Chapter 253 - 151: No Divergence

Chapter 253: Chapter 151: No Divergence

The sound of footsteps from the end of the hallway grew clearer.

A cold draft swept past Zhou Qiping’s cheek, and the air in the office seemed to freeze.

He leaned back in his large leather chair, hands folded on the desk. His gaze passed over several stacks of files to fix on the closed door.

On the sofa to the side, Fang Shi, the associate dean of the physics department, sat bolt upright. The blue review report in his hand was slightly curled from the force of his grip.

His eyes darted nervously between the doorknob and Li Jianming, his Adam’s apple bobbing.

Standing directly in front of the desk, Li Jianming’s breathing grew heavier.

His eyes, bloodshot from five months of sleepless nights, were glued to the doorway. The hands at his sides unconsciously clenched and unclenched.

Li Jianming had pictured the person countless times in his mind.

The one who could write a discrete algebraic matrix, the one who had single-handedly broken a computational deadlock: C. Zhuo.

Even though he had just seen the photo from the fax a few minutes ago, as the real person was about to push open the door, he still felt a stone weighing on his chest. The sound of his own heartbeat pounded wildly in his ribs.

The footsteps stopped.

After two seconds of silence, the heavy wooden door was pushed open a crack. Light from the hallway streamed through the gap, casting a long, slanted shadow on the dark wood floor.

The door was pushed all the way open.

There was none of the steady presence of an academic titan, nor the oppressive air of arrogant genius he had expected.

Standing in the doorway was a boy in a plain white, short-sleeved, collared T-shirt. The shirt was clean, the collar neat yet casual. He held a black softcover notebook with a silver mechanical pencil clipped to it.

A cross-breeze swept through, ruffling the bangs on his forehead and revealing a pair of clear, calm eyes.

Twelve years old.

He was just a boy, his frame not yet fully developed, possessing the characteristic slightness of his age.

If you were to bump into him on campus, you’d think he was just some kid from the Keda faculty housing, barely in middle school, out playing during his summer break.

But as he walked into this office—a symbol of Keda’s administrative power and academic authority—the stark visual contrast sent the administrators and the old professor in the room into a momentary daze.

Zhou Qiping unconsciously leaned forward, pushing his reading glasses further down his nose.

He had met countless people and seen too many so-called geniuses. The standouts from the gifted programs were either insufferably arrogant, their pride impossible to conceal, or lost in their own worlds, appearing dull and withdrawn.

But this boy was different.

He stepped inside and surveyed the room with a placid gaze. There was no stage fright, no awkwardness in front of the university leadership. He was as natural as if he were walking into a lecture hall for a regular class.

Chen Zhuo closed the door behind him. He looked at Zhou Qiping, then at the tense-faced Fang Shi, and finally, his gaze settled on Li Jianming, who was staring intently at him.

The atmosphere in the room was strangely oppressive.

Chen Zhuo stopped and bowed slightly. His voice was clear and gentle:

"Principal Zhou, Dean Fang. Hello, Teacher."

No one spoke.

The three men, whose ages combined to nearly two hundred years, were frozen in place as if under a spell.

Fang Shi was the first to react. He shot to his feet, strode over to Chen Zhuo’s side, and subtly shielded him from Li Jianming’s view. His tone was urgent, like a mother hen protecting her chick.

"Xiaozhuo, you just came from the lab, right? Sorry to make you run over. Did I interrupt you from adjusting your parameters?"

He was trying to keep the conversation confined to matters of the physics department, but Li Jianming gave him no such opportunity.

"Move."

Li Jianming’s voice was as hoarse as sandpaper on wood. He ignored Fang Shi, his eyes fixed on the obsession that had tormented him for five months.

He moved past Fang Shi and stood directly in front of Chen Zhuo.

Up close, Chen Zhuo could see the fine beads of sweat on the old professor’s hairline and smell the strong scent of tea that came from years of late nights.

Li Jianming’s hands were trembling.

He pulled out a sheaf of frayed draft paper, densely covered with derivations in black and blue ink, and thrust it in front of Chen Zhuo.

"Li Jianming! What are you doing!"

Fang Shi grew anxious, hissing in a low voice.

"He’s only a sophomore! His head is full of fluid dynamics models. Are you trying to corner him with that dead-end graph theory from the School of Mathematics? They’re not even in the same field!"

"You shut up!"

Li Jianming violently shook off Fang Shi’s hand with surprising strength. He turned to glare at Fang Shi, his eyes webbed with red.

"Not the same field? Then who wrote the matrix in that *Discrete Mathematics* textbook? Who created that nonlinear compensation term that forcibly severs continuous variables? Fang Shi, don’t give me that crap! That was pure theoretical mathematics! If he could write that compensation term, he can understand my Laplace expansion!"

After speaking, he turned back to Chen Zhuo. The ferocity in his eyes faded, replaced by an urgency that bordered on pleading.

This renowned scholar had dropped all pretense in front of the twelve-year-old boy.

"Classmate Chen,"

Li Jianming struggled to keep his voice steady, but the papers in his hand were still shaking.

"I’ve read your paper. Now, I’ve hit a wall."

He pointed to a series of terms circled in red among the equations.

"This is a pure mathematics conjecture on complex network topology. The framework is sound, but after the Laplace Matrix expansion at the core nodes... by the eighth order, the number of terms begins to explode factorially. Singular terms proliferate like crazy. I tried to simplify it using traditional spectral graph theory, but I can’t find a general formula. They won’t cancel out, and it ends up as a completely divergent infinite series."

He looked at Chen Zhuo, his voice laced with deep exhaustion.

"For the past few months, my students and I have manually checked the first two hundred terms and found no convergence pattern. Take a look for me. This explosion... how on earth does it converge?"

The office fell into a dead silence once more.

Fang Shi no longer tried to intervene, and Zhou Qiping watched with bated breath.

Chen Zhuo’s previous calm expression vanished.

Faced with these derivations, the culmination of an old professor’s lifeblood, he did not give a perfunctory reply, nor did he put on an act and pretend to have an answer.

With a solemn expression, he accepted the heavy stack of papers and said in a low voice,

"Teacher, please wait a moment."

The only sound in the quiet room was the soft rustle of flipping paper.

Thirty seconds passed.

Chen Zhuo’s eyes scanned line by line, following the complex summation signs and subscripts.

Li Jianming stood rooted to the spot, not daring to breathe, his heart in his throat.

Two minutes later, Chen Zhuo finished with the core pages, straightened the stack of paper, and looked up at Li Jianming.

"Well?"

Li Jianming’s voice trembled slightly.

"Can you find a general formula to cancel out the singular terms?"

Chen Zhuo looked at him, his gaze clear, and stated the facts impartially.

"Teacher Li, your preceding derivations are extremely rigorous. There are no logical flaws. However."

Chen Zhuo pointed to the eighth-order expansion.

"If you follow traditional spectral graph theory, the factorial proliferation of singular terms is an inherent property of this type of continuous topological space. As long as you stay within that framework, it is destined to diverge. A general formula simply doesn’t exist."

Chen Zhuo was very frank.

"This is a logical dead end. Following this path, I can’t solve it either."

The moment he finished speaking, Fang Shi’s tense shoulders instantly relaxed.

’Good that he can’t solve it. If he can’t solve it, it means Chen Zhuo is still human, and Old Li can finally give up.’

The light that had just kindled in Li Jianming’s eyes was doused as if by cold water, extinguished in an instant.

His back slumped, the change visible to the naked eye.

Five months of day and night, half a cabinet’s worth of drafts, had all led to an insurmountable wall.

He gave a bitter laugh, his voice faint.

"It seems it really is a dead end. I was just grasping at straws. Even the person who proposed matrix dimension reduction says it can’t be simplified. This traditional spectral graph theory has truly reached its limit..."

However, just as he was about to pull the draft papers back, Chen Zhuo flicked his wrist, deftly avoiding his hand.

Li Jianming froze.

Chen Zhuo held the stack of papers, twirling the silver pencil half a turn between his fingers. His voice remained calm:

"Teacher, in traditional algebraic graph theory, this is indeed a dead end. But just because we can’t solve for the general formula in this space doesn’t mean the problem can’t be pushed further."

Li Jianming’s hand, extended in mid-air, stiffened. A light burst forth once more in his dimming eyes.

"You... what did you say?"

Li Jianming’s voice rose.

Even Fang Shi, who had been standing by ready to watch the show, had a change of expression.

Chen Zhuo paid no mind to the others’ reactions. He lowered his head slightly, his gaze returning to the draft paper.

"Teacher Li, you’ve read the short article I published in *Discrete Mathematics*."

"I have! Countless times!"

Li Jianming nodded repeatedly.

"You constructed a discrete algebraic matrix and used a nonlinear compensation term to forcibly sever an infinite series. I just wanted to ask you, can that matrix of yours be applied to my graph theory model?"

Chen Zhuo shook his head gently.

"It can’t be applied directly."

Chen Zhuo’s answer was crisp.

"My paper dealt with discrete, independent nodes, whereas you’re studying a continuous complex network. The boundary conditions don’t overlap at all. If you were to force that algebraic matrix into this, it would cause the entire topological structure to collapse."

The light in Li Jianming’s eyes, which had just brightened, dimmed again.

"It can’t be applied... Then... then how do you solve it?"

Chen Zhuo walked over to Zhou Qiping’s large mahogany desk and spread the draft papers flat. He gripped his pencil, leaned over, and fixed his gaze on the dense cluster of singular terms.

The gazes of the three professors followed the tip of his pencil. The air was so quiet that only the SCRITCH-SCRATCH of pencil on paper could be heard.

"Teacher, you’ve been trying to find a pattern within the original continuous topological network."

As he spoke, Chen Zhuo wrote a basic transformation function in a blank space.

"In this dimension, the proliferation of singular terms is a property of the space. But what if we give up on brute-forcing a general formula?"

He added a group space symbol, his voice steady yet each word carrying immense weight.

"What if we introduce a homology group mapping at the eighth-order node? Instead of looking for a cancellation pattern, we use the homology mapping to project these continuous variables as a whole into a brand-new discrete algebraic space."

The tip of his pencil tapped on the symbol.

"In the new space, the originally divergent singular terms would lose their continuous basis. Under the new algebraic structure, they wouldn’t need to be cancelled out; they would spontaneously collapse."

Chen Zhuo stopped writing and looked at Li Jianming.

"At that point, you would no longer need to worry about the infinite series. You would just need to construct a closure in the new discrete space, connecting the logic from end to end."

Dead silence.

Fang Shi was completely lost; this cross-dimensional homology group theory was far beyond his applied field. Zhou Qiping, though he didn’t understand it either, looked towards Li Jianming.

At this moment, Li Jianming was like a man under a petrification spell.

He stared intently at the line of penciled words.

Homology group mapping.

Project as a whole.

Spontaneously collapse.

These words were like a bolt of lightning, splitting apart the mountain of combinatorial explosion that had plagued him for five months.

His breathing became ragged, his face flushed red, and his previously slumped back went rigid with extreme excitement.

"Homology group mapping... projection... spontaneously collapse..."

Li Jianming muttered to himself, then suddenly snatched the pencil from Chen Zhuo’s hand and threw himself over the desk. As if possessed, he began calculating along that line of thought.

Li Jianming’s calculations were astonishingly fast. Under his pencil, the two troublesome singular terms rapidly transformed, dragged forcibly into the new discrete structure.

Three minutes later, Li Jianming’s movements came to an abrupt halt.

He stared at the result at the bottom of the draft paper.

The two singular terms, which should have diverged infinitely, had truly collapsed into two quiet constants in the discrete space.

No divergence.

The path was clear.

Li Jianming remained hunched over the desk, his shoulders beginning to tremble violently. The pencil fell from his hand, clattering sharply on the wood.

He slowly straightened up and turned to look at Chen Zhuo, the bloodshot veins in his eyes burning with fanaticism.

He strode forward and seized Chen Zhuo’s arm, his grip so strong his voice cracked as his roar echoed down the hallway:

"What’s so great about studying physics?!"

"That’s all just engineering work, calculating approximations! For a mind like yours to be wasted on physics is a crime against mathematics!"

He gripped the boy tightly, his eyes filled with an imperious look that brooked no refusal.

"Xiaochen, come to the School of Mathematics! I, Li Jianming, will personally mentor you! Forget the basic courses; I’ll help you apply for research projects, for funding! You were born for pure math. If anyone dares make you work on a wind tunnel, I, Li Jianming, will tear down their lab!"

At the side, Fang Shi’s face instantly turned ashen.