Lu Zhou originally thought that he was used to this feeling.

What he didn't expect was that when he stood here, it was still difficult to restrain the surging heart.

Unlike the lecture in Lecture Hall 1 of the Institute for Advanced Study in Princeton, this time he was facing not only the number theory community, but the entire mathematical community......

Standing on the lecture table, Lu Zhou took a deep breath and gradually calmed his heart rate.

The Nth time I looked at my watch.

Looking at the second hand that was getting closer and closer, his face changed to a serious look and cheered up.

"It's time to start!"

Nine o'clock sharp.

There was no need for discipline at all, and when the time reached the hour, the venue, which had been noisy and chaotic due to whispered discussions, fell silent in an instant.

Under the watchful eye, a clear line of titles emerged from the silver-white curtain.

Proof of the existence and smoothness of the solution of the three-dimensional incompressible Navier-Stokes equation

In response to the pair of eyes from the audience, Lu Zhou slowly spoke and began the opening remarks of the report meeting.

"Why doesn't a car decompose at high speed, and why doesn't a still lake explode suddenly?"

"For too long, we have been plagued by the obvious, because the truth we desire has always been disguised as obvious."

"Even though we have summarized the equations that summarize the laws of fluid motion as early as the 19th century and made them seem concise enough, to this day we are still at a loss for the deeper mathematical and physical connotations behind the equations."

"Mathematics is a rigorous discipline that involves propositions about numbers, and it should not be used in the context of maybes or possibly. Ambiguous words to describe. ”

"Going back to the original question, why doesn't a car at high speed decompose itself? Why doesn't a still lake explode suddenly? Is there such a mysterious singularity on an infinite time scale that allows our equations to diverge in a finite amount of time? ”

"Now, it's time to answer that question."

The short opening remarks ended, and the PPT on the curtain turned to the next page.

And the report meeting also entered the main topic.

In three seconds, Lu Zhou quickly sorted out the thoughts of his speech in his brain. Then he faced the audience and spent a minute giving a brief summary of his proof ideas.

The audience was silent.

Everyone stared at the pictures and calculations on the screen, and everyone listened carefully, unwilling to miss a single detail, unwilling to miss a moment.

【μ（t）=e^（t△）·μ0+∫e^（t-t）△B（μ（t‘），μ（t））dt】

【……】

"When we give the equation a Schwartz divergence-free vector field μ0 and set the time interval I?[0,+∞], we can continue to define a generalized solution of the Navier-Stokes equation H10 as a continuous mapping obeying the integral equation μ(t), i.e., μ→H10df(R3)......"

The PPT in the curtain was being screened, and Lu Zhou, who was holding a laser pointer in his hand, was explaining at an even speed.

There is nothing special to say about the previous sections.

Something similar can be seen in many papers on the study of the NS equation.

This part is indispensable whether he uses the abstract proof method to construct the abstract bilinear operator B, or the "L manifold" method he employs.

But the next part is the crux of the whole proof idea!

He will introduce the concept of differential manifolds to the problem of partial differential equations.

And this is the core of the theory of "using topological methods to study partial differential equations"!

……

Offstage, Xu Chenyang's face was solemn, and the tip of the pen in his hand was lightly clicked on the notebook.

After a while, he whispered to Zhang Wei, who was sitting next to him, in a voice that only two people could hear.

"Do you understand?"

Zhang Wei shook his head: "I don't study much more partial differential equations than you, and if you start to feel struggling, then I'm almost there." ”

Zhang Wei's direction is similar to that of his mentor Zhang Shouwu, mainly focusing on representation theory, Langlands program, and also studying Dirichlet L-function.

Partial differential equations are not his area of expertise, and he has only learned about NS equations out of interest.

After all, it is impossible for everyone to be as genius as Tao Zhexuan to prove the weak conjecture of Goldbach's conjecture while studying the abstract proof of the NS equation, and even find time to read Shinichi Mochizuki's paper......

In the world of mathematics, it is not without all-rounders.

But it's rarer than giant pandas......

Looking at the equation on the screen, Xu Chenyang couldn't help but sigh: "It's unbelievable......

Zhang Wei: "Unbelievable what? ”

Xu Chenyang: "Number Theory, Abstract Algebra, Functional Analysis, Topology, Differential Geometry, Partial Differential Equations...... Is there a direction he's not good at? ”

"Perhaps...... Algebraic geometry? When he said this, Zhang Wei's voice was full of uncertainty.

Because as soon as he said this sentence, he remembered that Lu Zhou's mentor was Deligne, and his grandfather was the legendary "father of modern algebraic geometry" and "the pope of mathematics" Grothendieck!

The core theories of modern algebraic geometry are largely derived from several of Grothendieck's unlost works.

To say that he doesn't know algebraic geometry, Zhang Wei won't believe it.

At most, it hasn't been studied yet, and the results are still in the making......

……

On stage, the presentation will continue.

Lu Zhou's speed of speech is getting faster and faster, and his thoughts are becoming clearer and smoother.

The introduction of the L manifold plays a decisive role in the solution of the whole proposition.

It was like a hammer, blasting a gap in the impregnable labyrinth wall.

With the arrival of this moment, the originally confusing situation became clear and clear in an instant.

At the same time, the atmosphere in the venue was also pushed to Gao Chao.

Sitting in the corner of the venue, Feverman had a smile on his face, and from this moment on, he had seen the end.

Tao Zhexuan, who was on the other side of the venue, whispered "I see" in his mouth, and his eyes flashed with excitement.

In the back row of the venue, feeling the scorching heat in the atmosphere of the scene, Vera clenched her right hand, and her originally calm heartbeat began to accelerate. In this moment, she is proud of her mentor from the bottom of her heart......

Also sitting in the back row of the venue, the corners of Faltins' originally tense mouth suddenly hooked up an unusual angle.

Noticing the change in the expression on his old friend's face, Deligne asked casually.

"How does it feel?"

Faltings said expressionlessly, "Normal." ”

"Don't you blush when you say that?" Deligne smiled faintly and returned the gift he had given him as it was.

The corners of his mouth twitched, and Faltins ignored his old friend's teasing, glanced at his watch, and slowly stood up.

Deligne: "It's almost over, don't see the end?" ”

"There's no need for that."

Anyway, I already understand it all.

It's better to leave boring questions to others.

With these words, Professor Faltins did not stop, and walked through the crowd of people sitting on the floor in the aisle, and went straight to the exit of the venue.

Almost as soon as Professor Faltins left the lecture hall, the whole lecture came to an end.

When the last line of calculation came into the eyes of the audience, there was almost no need for Lu Zhou to make any more explanations.

Because, as the audience could see, the final answer was already on the horizon.

“…… Combining all of the above inferences, it is already clear that the solution of the 3D incompressible Navier-Stokes equation exists and is as smooth as we expected! ”

The voice, clear and affirmative.

It's not loud, but it's magical.

And the source of that magic is knowledge.

Almost as soon as the words fell.

The audience scrambled to their seats.

The thunderous applause resounded in an instant, and it lasted for a long time in this wide and crowded lecture hall......

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