The blackboard in this large conference room is large enough for any mathematician to write down enough formulas 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 exactly what he wants.

Over time, he had written nearly three-quarters of the vast blackboard.

The rigorous derivation process made it impossible for any math master in the field to find a point to question, and he couldn't even pick a bone from the egg.

【f/t+P/m·▽f+F……】

When the last formula filled the last blank space of the blackboard, Li Mu turned around and faced the audience, and said, "At this point, we can integrate the collision items." ”

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

"All the complexity of a fluid is based on the various collisions of the particles inside."

"It's like a chaotic model, and what we want to do is to analyze the changes in the fluid traceably through these collisions."

“这对于外力源内化空间来说，极为的重要。 ”

"The shortcoming of the internalization space of external force sources is the integration of internal forces, and we can make up for this problem by using the Boltzmann equation."

"But obviously, the Boltzmann equation, such as a quadratic differential equation, cannot be directly integrated into it, so what do we do with the Boltzmann equation?"

Li Mu smiled slightly, and in the eyes of everyone, he first began to erase the front part of the blackboard, and then began to write.

"Wait...... Is this the Fourier transform? ”

When they saw what Li Mu wrote next, the people below all showed incredible expressions, they couldn't imagine that they could use the Upper Fourier Transformation here!

However, mathematics is like this, and when the method has not yet been revealed, the person who can't imagine it will only never be able to imagine it anyway.

And once the method is revealed, it brings a kind of sudden realization.

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

As Li Mu continued to write downward, his thoughts gradually revealed.

Faltins squinted his eyes in the audience, and as Li Mu wrote out every step, his head nodded from time to time, obviously expressing his agreement.

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

"He actually used number theory to deal with Boltzmann equations......"

"It's incredible, it's hard to imagine, although the method of using number theory can indeed deal with some problems in statistical physics, I can't imagine that it can be used to change the Boltzmann equation!"

"I can't believe it."

He couldn't stop shaking his head.

Wiles, who was separated from him by a Faltins, said with a smile: "After all, Li Mu is now known as the Emperor of Number Theory, and it is not strange for him to use the idea of Number Theory to solve problems. ”

Tao Zhexuan sighed: "Sometimes I really can't imagine how his mind is done, is there a quantum computer hidden in it?" ”

"Maybe?" Wiles followed suit.

Of course, it's just a joke.

After all, who has a computer in their head?

Do you believe it?

I don't believe it.

……

Time flew by as the report spoke.

It wasn't until the blackboard was filled for the second time that Li Mu's hand stopped again - of course, he was able to fill the blackboard exactly every time, basically because he was able to use the computer in his mind to estimate the layout of the blackboard and the content he wanted to write, so as to control the size of the text he wrote and the gap between lines.

Turn around.

"At this point, the main content of this report has been fully covered."

"The external force source internalized the space and successfully completed the integration with the Boltzmann equation."

"For this new space, I think it's more appropriate to call it a holistic space."

Li Mu said with a smile.

Then, his hands spread out, and he said, "Then that's it." ”

In the audience, after many audiences came back to their senses from his narration, applause gradually rang out, gradually moving from the low tide to the climax.

"Papapa~"

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

If the previous external source of internalized space can bring surprises to researchers of fluid mechanics, then this holistic space is like a blessing from God to them - of course, this God can only refer to Li Mu here.

The internalization space 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 overall 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 the direct numerical simulation of DNS in fluid mechanics analysis.

Therefore, for the experts in this part, their eyes now look at Li Mu as if they are glowing.

However, the big guys in the front row, especially those who have studied the Neville-Stokes equations, do not study direct numerical simulations of DNS, because DNS is purely mathematically applied.

And they can see something different from this holistic space.

"Wait...... Can you see something else coming out of this holistic space? ”

Tao Zhexuan squinted his eyes and said, "This integral space, if you change it again, such as the part about collision in it, do it differentially......

"You can use it directly on the Neville-Stokes equation."

Faltins, who was next to him, gave an answer.

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

"And then ......"

Suddenly, his eyes widened and he was completely aware.

"Then we will be able to prove the existence and smoothness of the solution of the NS equation!"

作为在纳维尔-斯托克斯方程上面做出过一份相当重要成功的数学家，陶哲轩对于这个问题的研究不可谓不深，所以他很容易就能够看出来整体化空间在这上面的作用。

He was not the only one who was aware of this, but the other people sitting around him, Faltins, Wiles, Deligne, and Laurent Laphguet and Pierre-Louis Lyon.

Laurent Laphguer said: "It should be impossible for Li Mu not to see this...... So, maybe he's really close to solving the NS equation. ”

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

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

The content on the PPT flipped over and came to the content of his preview.

When the big bulls in front saw the content of this preview, their eyes immediately widened.

Obviously, they were not wrong, Li Mu not only saw it, but also completed it to a deeper extent than they imagined!

To some extent, Li Mu's purpose has been revealed - it is the seven mathematical problems of the millennium, the last piece of the puzzle in classical physics, [prove: the existence and smoothness of the solution of the Neville-Stokes equation]!

And in the audience, the people who reacted a little slower gradually saw it after being sluggish for a while, and then they were dumbfounded.

There was a moment of silence in the room, and then there was a gradual uproar and discussions.

Although this report is not completely over, these scholars who are aware of it have been somewhat restrained.

That's the Nass equation, one of the seven math puzzles of the millennium!

To some extent, the mathematicians who have studied this problem can be said to be the most numerous of the seven problems.

In this way, accompanied by pieces of uproar and discussions, even those students or ordinary scholars who did not understand what Li Mu's announcement was revealing understood the reason from those discussions, which brought a wider range of shocks.

It has been rumored that Li Mu may have proved the NS equation before, how did it become true when it was circulated?

Li Mu on the stage said at this time: "After I discovered the global space, there was a very obvious thing - the global space can be fused with the Neville-Stokes equation. ”

"So, I did a partial differential of the terms about collisions in the monolithic space, and then the magic happened."

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

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

“那么，我的下一场报告主题就是——”

说到这，李牧顿了顿，随后彻底摊了牌：“纳维尔-斯托克斯方程解的存在性和光滑性！ ”

……

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

[Li Mu has killed another millennial problem? 】

[The Math Conjecture Crusher is working again!] 】

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

The proof of the seven mathematical problems of the millennium is destined to be able to cause an earthquake in the entire mathematical community.

Almost not long after Li Mu's report ended, those mathematicians who did not come to the scene of the international mathematicians learned the news, which immediately attracted all kinds of frustrated voices, they actually missed such a report!

Of course, the only thing to be thankful for is that the report proving that there is a smooth solution to the NS equation has not officially started, and Li Mu only advertised his next report, but did not say when his next report will start.

However, for the time being, it is clear that the International Congress of Mathematicians has no time for his presentation.

This year's International Congress of Mathematicians began on the 6th and ended on the 14th, and on the 10th, Li Mu had already given two presentations, 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 take place?

就在全世界的数学家都在猜测的时候，国际数学联盟以及本届国际数学家大会的组委会也急忙召开了数场会议。

The topic of discussion in these meetings was whether to extend the International Congress of Mathematicians by one day and provide it exclusively for Li Mu to give his third and most critical presentation.

The results of the discussion on this issue are also very obvious.

The International Congress of Mathematicians cannot afford to lose such an important report, just like the 3D area, ahem...... Just like the West cannot afford to lose Jerusalem.

As the most important congress in the field of mathematics, the International Congress of Mathematicians certainly hopes that such a historic moment can take place 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 to show you how you demonstrated the existence and smoothness of the solution to the Neville-Stokes equation."

In the hotel room where Li Mu was staying, Carlos Kenig, president of the International Mathematical Union, personally came to his door and invited him.

"As you foretold at the end of your last report."

"This is important for the International Congress of Mathematicians, and we are sure that more than 4,000 mathematicians from all over the world who are in St. Petersburg are looking forward to your presentation. ”

“不知道你的意下如何？ ”

Kenig's attitude was very sincere.

而面对凯尼格的邀请，李牧笑了起来，随后说道：“凯尼格理事长，你言重了，能在国际数学家大会上完成我这第三场报告，也是我的心愿，毕竟，这样也算是有始有终嘛。 ”

Hearing Li Mu's agreement, Kenig immediately became happy: "That's really good!" Thank you, Professor Lee, for agreeing. ”

"We, the Council 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 15, what do you think?"

Li Mu's eyebrows raised: "I remember that on July 14th, the International Congress of Mathematicians was over." ”

"We have decided to extend this conference by one day, and the closing ceremony and dinner will be held after the afternoon of July 15th, after your presentation," Kenig smiled. ”

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

Li Mu's face showed surprise.

In the end, the International Congress of Mathematicians was extended by one day specifically for his presentation!

The International Congress of Mathematicians was held for one day because of one person, which was the first time in the history of the International Congress of Mathematicians that it has been held since 1897 and can be called one of the world's oldest academic conferences.

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

As a result, now such treatment ...... It's not over-spec.

……

Kenig left and returned with news, apparently informing the outside world on behalf of the International Congress of Mathematicians.

Of course, such an important matter must be communicated to all participants, as well as those who did not attend.

At the same time, in Li Mu's room, Wiles was always next to him.

It wasn't until Kenig left that Wiles said to Li Mu in amazement, "You did it. ”

"The International Mathematical Union has given you this face!"

Li Mu smiled slightly, such a thing is expected.

"The first scholar in history to give three presentations at an international congress of mathematicians."

"It is also the first scholar in history to have an international congress of mathematicians extend the day for it."

"Incredible."

Wiles shook his head, "Oh yes, I almost forgot, you proved a millennial conundrum, but this is the second one." ”

Li Mu suddenly cried and laughed: "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 bother you, in a few days, you are about to start your century report, I have already waited." ”

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

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

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

Several people immediately pointed at Wiles and said, "Wiles! You also said that you didn't know that Li Mu had proved the NS equation! ”

And at this time, Wiles didn't pretend anymore, there was a showdown, crossed his waist, and said arrogantly: "Yes, that's right, I already knew!" ”

……

随着凯尼格的返回，国际数学家大会延长一天，并且在7月15号举办李牧的第三场报告的事情，就飞快地传遍了数学界。

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

The mathematicians who had already booked a plane to leave St. Petersburg on July 15 immediately began to change their bookings, and those mathematicians who did not come to St. Petersburg began to book tickets to St. Petersburg on the same day.

At such a short 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, especially the Hail Conjecture, the Twin Prime Conjecture, and the Goldbach Conjecture, especially the Neville-Stokes equation.

And just like that, time passed quietly.

July 15th, it's here!

……

(End of chapter)