Lu Zhou thought that he was used to this feeling.
However, he didn't expect that even though he was standing here, he still couldn't control the surging emotions in his heart.
This was different from the report at the Princeton Institute for Advanced Study. This time, he wasn't just facing the number theory community, he was facing the entire mathematics community …
Lu Zhou stood on the stage and took a deep breath. He gradually calmed his heart rate down.
He looked at his watch for the nth time.
He looked at the second hand that was getting closer and closer. He put on a serious look on his face.
"It's about to start!"
At nine o 'clock sharp.
There was no need for anyone to maintain discipline. When the time arrived, the venue, which was originally noisy and chaotic because of the whispers, instantly quieted down.
Under the gazes of tens of thousands of people, a clear title appeared on the silver-white screen.
[Proof of the existence and smoothness of the solution to the three-dimensional incompressible Navier-Stokes equation]
Lu Zhou responded to the pairs of eyes in the audience. He slowly spoke and began the opening remarks of the report.
"Why doesn't a high-speed car decompose itself? Why doesn't a still lake suddenly explode?
"For a long time, we have been troubled by the obvious, because the truth that we desire is always disguised as the obvious.
"Even as early as the 19th century, we had already summarized the equations that summed up the laws of fluid motion and made them look concise enough. However, to this day, we are still unable to understand the deeper mathematics and physics behind the equations."
"Mathematics is a rigorous discipline. Propositions involving numbers shouldn't be described with ambiguous words like 'maybe' or 'maybe'."
"Back to the original question. Why doesn't a high-speed car decompose itself? Why doesn't a still lake suddenly explode? Is there a mysterious singularity on an infinite time scale that causes our equations to diverge in a finite time?
"Now, it's time to answer this question."
After the brief opening remarks, the PowerPoint on the screen flipped to the next page.
The report also entered the main topic.
Lu Zhou used three seconds to quickly organize the thoughts of his speech in his mind. After that, he faced the audience and used a minute to make a simple summary of his proof ideas.
The audience was silent.
Everyone was staring at the pictures and calculations on the screen. Everyone was listening carefully. They did not want to miss a single detail, and they did not want to miss a single moment.
[μ (t) = e ^ (t △) · μ0 + = e ^ (t-t ') △ B (μ (t'), μ (t ')) dt']
[…]
"When we are given a Schwartz divergence free vector field μ 0 and set the time interval I? Then, we can continue to define a generalized solution H10 of the Navier-Stokes equation as a continuous mapping obeying the integral equation μ (t), that is, μ → H10df (R3) … "
Lu Zhou, who was holding a laser pointer in his hand, explained the PowerPoint on the screen.
There was nothing special about the first part.
There were many similar theses on the Navier – Stokes equation.
Whether it was using the abstract proof method to construct the abstract bilinear operator B 'or the "L Manifold" method, this part was essential.
However, the next part was the key to the entire proof idea!
He would introduce the concept of differential manifolds to partial differential equations.
This was the core of the theory of "using topology methods to study partial differential equations"!
…
In the audience, Xu Chenyang had a dignified look on his face. The pen in his hand gently tapped on his notebook.
After a while, he whispered to Zhang Wei, who was sitting next to him, so only the two of them could hear him.
"Do you understand it?"
Zhang Wei shook his head and said, "I don't know much more about partial differential equations than you. If you're starting to feel tired, then so am I."
Zhang Wei's area of expertise was similar to his mentor, Zhang Shouwu. He mainly focused on representation theory, Langlands program, and Dirichlet's L function.
Partial differential equations were not his area of expertise. He only knew about the Navier – Stokes equation out of interest.
After all, not everyone was a genius like Tao Zhexuan. He could prove the weak conjecture of Goldbach's conjecture while studying the abstract proof of the Navier – Stokes equation. He could even take time to read Shinichi Mochizuki's thesis …
In the mathematics world, there were geniuses.
But they were rarer than pandas …
Xu Chenyang looked at the calculations on the screen and couldn't help but say, "This is unbelievable …"
Zhang Wei, "Unbelievable about what?"
Xu Chenyang, "Number theory, abstract algebra, functional analysis, topology, differential geometry, partial differential equations … Is there anything he's not good at?"
"Maybe … algebraic geometry?" Zhang Wei's voice was full of uncertainty.
Because as soon as he said this, he remembered that Lu Zhou's mentor was Deligné. Lu Zhou's mentor was the legendary "father of modern algebraic geometry" and "pope of mathematics", Grothendieck!
The core theory of modern algebraic geometry was basically derived from Grothendieck's works.
Zhang Wei didn't believe that Lu Zhou didn't know algebraic geometry.
At most, he hadn't researched that area yet. The results were still brewing …
…
The report continued on stage.
Lu Zhou's speech speed was getting faster and faster, and his thoughts were getting clearer and smoother.
The introduction of the L Manifold played a decisive role in the solution of the entire proposition.
It was like a hammer that blasted a hole in the unbreakable wall of the labyrinth.
With the arrival of this moment, the originally bewildering and confusing situation instantly became clear.
At the same time, the atmosphere in the venue was pushed to a climax.
Fefferman was sitting in the corner of the venue. He had a smile on his face. He had seen it all.
Tao Zhexuan, on the other side of the venue, whispered "I see". His eyes were flashing with excitement.
At the back row of the venue, Vera clenched her right hand as she sensed the heat in the atmosphere. Her originally calm heart began to race. At this moment, she felt proud of her mentor from the bottom of her heart …
Faltings, who was also sitting in the back of the venue, suddenly had a smile on his face.
Deligné noticed the change in his old friend's expression, so he asked casually.
"How do you feel?"
Faltings said expressionlessly, "It's so-so."
"Aren't you embarrassed to say that?" Deligne smiled faintly and returned the greeting gift that he had given him earlier, untouched.
Faltings's mouth twitched. He looked at his watch and slowly stood up.
Deligné: "It's almost over, don't you want to watch until the end?"
"There's no need."
Anyway, he already understood everything.
I'll leave the boring questions to others.
Professor Faltings didn't stop. He walked through the crowd and walked straight to the exit of the venue.
The second Professor Faltings left the lecture hall, the entire report came to an end.
When the last line of calculations appeared in the audience's eyes, there was no need for Lu Zhou to explain anything.
Because just as the audience could see, the final answer was already on the verge of being revealed.
"… Combining all of the above inferences, the result is obvious. The solution of the three-dimensional incompressible Navier-Stokes equation exists, and it's as smooth as we expected!"
His voice was clear and certain.
Even though it wasn't loud, it had a convincing magic to it.
And the source of that magic was knowledge.
Almost at the moment when he finished speaking, a voice rang out.
The audience stood up from their seats.
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