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Chapter 228: Chapter 219: Sorted by Surname

Zhou Qifeng left with only one question on his mind.

’What on earth is this kid?’

In truth, Zhou Qifeng wasn’t the only one wondering about this.

The entire Yan University School of Mathematics, and even the entire Huaxia Mathematical Community, was asking the same question.

What on earth was Li Dong?

...

The moment Zhou Qifeng left, Professor Penrose shot up from the chair beside him.

He had clearly been holding it in.

For the past hour-plus that Li Dong and Zhou Qifeng had been speaking Chinese, he had sat quietly to the side, not interrupting or losing his temper.

But in his peripheral vision, Li Dong saw him sketch some sort of recursive framework on a piece of scratch paper at least a dozen times.

The instant Zhou Qifeng left, he grabbed Li Dong’s arm.

”Dong! Dong!”

”Come on, come take a look at this!”

Li Dong nearly stumbled from the pull.

”Professor, slow down...”

”Let me explain!”

Penrose paid him no mind, grabbing a marker and writing furiously on the whiteboard.

”I went back and reviewed the condition for the self-adjointness of the spectral operator you left me with yesterday.”

”And then, it hit me.”

He spoke as he wrote.

”Look here. Didn’t we say before that we wanted to adapt the universality theorem for high-dimensional random matrices for use in the GL(n) case?”

”But there’s a very tricky part.”

”In their work, Terence Tao and Van Vu only proved GUE universality for the case where the matrix entries follow a sub-Gaussian distribution.”

”What we need, however, is the setting for the statistics of zeros of automorphic L-functions.”

”The matrix entries there aren’t independent and identically distributed at all; they have a very complex local ramified coupling structure.”

Li Dong nodded.

He had thought about this sticking point himself last night.

The solution he’d previously given Penrose was to just brute-force a more general universality theorem, treating the coupling structure as a perturbation term.

That approach would have worked, of course, but the workload was immense. That step alone could have consumed the better part of a year.

Penrose continued sketching on the board.

”So I kept mulling it over.”

”And then, it suddenly clicked...”

”We don’t need to prove the complete universality theorem at all!”

”We just need to prove its approximate universality on a narrow band!”

He drew a very narrow interval on the whiteboard.

”See, the zero criterion requires proving that F_π(α) converges to the GUE predicted value, n|α|, on |α|∈[0, 2/n].”

...

He paused, his eyes glinting.

”For the latter section, we only need to prove that the difference between it and the former section is a quantity of the Schwarz class.”

”And that difference just so happens to be a standard output of your set of dynamic adaptive Fourier weight functions!”

Having said this, Penrose turned back to look at Li Dong.

”Dong, what do you think?”

Li Dong was taken aback.

This approach was even more elegant than his own.

His approach was viable, but it would have been quite laborious in comparison.

Penrose’s method, on the other hand, of restricting to a narrow band, bypassed the quagmire of complete universality entirely, using a difference estimate to bridge the two sections.

It was technically cleaner, and the workload was smaller by at least an order of magnitude.

The craziest part was...

The ”dynamic adaptive Fourier weight functions” used for this difference estimate were the very set of tools that Li Dong himself had constructed in his paper on Montgomery’s work.

In other words, Penrose had taken a weapon from Li Dong’s arsenal and applied it in a way Li Dong himself hadn’t even considered.

Li Dong gave Penrose a peculiar look.

’I’ve been underestimating these top scholars a bit.’

On second thought, it was to be expected.

This was Penrose, after all.

A top expert in analytic number theory from Princeton, he had given an hour-long address at the International Congress of Mathematicians before he was sixty, had published multiple *Annals*-level papers on the subconvexity problem for GL₂ automorphic L-functions, and had mentored a student who went on to win the Cole Prize in Number Theory.

For a professor of his caliber, when he truly set his mind to something, it would be stranger if he *didn’t* produce something that turned heads.

Li Dong had previously thought that the old professor’s Basic Attributes were probably all above 0.2.

But now it seemed...

He had underestimated. His Logic and Concentration Attributes were possibly as high as 0.3.

His initial reason for inviting Penrose to join the project was actually very simple: to keep Penrose at Yan University.

This was the idea Liu Ruochuan had given him at the time.

That part of the plan had been a success.

Penrose had already arranged with the university to teach several public courses at Yan University next semester, on the topic of analytic number theory over p-adic numbers.

Those lectures alone would be enough to have the graduate students at the Yan University School of Mathematics fighting tooth and nail for a spot.

But now it seemed that having Professor Penrose stay would benefit not only Yan University, but the project as well.

He could genuinely accelerate the project’s progress.

Li Dong looked up at Penrose.

”Professor.”

”That’s brilliant.”

He wasn’t being the least bit perfunctory when he said those two words; he was completely sincere.

Penrose paused, stunned.

Then a huge, uncontrollable smile spread across his face.

He looked just like a student who had earned their advisor’s approval.

Watching the sixty-year-old professor’s reaction, Li Dong felt a swirl of complicated emotions.

Normally, wouldn’t someone in Penrose’s position be insufferably arrogant?

A top professor of analytic number theory at Princeton. If he wished, becoming a foreign member of the academy wouldn’t be out of the question.

’It’s not me he’s acknowledging.’

Li Dong knew this very well.

He was acknowledging the person standing behind Li Dong.

He was acknowledging Riemann.

That great nineteenth-century master of analytic number theory had used an old notebook to conquer generation after generation of analytic number theorists over the past two centuries.

For someone like Penrose, reverence for Riemann was etched into his very bones.

And in Penrose’s eyes, Li Dong was, in a sense, a ”projection” of Riemann in the modern era.

This realization made Li Dong feel a little ashamed...

”Professor Penrose.”

”When this paper is finished, let’s list the authors alphabetically by surname.”

Penrose, who was about to continue writing on the whiteboard, froze, marker in hand.

”Alphabetically?”

Li Dong nodded.

”Yes.”

In the field of pure mathematics, listing authors in alphabetical order by surname has been an international convention for decades.

The reason for this convention is that mathematics as a discipline is different from the experimental sciences.

In fields like chemistry, biology, and experimental physics, a single paper often involves dozens of different roles.

Some people propose the theory, some run the experiments, some operate the instruments...

Each person’s contribution to the overall work can be quantified, so it’s natural to use first, second, and third authorship to distinguish between them.

But pure mathematics isn’t like that.

A collaborative paper in pure mathematics is, in essence, a few people shut in a room, facing the same whiteboard, and summiting a mountain together.

Who came up with which key idea, who got stuck on a lemma for two days before having a breakthrough, who ultimately pieced together all the scattered arguments into a clean framework... these things simply can’t be quantified by first or second authorship.

Thus, starting in the mid-twentieth century, the mathematical community established an unspoken rule.

The prevailing convention for collaborative papers is to list authors alphabetically by surname, irrespective of the magnitude of their contribution or their primary or secondary roles.

In recent years, however, things have slowly begun to change.

More and more pure mathematics papers, especially in interdisciplinary fields tending toward Computational Mathematics, applied mathematics, statistics, and even data science, have begun to adopt contribution-based ordering.

The reasons are quite practical.

On one hand, the workload disparity in these interdisciplinary fields is often huge. A postdoctoral researcher who spent six months running numerical experiments isn’t necessarily going to accept being listed as an equal author with a collaborator who merely mentioned a potential direction.

On the other hand, when it comes to evaluations for promotions and grants, the administrative systems at many universities and institutions only recognize ”first author” and ”corresponding author.”

The pure mathematics tradition of ”alphabetical by surname” runs into a wall when it meets these administrative systems.

Therefore, over the last decade or so, especially within universities in Huaxia and the United States of America, some research groups have begun to explicitly switch to contribution-based ordering.

When Penrose heard what Li Dong said, his expression froze.

Honestly, he never expected Li Dong to be the one to bring it up.

After all, the overarching framework and the most critical tools for this project all belonged to Li Dong.

Without Li Dong, the project could never have even been started.

And without him, Penrose, Li Dong could have still pushed forward, just perhaps a bit more slowly.

Under the circumstances, Penrose had originally assumed Li Dong would awkwardly hint, ”We should discuss the authorship later,” and he would then proactively step aside and leave the first-author position to Li Dong.

Instead, Li Dong had just come right out and said, ”Let’s list them alphabetically.”

This did away with all the polite maneuvering.

What was the subtext behind the phrase ”list them alphabetically”?

It was, ”We are equal collaborators.”

It was, ”I see you as my peer, standing shoulder to shoulder with me.”

Penrose was silent for two seconds, then gave a firm nod.

”Alright.”

”We’ll list them alphabetically.”

He paused, then added another sentence.

”Dong, thank you.”

The ”thank you” was spoken softly, but with great sincerity.

Li Dong shook his head and said with a smile.

”Professor, you’re very important. We need you.”

He then briefly discussed the next steps for this line of inquiry with Penrose.

He asked him to continue moving forward along these lines, and they would all meet again tomorrow morning to sync up on the details.

After settling everything, Li Dong packed his things and left the seminar room.