Chapter 271 - 255: Excuse Me, Could You Folks Inside Please Make Way?

Chapter 271: Chapter 255: Excuse Me, Could You Folks Inside Please Make Way?

At this thought, an idea suddenly struck E Weinan.

If it were possible to really pin down an implicit constraint...

...then what Li Dong had just said about Professor Levan’s "three basis sets with a phase difference of π" would no longer just be bad luck on an application level.

It would be a structure with a global geometric characterization.

And this characterization would lead directly to the core theorem of Li Dong’s paper.

Thinking this, he beckoned to Li Dong.

"Li Dong, come on up."

Li Dong didn’t refuse and walked straight to the front.

E Weinan turned his head to look at the female doctoral student sitting at the innermost part of the U-shaped table.

"Xiaozhao."

"Let me borrow your computer for a moment."

Senior Sister Zhao froze for a second, then immediately moved the numerical program she was running to the background and handed her laptop over.

E Weinan opened the official website for the *Mathematical Annals* on the laptop.

Then he found Li Dong’s paper.

E Weinan was just about to scroll down.

But Li Dong, who had reached the front, spoke up.

"Teacher E, please turn to page thirty-two, line seven."

E Weinan paused.

"Hmm?"

"The estimation formula for the second moment of F_π(α)."

"The inverse constraint you were just thinking about—it starts from that line," Li Dong said.

E Weinan nodded and jumped directly to page thirty-two, line seven.

It was exactly that estimation formula.

...Not off by a single line.

A strange feeling suddenly washed over E Weinan.

He had published papers before.

*Nature*, *Science*, *Annals*, *Inventiones*...

He had more top-tier journal publications to his name than he could count on one hand.

But if he had to find a specific part of a paper he himself had written, could he remember the exact page and line number like Li Dong?

’Of course not. This isn’t just a good memory—this is a damn photographic memory, isn’t it?’

E Weinan had read about such things in apocryphal stories before, and he had always scoffed inwardly at them.

’Impossible.’

But now?

A living, breathing example had appeared right under his nose.

"...Continue."

He turned the screen so the PhD students at the U-shaped table could also see.

"To modify this line—the second moment of F_π(α)—to pin down an implicit quantity, what’s the first step?"

"We need to borrow the spectral curvature characterization you just mentioned."

Li Dong walked over to the screen and tapped the right side of the formula with his finger.

"Here, treat α as an energy parameter, not a complex variable."

"The interval of convergence for F_π(α) then translates into an interval within the continuous part of the spectral measure."

"The integration changes from [0, 4] to the neighborhood of an accumulation point..."

...

"You see, this gives us a strict upper bound for that implicit constraint."

"The decay rate of the upper bound is just enough to resolve the third peak from the blur."

E Weinan stared for a good ten seconds.

The PhD students around the U-shaped table could no longer sit still.

Three of them picked up their chairs and moved over, gathering around the front of the room.

Not to mention the undergraduates in the back rows.

They had long since slipped from the last row to the front, standing on the periphery.

To be honest, more than half of them didn’t understand the line of formulas on the screen at all.

But strangely...

...following the back-and-forth between Li Dong and E Weinan, their minds felt surprisingly clear.

Later, when the short undergraduate student told others about this class, he summed it up like this:

He couldn’t say he completely understood every sentence he heard back then.

But after hearing each sentence, he knew with perfect clarity exactly what it was he didn’t understand.

For someone studying mathematics, this was a state they could only dream of achieving.

The discussion continued.

E Weinan asked about another point.

"This modification you mentioned above, the lemma it references..."

"Where is it, roughly?"

"Page nineteen, fifth line from the bottom."

"Lemma 3.4.2, the exact expansion of the Ramanujan sum at p²."

"The singularity decomposition at the edge of the continuous spectrum you mentioned comes from its convolution structure."

E Weinan’s finger moved, and the scroll bar slid up.

Page nineteen, fifth line from the bottom.

It was exactly Lemma 3.4.2.

"..."

The PhD students at the U-shaped table were truly silent this time.

In the span of just two or three minutes, Li Dong had pinpointed two different locations in the paper.

Page number, line number, lemma number—every detail was perfectly accurate.

’This isn’t just remembering a paper!’

’This is like he’s stuffed the entire paper into his brain and is just casually flipping through the pages at will.’

A PhD student with glasses cursed under his breath.

"Damn..."

He really couldn’t hold it in.

E Weinan paid no mind to the profanity.

His attention was entirely on the screen.

"There’s another place..."

"Your weighted estimate for the cross-level coupling, I think that was in an appendix."

"Appendix B, page forty-three, second paragraph."

"The line with the scale transformation of the weight function."

"If you change w(u) to w(u/2), the cross-level step automatically aligns with the edge of the continuous spectrum."

E Weinan scrolled to Appendix B.

Page forty-three, second paragraph.

The line with the weight function was lying right there.

E Weinan didn’t speak.

He stared at Li Dong for a full two seconds.

Memory isn’t necessarily the most important thing when it comes to scientific research.

Because being able to remember something doesn’t mean you can understand it.

But for those who can remember, the time spent looking up references is cut by eighty percent.

More importantly...

When you have five books, ten papers, and twenty theorems stored in your brain, those pieces of knowledge will start to connect on their own.

Two paths that were once far apart might suddenly leap together in a single moment.

But the prerequisite is that you actually have to remember that much.

And how much can a person remember?

Most people would struggle to recall which paragraph of an article they read two weeks ago contained a key observation.

But this kid...

E Weinan sighed to himself.

He looked at Li Dong, marveling once again.

’What incredible raw talent.’

’Why did he have to go into pure mathematics?’

He shook his head, forcefully suppressing these feelings of "what a waste."

The discussion continued.

The deeper they delved, the more he felt that the angle of attack Li Dong had proposed was truly elegant.

The entire set of estimates for the second moment of F_π(α), and the Gikhmanov inversion method that Professor Levan was working with...

...they actually resonated at this single point: the "implicit constraint."

...

As the discussion grew more intense, the circle of PhD students at the U-shaped table gradually got into the zone.

They weren’t just there for show.

PhD students under an academician were the true cream of the crop.

Senior Sister Zhao, sitting at the very back, suddenly interjected in a low voice.

"Teacher E, Junior Li."

"For the local singularity at the accumulation point, if we use a Mellin transform to pull it into a multiplicative structure, wouldn’t that let us skip the w(u/2) step entirely?"

Hearing this, Li Dong’s eyes lit up.

"Yes."

"And if we do that, the phase difference between the third and second peaks will directly degenerate into a rational number."

"That’s even cleaner than what I just proposed."

Senior Sister Zhao was taken aback.

She hadn’t expected him to take her off-the-cuff remark and instantly push the idea one step further.

The atmosphere was instantly electrified.

Then, a male PhD student who researched stability estimation for inverse problems added a comment about the Hilbert-Schmidt norm...

...which Li Dong also effortlessly caught and built upon.

E Weinan, meanwhile, only interjected occasionally to point them in a direction before falling silent again.

The discussion grew deeper and deeper.

And more and more intense.

No one paid any attention to the time.

...

In the hallway outside the classroom.

A male junior stood outside the back door, looking into the classroom.

"Hey... why haven’t they left yet?"

"Isn’t our class supposed to be in this room?"

A classmate next to him, who was half a head taller, pulled out his phone and glanced at the time.

"Class has already started."

"Why don’t you go in and remind them?"

"Me?"

The first student’s face went pale.

"That’s Academician E Weinan in there, you know? An academician!"

"And the one next to the academician..."

He squinted, trying to get a better look.

"I think that’s East God."

"And you want *me* to go in there??"

"What if they’re in the middle of discussing a paper that could be published in a top-tier journal, and I interrupt them..."

"How the hell could I afford to take responsibility for that?"

"Forget it, forget it. I’m not going in."

The two of them looked at each other, then, as if by silent agreement, they both pulled out their phones and started playing, leaning against the wall.

Less than two minutes later, a few more students arrived and repeated the same experience.

Before long, a small line of students had formed in the hallway, all of them scrolling on their phones.

About ten minutes later, the class monitor arrived late.

He saw the line of students blocking the classroom door and walked over, a confused look on his face.

"What’s everyone doing standing at the door?"

"Why don’t you go in? Teacher Liu will be here any minute, you know."

One of the students on their phone pointed into the classroom.

The class monitor followed his finger and glanced inside.

Around the U-shaped table was a circle of PhDs, including a few senior students he recognized from academic seminars.

Further in, there was a figure with graying hair.

Academician E Weinan...

And next to him, a young man in an ordinary dark jacket was pointing at a formula on the screen and speaking.

He was very familiar with that face.

After all, it was the most famous face at Yan University for the past month.

East God.

"..."

The class monitor silently joined the ranks of those scrolling on their phones.

A little while later.

The teaching assistant for the next class arrived.

He had come to turn on the lights and the projector.

When he reached the door and saw the line of people blocking it, he frowned.

"Why aren’t you going in? It’s time."

The class monitor just pointed inside again.

The TA peeked his head in for a look.

Then he instinctively pulled out his phone and stood next to the class monitor.

The line grew by one.

About ten minutes later, Associate Professor Liu arrived, holding a lesson plan.

He was wearing a dark gray jacket and a pair of ordinary black pants.

To anyone unfamiliar with him, his attire would make them mistake him for one of the old janitors.

But any PhD student who had been grinding it out in the School of Mathematics for a few years knew...

...that this Teacher Liu was the second-in-command in Professor Wang’s GL₂ to GL₃ research group.

His focus was on automorphic forms.

He was also Professor Wang’s most trusted deputy.

Lately, this research group had been having a really hard time.

Their proof for GL₂ to GL₃, which they had painstakingly worked on for over a year, had been rendered completely obsolete by Li Dong’s paper.

So he wasn’t in a very good mood coming to class today.

But when he got to the door, he found a line of students blocking the entrance, heads down, scrolling on their phones.

His brow furrowed slightly.

"Why is no one going in?"

The TA sighed, said nothing, and just pointed into the classroom.

Associate Professor Liu’s annoyance immediately flared up.

’What is the meaning of this?’

’It’s my class. Am I not allowed in?’

He didn’t say anything more, and he couldn’t be bothered to look where the students were pointing.

He raised a hand and pushed the door open.

"Excuse me... you folks inside, could you please make some room?"

"This class..."

The moment the door swung open,

...his voice came to an abrupt halt.

He froze on the spot.