Ultimate Scholar

The blackboard in this large conference room is large enough for any mathematician to write enough equations on it.

I heard that this is 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.

With the passage of time, nearly three-quarters of this huge blackboard has been written by him.

The rigorous derivation process made it impossible for any of the mathematics masters off the field to find anything to question, or even pick a bone in the egg.

[f/t+P/m·▽f+F……]

When the last formula 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 items."

"Collision is the most critical element in fluid mechanics."

"All the complexity of fluids is based on various collisions of internal particles."

"Like a chaotic model, what we want to do is to analyze the changes of the fluid through these collisions."

"This is extremely important for the internalization of external force sources."

"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, an integral-differential equation like the Boltzmann equation cannot be directly integrated into it, so how do we deal with the Boltzmann equation?"

Li Mu smiled slightly. In the eyes of everyone, he first erased 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 showed incredible expressions. They could never have imagined that the Fourier transform could be used here!

However, mathematics is like this. When the method has not been revealed, people who cannot imagine it will always be unable to imagine it anyway.

And once the method is revealed, it will bring about a sudden realization.

Now in this venue, except for Li Mu, the other mathematicians suddenly realized.

As Li Mu continued to write down, his train of thought was gradually revealed.

Faltings in the audience squinted his eyes, and as Li Mu wrote every step, he nodded his head from time to time, obviously expressing his approval.

On the side, Tao Zhexuan began to act as the official commentator: "This is... the thinking of number theory."

"He actually used number theory methods to deal with the Boltzmann equation..."

"It's unbelievable, it's unimaginable. Although the method of number theory can indeed be used to deal with some problems in statistical physics, I have no idea that it can be used to change the Boltzmann equation!"

"I can't believe it."

He couldn't stop shaking his head.

There was a Faltings between him and Wiles 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 to solve problems."

Tao Zhexuan sighed: "Sometimes I really can't imagine how his mind was made. Could it be that there is a quantum computer hidden inside?"

"Maybe?" Wiles also joked.

Of course, it was just a joke.

After all, who has a computer in their head?

Do you believe it?

I do not believe.

...

Time passed quickly as the report narrated.

Until the blackboard was filled for the second time, Li Mu's hand stopped again—of course, he was able to fill the blackboard just right every time, basically because he was able to use the computer in his mind to calculate the layout of the blackboard, And estimate what you want to write to control the size of the text he writes and the gap between lines.

turn around.

"At this point, the main content of this report is all finished."

"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 audiences came back to their senses from his narration, the applause also gradually sounded, from low tide to high tide.

"Pa bang bang~"

At this moment, everyone in the audience was excited about Li Mu's integrated space.

If the previous internalization of external force sources can bring surprises to the researchers of fluid mechanics, then this integrated space is like a gift from God to them-of course, this God refers to It can only be Li Mu.

The internalization of external force sources can greatly reduce the difficulty of data processing and reduce the amount of data they have to process, which has a great effect on 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 to the direct numerical simulation of DNS in fluid mechanics analysis.

Therefore, for this part of the experts, their eyes seem to be shining when they look at Li Mu now.

However, the difference is that the big cows sitting in the front row, especially those who have studied the Navier-Stokes equation, they do not study the direct numerical simulation of DNS, because DNS is a purely applied mathematical method .

And they can see some different things 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 holistic space, for example, if we make some partial differentials on the collision part..."

"It can be directly applied to the Navier-Stokes equation."

Faltings next to him gave an answer. \b

"Yes." Tao Zhexuan nodded slightly: "Then..."

"then……"

Suddenly, he opened his eyes wide, fully aware of it.

"Then it can be proved that the existence and smoothness of the solution of the NS equation!"

As a mathematician who has made a very important success on the Navier-Stokes equation, Terence Tao's research on this problem is quite deep, so he can easily see the importance of the overall space on it. effect.

It is not only him who is also aware of this matter, but the other people sitting around him, Faltings, Wiles, Deligne, and Laurent Laphrogue and Pierre- Louis Leon, all of them.

Laurent Laphrogue said: "It is impossible for Li Mu not to see this... So, maybe he is really close to solving the problem of the NS equation."

Lion was silent for a moment, and said, "Is there a possibility—he has already solved it?"

At this time, the applause around gradually stopped, and Li Mu on the stage smiled slightly, and then continued: "Then, I will make a preview for my next report."

After flipping through the content on the PPT, he came to the content he had previewed.

The big cows in front of them all opened their eyes wide when they saw the content of the trailer.

Obviously they were not mistaken, not only did Li Mu see it, but the degree of completion was far more profound than they imagined!

To a certain extent, Li Mu's purpose has been clearly revealed - that is the seven major mathematical problems of the millennium, the last piece of the puzzle in classical physics, [Prove: the existence of solutions to the Navier-Stokes equations] sex and smoothness]!

In the audience, those who reacted a little slower gradually noticed it after being dull for a while, and then became dumbfounded.

After a moment of silence in the venue, there was gradually a burst of uproar and discussions.

Although this report is not yet completely over, these aware scholars have been somewhat unable to restrain themselves.

That is the Nass equation problem, one of the seven major mathematical problems of the millennium!

To some extent, the mathematicians who study this problem can be regarded as the most of these seven problems.

In this way, with the uproar and discussions, even those students or ordinary scholars who didn't understand what Li Mu's notice revealed, they all understood the reason from those discussions, which brought a wider range of vibrations.

It has been rumored that Li Mu may have proved the problem of the NS equation, how can it become true after it is circulated?

And Li Mu on the stage said at this time: "After I discovered the holistic space, a very obvious thing appeared—the holistic space can be integrated with the Navier-Stokes equation."

"So, I partially differentiated the terms of the collision in the global space, and then something magical happened."

"The NS equation as a whole has become very refined."

"In this way, the original complexity of the NS equation will become traceable."

"Then, the subject of my next presentation will be—"

Speaking of this, Li Mu paused, and then completely showed his cards: "The existence and smoothness of the solution of the Navier-Stokes equation!"

...

[Li Mu has already proved the smooth solution of NS equation? 】

【Li Mu solved another millennium problem? 】

[Mathematical conjecture crusher is working again! 】

With the end of Li Mu's Fields Medal lecture, overwhelming news spread throughout the entire mathematics community.

The proof of the seven major mathematical problems in the millennium is destined to set off an earthquake in the entire mathematics world.

Almost not long after Li Mu's report ended, the mathematicians who did not come to the international mathematician site heard the news, and immediately attracted all kinds of annoyed voices. They actually missed such a report!

Of course, the only thing to be thankful for is that the report proving the existence of smooth solutions to the NS equation has not yet officially started. Li Mu just advertised his next report, but he did not specify when his next report will start .

However, as far as the current situation is concerned, the International Congress of Mathematicians obviously has no time for him to report.

This year's International Congress of Mathematicians started on the 6th and ended on the 14th, and on the 10th, Li Mu had 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 all over the world were guessing, the organizing committee of the International Mathematical Union and the International Congress of Mathematicians hastily held several meetings.

And the topic discussed in these several meetings is whether to extend this International Congress of Mathematicians by one day, and provide it exclusively to Li Mu for 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 mathematics world, the International Congress of Mathematicians certainly hopes that such a historic moment will 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 invite him. \b

"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 mathematicians from all over the world are looking forward to your report in St. Petersburg."

"I don't know what you mean?"

Koenig's attitude is very sincere.

Facing Koenig's invitation, Li Mu laughed, and then said: "Chairman Koenig, you are too serious, it is also my wish to complete my third report at the International Congress of Mathematicians, after all , so it can be regarded as a beginning and an end.”

Hearing that Li Mu agreed, Koenig immediately became happy: "That's really great! Thank you Professor Li for agreeing."

"Our Council of the International Mathematical Union and the Organizing Committee of the International Congress of Mathematicians have made a decision to arrange this report on the morning of July 15th. What do you think?"

Li Mu frowned: "I remember that the International Congress of Mathematicians had already ended on July 14."

Koenig said with a smile: "We have decided to extend this conference by one day. The closing ceremony and dinner will be held after the afternoon of July 15th, which is after your report is over."

"Your report will be the last project before the closing ceremony."

Li Mu showed surprise on his face. \b

In the end, the International Congress of Mathematicians was extended for one day just for his report!

The time of the International Congress of Mathematicians was extended by one day because of one person. In the history of the International Congress of Mathematicians, this has been held since 1897, and it can be regarded as one of the oldest academic conferences in the world. It is the first time.

At most, he thought that his third report would be scheduled for a certain night.

As a result, the current treatment... can be said to be beyond the standard.

...

Koenig left and returned with the news. Obviously, he will inform the outside world on behalf of the International Congress of Mathematicians next.

Such an important matter must of course be notified to all participants, as well as those who did not attend.

At the same time, in Li Mu's room, Wiles was always by his side.

After Koenig left, Wiles exclaimed to Li Mu and said, "You did it."

"The International Mathematical Union gave you this face!"

Li Mu smiled slightly, such a thing was expected.

"The first scholar in history to give three reports at one International Congress of Mathematicians."

"It is also the first scholar in history to have the International Conference of Mathematicians extend it by one day."

"Unbelievable."

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 didn't know whether to laugh or cry: "My thesis hasn't been released yet, how can you be sure that I have completed the proof?"

Wiles shrugged his shoulders and said: "Although mathematics is realism, not empiricism, but in this matter, empiricism has the upper hand."

Then he waved his hand: "Okay, I won't bother you anymore. In a few days, you will start your report of the century. I have already waited for it."

Then, he turned around and left Li Mu's room.

It's just that when he went out, he ran into Tao Zhexuan, Deligne and others who also lived in this hotel.

They saw Wiles come out of Li Mu's room, and then remembered the news that Koenig had revealed to them when they met Koenig just now.

Several people immediately pointed to 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 had a showdown. With his hips on his hips, he 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 15th, and it spread rapidly throughout the mathematics community.

Today is July 11th, basically there are less than four days left.

The news had spread, and the mathematics world was in a state of panic. The mathematicians who had already booked the flight to leave St. Petersburg on July 15 immediately began to change their bookings, and those who did not come to St. Petersburg began to book one after another. Airfare to St. Petersburg for the day.

With such a short amount of time, they had to hurry up to catch up with Li Mu's report.

No one wants to miss the solution of a major problem. This is true of the Hail conjecture, the twin prime conjecture, and the Goldbach conjecture, and the Navier-Stokes equation is even more so.

In this way, time passed quietly.

July 15th, here we come!

...