Translator: Henyee Translations Editor: Henyee Translations
“Of course you can…”
Lu Zhou made a gesture to invite Professor Fefferman to the whiteboard.
Professor Fefferman picked up a marker and stared at the whiteboard for a while. He then started to write.
The lecture was technically over, but not a single person left the lecture hall.
Everyone, including Lu Zhou, stared at the whiteboard.
Lu Zhou looked at what Professor Fefferman was writing, and his eyes gradually lit up.
Amazing…
This was an interesting part of mathematics.
A method that was unfeasible would never work, no matter how many times one tried.
But once one embarked on a method that might work, one could feel the victory ahead.
Although Fefferman hadn’t finished writing, Lu Zhou was 90% certain that his method was correct.
As expected, this big name didn’t let him down.
Professor Fefferman swiftly filled in the rest of the calculation steps and wrote one final line.
[Pμi:= μi – (Δ^-1)·δi·δj·μj]
There was a commotion in the classroom. Although this content was too difficult for undergraduate students, this was still Princeton.
They couldn’t think of the method, but they could understand it.
Obviously, their comprehension speed was slower than Lu Zhou’s, but just like Lu Zhou, they saw the ingenuity of Professor Fefferman’s workings.
Professor Fefferman placed down the marker and carefully read his calculations from beginning to the end. After that, he smiled and said, “This question isn’t easy… A bit too difficult for undergraduate students.”
Lu Zhou coughed and said, “Hence, it is supposed to be a thought-invoking question.”
Lu Zhou only planned to lecture the students. He wouldn’t have written his research problem on the whiteboard if there weren’t so many students interested.
Lu Zhou definitely didn’t expect this big name to sit at the back of the lecture hall.
Professor Fefferman placed his attention back to the contents on the whiteboard and rubbed his chin as he spoke in a thoughtful manner.
“(Δ^-1)·δi·δj is defined as the Fourier multiplier of ξiξj/|ξ|2… But what I want to know is that even if you have derivation equation of Pμi, what is the point? I can’t seem to grasp it… Can you explain it to me?”
“Of course,” Lu Zhou smiled and said, “but I’ll need a new whiteboard.”
“Princeton has plenty of whiteboards, I’ll find one for you.”
Professor Fefferman left the lecture hall and came back with a whiteboard.
Lu Zhou erased the writing on the new whiteboard and picked up the marker. He then began to explain while writing.
“If we get Pμi: = μi-(Δ^-1)·δi·δj·μj, we can find the non-diverging property of μ for conventional integration…”
Lu Zhou’s research was only up to the “Pμi:=?” step. Therefore, he was deriving equations on the spot.
This sounded difficult.
But actually, it was very easy.
After all, all he needed to do was to use the new conclusion to continue his train of thought.
However…
[ <B(μ,v),w〉= -πi∫Λξ1,ξ2,ξ3(μ(ξ1),v(ξ2),w(ξ3))…]
Lu Zhou suddenly stopped writing.
Professor Fefferman suddenly looked interested.
Lu Zhou looked back at Fefferman.
“What do you think?”
Professor Fefferman rubbed his index finger on his chin as he said, “It’s… interesting.”
The students stared at the two men standing on the podium silently; they were afraid of interrupting the thought process of the two big names.
There was nowhere else in America that respected knowledge as much as Princeton.
Five minutes passed by before Professor Fefferman suddenly spoke up.
“It seems that this problem isn’t that easy to solve.”
Lu Zhou was still staring at the whiteboard, and he nodded. “You’re right.”
If this problem were easy to solve, the Clay Institute wouldn’t have included it in the Millennium Prize Problems.
“However, I’m surprised you are able to get to this step.” Professor Fefferman said, “The Navier–Stokes equations is an interesting topic; it is the basis of fluid mechanics, but it is also a partial differential equation problem. If someone can find a smooth solution of the equation, not only will it be a glory to the human spirit, it will also have a profound impact on multiple disciplines.”
Dieudonne was one of the founders of the Bourbaki Group, and “Mathematics is the glory of the human spirit” was one of his famous quotes. Professor Fefferman didn’t agree with the views of the Bourbaki Group but he agreed with the quote.
Professor Fefferman smiled and started to clap his hands.
“I think this has been a very fulfilling lecture… although we might not be the best judge of that… What do you think?”
He turned around and looked at the students.
Obviously, a round of applause ensued.
Lu Zhou couldn’t help but smile in the midst of the thunderous applause.
Although he didn’t say anything, he felt pretty proud in his heart.
The sense of accomplishment in a classroom was different than doing a serious report.
It seemed that even though he had barely seen his students, his student still quite liked him.
“Oh yeah, I solved the question,” Professor Fefferman said when he suddenly remembered something. He then pointed at the calculations on the whiteboard and asked, “Do you keep your promise?”
Lu Zhou was stunned.
“Promise?”
The girl with the long maroon hair raised her hand and said, “Professor, you said that whoever solves this problem can become your PhD student.”
The classroom started to jeer playfully.
Lu Zhou coughed and said, “Stop joking around.”
“No, no, I’m not joking,” Professor Fefferman said. He smiled and continued, “If you want, I wouldn’t mind doing another PhD.”
Although Professor Fefferman didn’t sound like he was joking, Lu Zhou thought that he was definitely joking.
Compared with Professor Faltings who had left Princeton, Fefferman was on the other end of the spectrum in terms of arrogance. Only he would make a joke like this.
Seeing that Lu Zhou was confused, Fefferman coughed and spoke in a more serious tone.
“Okay, since you don’t plan on taking in a PhD student, I hope you can do one favor for me.”
Lu Zhou asked, “What favor?”
“It’s about the existence of a smooth Navier-Stokes equation,” Professor Fefferman said with a smile. “I want to work with you on the problem!”
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