While Li Dong was still explaining his paper to a group of doctoral students.
Capital University, School of Mathematical Sciences.
In a fourth-floor seminar room, the curtains were half-drawn. An open copy of the *Mathematical Annals* lay on the table.
Jiang Yubai sat at one end of the table, holding a cup of tea that had long since gone cold.
Zhou Shenzhi sat across from him, a thin layer of sweat beading on his forehead.
For nearly forty minutes, he had been staring at the *Mathematical Annals*. Specifically, at Li Dong’s derivation separating the main term of the pair correlation function for zeros in the interval |α|∈[1, 2].
He hadn’t said a single word.
Jiang Yubai didn’t rush him.
He simply gazed at the ginkgo tree outside the window.
But his mind was drifting to events from long ago.
A long time ago—he couldn’t even remember the exact year anymore.
It had happened in this very building.
Back then, Jiang Yubai had just returned from Paris. He was full of ambition, determined to establish himself in the mainstream of the Langlands Program.
The local-global compatibility for GL2 automorphic representations—this was the main direction he had chosen.
The core problem wasn’t complicated to state: when the ramification index e_v takes different values, is the Galois representation of the GL2 automorphic representation at a local prime identical to the representation given by the global automorphic form?
The case where e_v=1 was a classic result, long since proven by his predecessors.
The real challenge—the hard nut to crack—was e_v=2.
After returning to the country, Jiang Yubai spent three full years on it but couldn’t crack it.
He had tried a direct assault from the direction of Algebraic Geometry, tried a detour using Galois cohomology, and even attempted to introduce the framework of p-adic Hodge theory.
All of his attempts had failed.
Then, one of his students came up with a new path.
The student was just a master’s candidate at the time, not even graduated.
During a group meeting, in less than ten minutes, he sketched out a p-adic integral path deformation scheme on the blackboard that no one had ever considered.
The underlying Logic of that scheme was completely different from the path Jiang Yubai himself had been researching for three years.
It didn’t attack the problem head-on from the angle of Algebraic Geometry. Instead, it started from the Hodge-Tate decomposition in p-adic analysis, cleverly bypassing the most troublesome universal obstruction when e_v=2.
Jiang Yubai was stunned.
His academic judgment was top-notch. He realized immediately that if they followed this path, the e_v=2 case could be solved.
But the problem was...
He needed to establish his own foothold in the mainstream of the Langlands Program.
And that person was just a master’s student who hadn’t even graduated.
If he, Jiang Yubai, wasn’t listed as the first author, the paper would be meaningless for his academic standing.
So, when he had a "talk" with that person, he proposed that the student be listed as the second author.
The student fell silent.
Jiang Yubai, of course, knew what that silence meant.
Disagreement.
’But so what?’
A master’s student who hadn’t even graduated was a nobody in this circle.
His thesis defense, his doctoral recommendation letters, his entire future academic career—it was all in Jiang Yubai’s hands.
And so, what happened next, happened.
The student’s thesis defense was delayed again and again.
His doctoral recommendation letters were never sent.
And that ingenious p-adic integration scheme was handed over to another, more obedient student in the research group, who followed the path and completed the remaining calculations.
That obedient student was Zhou Shenzhi.
The paper was published in the *Duke Mathematical Journal*.
Authors: Jiang Yubai1, Zhou Shenzhi2.
There was no third name.
Later, that student showed up and caused a huge scene.
In the end, not only were his hopes of pursuing a doctorate dashed, but he was also soft-banned from the entire academic circle, unable to find even a decent job.
Eventually, he disappeared.
The rumor was he returned to his hometown and became a math teacher at a very ordinary public middle school.
From then on, Jiang Yubai never mentioned the matter again.
And Zhou Shenzhi, the student who had stood on the right side at the critical moment, naturally became the successor Jiang Yubai decided to cultivate.
Zhou Shenzhi did, in fact, live up to expectations.
He published many papers, led several projects, and made a small name for himself in the field of the Langlands Program.
But now, karma had come for them.
Back then, Zhou Shenzhi had used someone else’s idea and had indeed managed to solve the e_v=2 case.
But he had never truly understood the underlying Logic of that idea.
He had only used it, not understood it.
The reason that p-adic integral path deformation scheme could bypass the universal obstruction back then was because for e_v=2, the Hodge-Tate weights only involved first-order structures, and the universal obstruction happened to fall into a subspace that could be directly eliminated.
Zhou Shenzhi knew how to perform the calculation for this step.
But he didn’t know *why* that step was correct.
So when it came time to generalize the method to e_v=3...
He was stuck.
Because generalization requires not repetition, but understanding.
If you don’t understand why a method works, you will never know under what other conditions it can still work.
For e_v=3, the coupling structure of the second-order Hodge-Tate weights changed completely, rendering the original elimination technique utterly useless.
Zhou Shenzhi tried countless methods: changing the path parameterization, introducing higher-order filtration decompositions, even trying to bypass it using Colmez’s (φ, Γ)-module theory...
He hit a wall every time.
What made him despair even more was that after Li Dong’s paper came out, their purely algebraic method had become completely obsolete.
In his proof of Montgomery’s Conjecture on Association, Li Dong had established a completely new set of criteria for zeros and a correspondence with ramification indices, directly providing a brand-new line of attack on the Langlands Program from the perspective of analytic number theory.
Others had already built a rocket, while he was still trying to figure out how to make his horse-drawn carriage go a little faster.
Jiang Yubai sighed.
Of course, he could see Zhou Shenzhi’s predicament.
For the past three months, Zhou Shenzhi’s complexion had grown worse by the day, the bloodshot veins in his eyes more pronounced.
But the harder he worked, the more it exposed that fatal problem...
His foundation was hollow, and he lacked that creative spark.
Zhou Shenzhi saw the fleeting disappointment in his teacher’s eyes, and his heart sank.
He was very familiar with that look.
It was the look a teacher gives a student who isn’t measuring up, right before giving up on them.
He stood up.
"Professor!"
"This p-adic integration... and Li Dong’s criterion for zeros... I will figure them out."
His voice trembled as he spoke.
He didn’t know if he was making a promise to his professor or just trying to convince himself.
With that, he pushed open the seminar room door and strode out.
Jiang Yubai remained in the seminar room, his gaze fixed on the open copy of the *Mathematical Annals* on the table.
Li Dong.
Only nineteen years old.
A freshman at Yan University.
And his paper was already being used as a cornerstone by the entire mathematics community.
Including his own research group, Jiang Yubai’s group.
Jiang Yubai closed his eyes.
"If only you were my student... how wonderful that would be."
Meanwhile, in a lecture hall at Yan University.
The students had mostly dispersed, leaving only Tian Gang and a few of his doctoral students.
These doctoral students were all gathered around Li Dong, asking him questions one after another about Montgomery’s Conjecture on Association.
Li Dong answered each one in turn.
Some questions required him to think for a few seconds, but for most, he could provide a directional answer as soon as the person finished asking.
Tian Gang watched from the side, nodding in satisfaction.
’Yep, that’s my student.’
Although the matter of who between him and Liu Ruochuan was Li Dong’s official advisor hadn’t been settled, in Tian Gang’s heart, it was already a done deal.
’You, Liu Ruochuan, were my student. Are you going to betray your own master?’
Just as the doctoral students, satisfied, were closing their notebooks and had run out of questions, Tian Gang opened his mouth to speak.
But Li Dong beat him to it, walking over to him first.
"Teacher Tian, could you do me a favor, too?"

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