Chapter 273 - 257: The Master Effect

Chapter 273: Chapter 257: The Master Effect

Professor Wang stood at the door for a moment.

He didn’t push the door open right away.

He peeked inside through the crack in the door.

Inside, about a dozen doctoral students were all crowded around the lecture platform.

In the middle of the crowd, E Weinan was sitting in a chair.

And next to the platform, Li Dong was pointing at something on a computer screen and speaking.

His voice, muffled by the door, wasn’t loud, but Professor Wang could make out the general gist.

Professor Wang subconsciously leaned his ear closer to the crack.

"...So, Teacher E, look at this line."

"In this estimation for the second moment of F_π(α), if we reduce α from a complex variable to an energy parameter, it no longer corresponds to the zero distribution itself."

"Instead, it corresponds to the local spectral curvature of the discrete spectrum near the accumulation point."

"This curvature is itself an implicit geometric object. So, taking this step, the constraint you were looking for now has a quantitative characterization."

"The groundwork for all of this was already laid out in the third Chapter of my paper on GL(n)."

"But I didn’t state it explicitly in that Chapter because the goal at the time was local-global compatibility. There was no need to push it over to the inverse problem side."

Professor Wang’s heart skipped a beat.

’Wait a minute.’

’GL(n) local-global compatibility?’

’Isn’t that my own specialty?’

He had read that paper over and over again.

He couldn’t help but quickly run through the structure of the third Chapter of Li Dong’s paper in his mind...

The beginning of that Chapter discussed the normalization of the zero-pair correlation function, the middle had an estimation of the second moment, and the end detailed the core technical step involving the upper bound of the ramification index. ℴ

On the surface, what Li Dong was talking about now and the technical line from that third Chapter seemed to be two completely different things.

One was pure math, the other was an inverse problem.

But if you took "the curvature of the discrete spectrum near the accumulation point" and used it as a pivot...

An image suddenly flashed in Professor Wang’s mind.

It was the sheet of scratch paper he had handed to a colleague at a small conference in Shanghai last year.

On it, he had drawn an "étale decomposition" of the GL₂ Hecke algebra at a prime place.

On that sheet, he had drawn a box with a dotted line.

Inside the dotted box, he had written a line in small characters:

"Suspected dual structure here, details unknown."

’Details unknown.’

And what Li Dong was talking about now...

If he worked backward from Li Dong’s point, the two words "details unknown" inside the dotted box in his mind suddenly seemed to take on a distinct shape.

Professor Wang shuddered.

As if pushed by some unseen force, he unconsciously pushed the door open.

Then he tiptoed inside.

The group around the platform was listening intently; no one noticed him enter.

Li Dong was still speaking.

"...You see, by projecting the Hecke operator onto the neighborhood of the accumulation point, you get a split."

"This part on the left is the automorphic side that I followed in my paper."

"This part on the right is the curvature that was the sticking point in the inverse problem."

"Both sides are actually two ways of writing the same thing from a dual perspective."

Professor Wang’s mind went BUZZ.

’Wait.’

’Projecting the Hecke operator onto the neighborhood of the accumulation point...’

On his "details unknown" scratch paper, inside that dotted box, he had repeatedly drawn three possible splitting positions but had never settled on one.

He didn’t know where to place the landing point of the projection.

But now, with that one sentence from Li Dong...

With a CLICK in his mind, out of the three possible positions, the one on the far edge—the option he had originally discarded—suddenly jumped out.

And it fit perfectly with another independent result from his own paper.

’This line of thought...’

’It’s my own.’

It wasn’t a simple retelling of what Li Dong had just explained.

It was the Hecke algebra decomposition he had been working on for nearly twenty years, sparked into existence at this very moment by Li Dong’s words.

Professor Wang was stunned.

He had spent the better part of his life working on automorphic forms.

He wouldn’t dare call himself a big shot, but no one would deny he was a veteran.

In all his time writing papers, he had never experienced something like "hearing one sentence and having a new conclusion pop into his head."

Anyone in mathematics knew that you had to gnaw at it, to grind it out, to be kept up in the dead of night by a tiny detail before an idea might spring forth the next morning.

It had never been so... so effortless before.

’What’s happening?’

Professor Wang took out a sheet of A4 paper from his bag but didn’t immediately start writing.

First, he silently retreated back to the classroom doorway.

The moment his foot crossed the threshold to the outside.

That image in his mind of "projecting the Hecke operator onto the neighborhood of the accumulation point" suddenly... faded a little.

The hierarchical structure of the three splitting positions, which had been so clear before, was now just a blurry outline.

Professor Wang narrowed his eyes.

He took another step back.

It became even blurrier.

One more step, and almost nothing was left but the two words "details unknown" inside the dotted box.

Professor Wang gasped.

He slowly started walking back.

One step.

The outline reappeared.

Two steps.

The hierarchy of the three splitting positions returned.

By the time he reached the outer edge of the discussion circle around the platform, he could see it even more clearly.

It was as if someone had turned on a light.

Professor Wang looked at Li Dong, and a term surfaced in his mind.

’The Master Effect?’

The term "Master Effect" wasn’t some internet joke; it was something real, passed down bit by bit from the predecessors his generation had looked up to.

You could say it was mystical.

And it really did seem a little mystical.

But to say it didn’t exist...

It was right there throughout the entire history of mathematical physics.

In the first two decades of the twentieth century, the reason Göttingen was once called "the center of the mathematical world" wasn’t because of the size of its dilapidated library, nor because the Germans loved mathematics.

It was because of one man: Hilbert.

Hilbert just sat there.

And the brightest young minds from all over the world—from Hungary, from Russia, from the United States—flocked to him like nails to a magnet.

Some of them had spent their whole lives in their own countries without producing anything of real substance.

But after going to Göttingen, strolling in the garden with Hilbert for half a month, they would return and start writing papers that would rewrite entire fields.

Hilbert himself once said:

"My best work was always thought up while walking with my students."

He wasn’t being modest.

He genuinely didn’t know what he had done.

Then there was Bohr...

Bohr’s own mathematical skills were not considered top-tier among the physicists of his generation.

His breakthrough contributions were proposing the hydrogen atom model and the complementarity principle.

Yet he was able to make people like Heisenberg, Pauli, and Dirac revolve around him, each producing some of the most important papers in the field.

This is what these three men wrote in their own accounts after completing their best work.

Heisenberg said that during his months in Copenhagen, "everything in my mind was crystal clear."

Pauli said he "became stupid again" as soon as he left Bohr’s side.

Dirac was a man of few words, but a sentence from one of his letters to Bohr has been quoted time and again by later generations:

"I understood more in your room than in a year elsewhere."

(Learning with you for a day is worth a whole year of fumbling on my own.)

And then there was Mr. Hua Luogeng in his later years.

It was said that just by sitting for a while at the small, square rosewood table in his home, young people who were stuck on a problem could complete their proofs on the way back.

Later, when several of his students were reminiscing, one of them put it most accurately:

"Mr. Hua doesn’t give you the answer. He just plucks the string inside your head that you already have, but didn’t know you had."

’Yes.’

’Just a single pluck.’

Professor Wang now felt as if that "details unknown" string in his own mind had just been plucked.

And the one who plucked it was Li Dong, the young man by the platform who looked no older than his own son.