Evening fell over the Mathematics Building, and the hallways were silent.
The office door was ajar, the lights unlit.
The air inside seemed stagnant.
Li Jianming leaned back in his old rattan chair, a pair of reading glasses perched on his nose. He held a copy of last month’s Mathematical Annals, but his gaze had been fixed on the second paragraph of the left-hand page for a full ten minutes, unmoving.
Across from the desk, Wu Tao held a spray bottle, watering the several pots of devil’s ivy on the windowsill.
"Wu Tao."
Li Jianming spoke suddenly, his voice startling in the quiet room.
"You’re going to rot the roots of that devil’s ivy."
Wu Tao’s hand paused.
He glanced down and saw that a layer of water had indeed collected in the saucer beneath the pot.
He silently set down the spray bottle, pulled a tissue, and bent over to wipe the water that had spilled over the saucer’s edge.
"I’m sorry, Teacher Li. I was distracted."
Wu Tao tossed the tissue into the trash can, straightened up, and instinctively glanced at the large blackboard on the side wall of the office.
The dense calculus formulas covering the bottom right half of the board remained just as they were days ago.
Untouched for several days, the edges of the white chalk markings had begun to blur, and a thin layer of dust had settled in the chalk tray.
’It was a dead end they couldn’t overcome.’
’That diverging integral term at the continuous domain boundary was like a splinter in the eye.’
Li Jianming had given strict orders not to touch the project for the past few days, so Wu Tao hadn’t dared to write a single related formula on paper.
But his mind never stopped working on it.
He thought about it while eating, while walking. Last night, he even dreamed he was trapped in an infinitely oscillating Riemannian manifold, completely unable to find an exit.
"Stop looking at it."
Li Jianming closed the journal in his hands, took off his reading glasses, and tossed them on the desk before pinching the bridge of his nose.
"A string stretched too tight is bound to snap. If you’ve hit a wall, just let it be for now. With mathematics, you can’t force inspiration by banging your head against a wall."
Wu Tao nodded without a word. He walked over to the water cooler, grabbed a disposable paper cup, and was about to get some water.
Suddenly, the sound of footsteps echoed from the hallway.
They weren’t the usual shuffling steps of students passing by, but a crisp, hurried pace.
The sound stopped abruptly at the office door.
The door was pushed open.
Li Jianming looked up. Wu Tao turned around, empty paper cup in hand.
Chen Zhuo stood in the doorway, his forehead beaded with sweat.
This was not the usual Chen Zhuo.
In Li Jianming’s and Wu Tao’s experience, this genius from the gifted program was always methodical, gentle, and calm, no matter how complex the topology problem he faced.
But right now, Chen Zhuo’s eyes were astonishingly bright.
He strode into the office.
He was clutching a crumpled sheet of printer paper in his left hand. The edge was stained with a spot of dark red grease, as if he’d accidentally brushed it against some soup.
"Teacher Li, Senior Brother Wu."
Chen Zhuo wasted no time on pleasantries. He walked to Li Jianming’s desk and spread the greasy, wrinkled paper out on its surface.
His speech was much faster than usual, but his enunciation was exceptionally clear.
"I’ve found the way."
Wu Tao froze for a moment, then took a step forward, paper cup still in hand.
"What do you mean?"
Chen Zhuo didn’t answer Wu Tao. He turned and walked straight to the blackboard.
He picked up the dust-covered eraser from the chalk tray.
Under the watchful eyes of Li Jianming and Wu Tao, Chen Zhuo didn’t hesitate for a second. He pressed the eraser directly onto the dense derivations for the continuous domain in the bottom-right corner.
Chalk dust cascaded down.
With a few swipes, Chen Zhuo wiped away the formulas that had cost them more than half a month of painstaking effort, formulas where they had tried countless scaling methods to smooth the boundary.
The oppressive blackboard was instantly cleared, leaving a large empty space.
"Chen Zhuo!"
Wu Tao cried out instinctively.
Chen Zhuo tossed the eraser back into the tray, clapped the dust from his hands, and picked up a piece of chalk.
He turned to face Wu Tao.
"Senior Brother Wu, what is the prerequisite for calculus? It’s the continuity of the manifold, the local smoothness."
Chen Zhuo’s voice echoed in the office.
"But this network structure we’re dealing with—on an extremely small scale, it’s not smooth at all."
Chen Zhuo pointed to the greasy paper on the desk.
"This afternoon in the cafeteria, I overheard a friend of mine talking about machining. Say you have an aluminum rod fitted inside a steel tube. When it’s heated, it expands. Aluminum has a large expansion coefficient, while steel’s is small. On a microscopic level, the atoms inside are furiously compressing and contending with each other."
Wu Tao frowned.
"What does that have to do with our project?"
"It has everything to do with it."
Chen Zhuo turned back to the board. He tapped the chalk firmly on the newly cleaned surface and drew a circle to represent a node.
"If you use continuous domain calculus to calculate the boundary forces of this piece of metal, you’ll never get a clear answer. The internal positive and negative errors will constantly diverge, oscillating infinitely."
With a flick of his wrist, Chen Zhuo wrote a symbol next to the circle.
"But in physical reality, no matter how much pressure builds up inside, as long as the outer frame is locked, the piece of metal is macroscopically motionless. Why? Because those divergent internal forces cancel each other out."
Li Jianming’s gaze sharpened. He said nothing, but his body leaned forward unconsciously.
Chen Zhuo’s chalk flew across the blackboard.
"Since the continuous domain is a dead end, we abandon it."
"We project the entire network into a discrete algebraic topological space."
Rows of algebraic symbols began to appear on the blackboard.

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