the text he writes and the gaps between lines.
Turn around.
"At this point, the main content of this report has been covered."
"The external force source internalizes the space and successfully integrates with the Boltzmann equation."
"For this new space, I think it is more appropriate to call it an integrated space."
Li Mu said with a smile.
Then, he opened his hands and said, "Then that's it."
In the audience, after many viewers came to their senses from his narration, the applause gradually started to ring out, gradually moving from the low point to the climax.
"Pa bang bang~"
At this time, everyone in the audience was excited about Li Mu's integrated space.
If the previous internalized space of external force sources can bring surprises to researchers in fluid mechanics, then this integrated space is like a favor given to them by God - of course, this God refers to here. It can only be Li Mu.
The internalization of external force sources into space can greatly reduce the difficulty of data processing and reduce the amount of data they have to process, which is of great significance for the application of fluid mechanics.
The current integrated space can further reduce the amount of data processed and at the same time help them greatly improve the accuracy of data processing.
This is of great significance for direct numerical simulation of DNS in fluid mechanics analysis.
Therefore, for this group of experts, their eyes seem to be shining when they look at Li Mu now.
However, the difference is that the experts sitting in the front row, especially those who study the Navier-Stokes equation, do not study direct numerical simulation of DNS, because DNS is a purely applied mathematics method. .
And they can see something different from this integrated space.
"Wait...can you see something else coming out of this integrated space?"
Tao Zhexuan squinted his eyes and said: "If we make some changes to this integrated space, such as partial differentiation of the collision part..."
"It can be used directly on the Navier-Stokes equation."
Faltins next to him gave the answer.
"Yes." Terence Tao nodded slightly: "Then..."
"then……"
Suddenly, he opened his eyes wide and realized it completely.
"Then we can prove the existence and smoothness of the solution to the NS equation!"
As a mathematician who has made a very important and successful work on the Navier-Stokes equation, Terence Tao has done a lot of research on this issue, so he can easily see the role of integrated space in this. .
It was not just him who was also aware of this matter, but the other people sitting around him, Faltings, Wiles, Deligne, and Laurent Laforgue and Pierre- Louis Lion, all the same.
Laurent Laforgue said: "It should be impossible for Li Mu not to see this...So, maybe he is really close to solving the problem of NS equation."
Leon was silent for a moment and said, "Is there a possibility that he has already solved it?"
At this time, the applause around him gradually stopped. Li Mu on the stage smiled slightly, and then continued: "Then, I will give a preview for my next report."
After flipping through the content on the PPT, I came to the content he had previewed.
The big guys in front opened their eyes wide when they saw the content of this trailer.
Obviously they were right. Not only did Li Mu see it, but he also accomplished it to a far greater extent than they imagined!
To a certain extent, Li Mu’s purpose is already obvious - it is the seven major mathematical problems of the millennium, the last piece of the puzzle in classical physics, [Proof: The existence of solutions to the Navier-Stokes equation Sex and smoothness]!
In the audience, those who reacted a little slower gradually saw it after being slow for a while, and then became stunned.
After a moment of silence, the venue gradually erupted into bursts of uproar and discussion.
Although this report is not completely over yet, these scholars who are aware of it are already unable to restrain themselves.
That is one of the seven major mathematical problems of the millennium, the Nass equation problem!
To a certain extent, the number of mathematicians studying this problem can be said to be the largest among the seven major problems.
In this way, with the uproar and discussions, even those students or ordinary scholars who did not understand what Li Mu's trailer meant, they all understood the reasons from those discussions, which brought about A wider range of vibrations.
It has been rumored that Li Mu may have proved the NS equation problem. How come it became true after it was spread around?
Li Mu, who was on the stage, said at this time: "After I discovered the integrated space, a very obvious thing happened - the integrated space can be integrated with the Navier-Stokes equation."
“So, I performed partial differential treatment on the collision terms in the totalized space, and then something magical happened.”
"The whole NS equation has become very refined."
"And in this way, the original complexity of the NS equation will become traceable."
"Then, the topic of my next report is——"
Speaking of this, Li Mu paused, and then completely showed his cards: "The existence and smoothness of the solution to the Navier-Stokes equation!"
…
[Li Mu has proved the smooth solution of the NS equation? 】
[Li Mu solved another millennium problem? 】
[The mathematical conjecture crusher is at work again! 】
As Li Mu's Fields Medal lecture ended, overwhelming news spread throughout the mathematics community.
The proofs of the seven major mathematical problems of the millennium are destined to cause an earthquake in the entire mathematical world.
Almost not long after Li Mu's report ended, those mathematics scholars who had not come to the scene of the international mathematicians learned the news, which immediately aroused various voices of annoyance. They actually missed such a report!
Of course, the only good thing is that the report proving the existence of smooth solutions to the NS equation has not officially started yet. Li Mu just advertised his next report, but did not indicate when his next report will start. .
However, as of now, there is obviously no time for his report at the International Congress of Mathematicians.
This year's International Congress of Mathematicians started on the 6th and ended on the 14th, and on the 10th, Li Mu had already given two reports, two one-hour plenary reports.
Such treatment is extremely rare in the entire history of the International Congress of Mathematicians.
So, where will his next report be held?
While mathematicians around the world were speculating, the International Mathematical Union and the organizing committee of this International Congress of Mathematicians also hurriedly held several meetings.
The topic discussed in these meetings is whether to extend the current International Congress of Mathematicians for one day, specifically for Li Mu to give his third report, which is also the most critical report.
The results of the discussion on this issue are also very obvious.
The International Congress of Mathematicians cannot lose such an important report, just like the 3D Zone, ahem... just like the West cannot lose Jerusalem.
As the most important conference in the field of mathematics, the International Congress of Mathematicians certainly hopes that such a historic moment can happen during the conference——
So, "Professor Li Mu, on behalf of the International Mathematical Union and the organizing committee of this International Congress of Mathematicians, I sincerely invite you to give another report."
"We hope that you can show everyone in this report how you proved the existence and smoothness of the solution to the Navier-Stokes equation."
In the hotel room where Li Mu was staying, Carlos Koenig, the chairman of the International Mathematical Union, personally came to the door and invited him.
"As you predicted at the end of your last report."
"This is very important to the International Congress of Mathematicians. We also believe that more than 4,000 mathematics scholars from all over the world who are in St. Petersburg are looking forward to your report. "
"I wonder what you mean?"
Koenig's attitude was sincere.
Faced with Koenig's invitation, Li Mu laughed, and then said: "Chairman Koenig, you are serious. It is also my wish to complete my third report at the International Congress of Mathematicians. After all, This can be regarded as having a beginning and an end.”
When he heard that Li Mu agreed, Koenig immediately became happy: "That's great! Thank you Professor Li for agreeing."
"We, the Board of Directors of the International Mathematical Union and the organizing committee of this International Congress of Mathematicians have made a decision to schedule this report on the morning of July 15th. What do you think?"
Li Mu raised his eyebrows: "I remember that on July 14th, the International Congress of Mathematicians was already over."
Koenig smiled and said: "We have decided to extend this conference by one day. The closing ceremony and dinner will be held after the afternoon of July 15th, that is, after the end of your report."
"Your report will be the last item before the closing ceremony."
Li Mu's face showed surprise.
In the end, the International Congress of Mathematicians was extended for one day specifically for his report!
The International Congress of Mathematicians has been extended by one day because of one person. In the history of the International Congress of Mathematicians, this has been held since 1897 and can be regarded as one of the oldest academic conferences in the world. This is considered a first time.
At best, he thought that his third report would be scheduled for a certain night.
As a result, the current treatment... is beyond the standard.
…
Koenig left and returned with the news. Obviously, he would then inform the outside world of this matter on behalf of the International Congress of Mathematicians.
Of course, such an important matter must be notified to all participants, as well as those who did not attend.
At the same time, Wiles was always beside Li Mu in his room.
After Koenig left, Wiles exclaimed to Li Mu, "You did it."
"The International Mathematical Union has given you this face!"
Li Mu smiled slightly, this kind of thing was expected.
"The first scholar in history to give three lectures at an International Congress of Mathematicians."
"He is also the first scholar in history to have the International Congress of Mathematicians extended for one day."
"Incredible."
Wiles shook his head, "Oh, by the way, I almost forgot, you also proved a Millennium Problem, but this is the second one."
Li Mu immediately couldn't laugh or cry: "My paper hasn't been released yet, how can I be sure that I have completed the proof?"
Wiles shrugged his shoulders and said: "Although mathematics is realism, not empiricism, in this matter, empiricism prevails."
Then he waved his hand: "Okay, I won't disturb you anymore. In a few days, you will start your report of the century. I'm already waiting."
Then, he turned around and left Li Mu's room.
But when he went out, he met Terence Tao, Deligne and others who were also staying in the hotel.
They saw Wiles actually walking out of Li Mu's room, and then they remembered the news that Koenig had revealed to them when they met him just now.
Several people immediately pointed at Wiles and said, "Wiles! You still said you didn't know that Li Mu proved the NS equation!"
At this time, Wiles stopped pretending and showed off his cards. He put his hands on his hips and said arrogantly: "Yes, that's right, I knew it a long time ago!"
…
With Koenig's return, the International Congress of Mathematicians was extended by one day and Li Mu's third lecture was held on July 15, which quickly spread throughout the mathematics community.
Today is July 11th, and basically there are less than four days left.
The news has spread, and the mathematics community is in a state of panic. Mathematics scholars who have booked a flight to leave St. Petersburg on July 15 immediately begin to change their bookings, while those who have not come to St. Petersburg have begun to make reservations one after another. Same day flight to St. Petersburg.
With such little time, they had to hurry up to catch up with Li Mu's report.
No one wants to miss the solution to a major problem, such as the hail conjecture, the twin prime conjecture and Goldbach's conjecture, especially the Navier-Stokes equation.
Just like that, time passed quietly.
July 15th is here!
…
(End of chapter)
