"Of course you can …"
Lu Zhou looked at Professor Fefferman and gestured for him to take a seat.
Professor Fefferman picked up the marker and stared at the whiteboard for a while. He then began to write on the whiteboard.
It was time for the class to end, but no one in the classroom left their seats.
Everyone, including Lu Zhou, stared intently at the content on the whiteboard.
Gradually, Lu Zhou looked at Professor Fefferman's steps and his eyes lit up.
Amazing …
This was the interesting part about mathematics.
If one thought didn't work, one wouldn't be able to get out of the maze.
However, if one thought seemed feasible, one didn't even need to be close to the exit. The moment one set foot on this thought, one would feel like victory was right in front of them.
Although Fefferman didn't write the last step, Lu Zhou was sure that his idea was at least 90% feasible!
Sure enough, this big name didn't disappoint him.
Professor Fefferman smoothly filled the remaining space on the whiteboard. He then drew the last stroke on the last line …
[Pμi: = μi- (Δ ^ -1) · δi · δj · μj]
There was a commotion in the classroom. Even though this content was a bit difficult for undergrad students, this was Princeton, after all, and the mathematics students were at the top of the academic hierarchy.
Just because they didn't think of this step didn't mean that they didn't understand.
Obviously, although they reacted a bit slower, just like Lu Zhou, they also saw the ingenuity of Fefferman's idea.
Professor Fefferman put away the marker on the whiteboard and carefully read the equation. He then smiled and spoke softly.
"This question isn't easy … It's a bit difficult for undergrad students."
Lu Zhou coughed and said, "Therefore, it's just a thinking question."
He only wanted to meet with the students. If it weren't for the fact that so many people were interested in his research progress, he wouldn't have written this question on the whiteboard.
What he didn't expect was that this big name was sitting in the back row of the lecture hall.
Professor Fefferman placed his attention back on the content on the whiteboard. He rubbed his chin and spoke thoughtfully.
"Where (Δ ^ -1) · δi · δj is defined as the Fourier multiplier of … But what I want to know is, even if you get the equation of Pμi, what's the point? I don't see it … Can you explain it for me? "
"Of course." This wasn't something worth hiding. Lu Zhou smiled and said, "But I need a new whiteboard."
"Princeton has plenty of whiteboards, I'll get one for you."
Professor Fefferman turned around and left the lecture hall. He quickly brought back a whiteboard from the classroom next door.
When Lu Zhou saw the whiteboard that Professor Fefferman brought back, he wiped off the writing on the whiteboard and picked up the marker again. He then began to write on the whiteboard and explained his steps in detail.
"If we get Pμi: = μi- (Δ ^ -1) · δi · δj · μj, we can use the non-divergence property of μ to perform conventional integration to find …"
During this period of time, he had been busy with experiments. His research on the Navier – Stokes equation was only at the "Pμi: =?" step. As for the rest of the content on the whiteboard, it was all derived on the spot.
This may sound a little difficult.
But in fact, it was actually quite easy to do.
After all, the train of thought was there. All he needed to do was to bring in the previous conclusion and continue to deduce along this train of thought.
However, this wasn't an easy task …
[ = -πiπλξ 1, ξ 2, ξ 3 (μ (ξ 1), v (ξ 2), w (ξ 3)) …]
Lu Zhou wrote down this line of calculations on the whiteboard. Suddenly, the pen in his hand stopped moving.
When Professor Fefferman saw this, he suddenly raised his eyebrows. He was intrigued.
Lu Zhou put away the marker in his hand and cast a questioning look at him.
"What do you think?"
Professor Fefferman rubbed his index finger and spoke to himself.
"Seems … interesting."
The students in the classroom stared at the two people on the podium without blinking. They were afraid to make any noise and interrupt the two big names' thoughts.
In the entire North America, there was probably no place that respected knowledge more than Princeton.
After five minutes, Professor Fefferman suddenly relaxed and spoke in a relaxed tone.
"It seems like this problem isn't that easy to solve."
Lu Zhou stared at the whiteboard and nodded in agreement. "You're right."
If it was that easy to solve, the Clay Institute wouldn't have listed it as one of the seven Millennium Prize Problems.
"But I didn't expect you to be able to do this." Professor Fefferman smiled and said, "The Navier – Stokes equation is a very interesting problem. It is the foundation of fluid mechanics and a classical proposition in partial differential equations. If we can solve the existence of a smooth solution, not only will it be for the glory of the human mind, but it will also have a profound impact on a series of related disciplines. "
Dieudonné was one of the founders of the Bourbaki school of thought. He once said, "Mathematics is for the glory of the human mind". Even though Professor Fefferman didn't agree with the Bourbaki school of thought, he agreed with Dieudonné's words.
Professor Fefferman smiled and clapped his hands.
"It was a very fulfilling class … Although I might be praising myself a little too much. What do you guys think? "
He looked back at the students in the classroom. Even though the class had already ended, they still hadn't moved their butts from their benches.
What responded to him was, of course, a round of applause.
Lu Zhou listened to the thunderous applause and smiled embarrassedly.
Even though he didn't say anything, he was actually a little proud of himself.
Compared to a serious report, the sense of accomplishment that a classroom gave him was a completely different experience.
It seemed like even though they hadn't seen each other for the entire semester, his students still liked him.
"Oh yeah, I solved this problem." Professor Fefferman suddenly remembered something. He pointed at the equations on the whiteboard and said, "Is your promise still valid?"
Lu Zhou paused for a second and said, "Promise?"
"Promise?"
The chestnut-haired girl, who was sitting in the front row, raised her hand and spoke excitedly.
"Professor, you said that if anyone solves this problem, you'll accept them as your PhD student."
A commotion broke out in the classroom.
Lu Zhou didn't look at the student. He coughed and said, "Don't joke around."
"No, no, no, I'm not joking," Professor Fefferman said with a smile. He then said, "If you don't mind accepting another PhD student, I don't mind accepting another PhD from you."
Even though Professor Fefferman didn't sound like he was joking, Lu Zhou knew that he was definitely joking.
Compared to Professor Faltings, who had already left Princeton, Professor Fefferman was on the other extreme when it came to "arrogance". At the Princeton Institute for Advanced Study, he was the only one who would make a joke like this.
When Fefferman saw Lu Zhou's helpless expression, he coughed and stopped joking. Instead, he spoke in a serious tone.
"Okay then, since you don't plan on accepting another PhD student, I hope you can make a request of me."
Lu Zhou didn't make any promises. Instead, he asked, "What request?"
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