The math department’s red-brick office building was old, its exterior covered in climbing ivy.
At the end of the second-floor hallway, the door to a private office was ajar. The main light was off, leaving the room somewhat dim.
Li Jianming stood before a large blackboard that took up an entire wall.
The board was covered in white chalk, filled from the top-left corner to the bottom-right with derived formulas, matrix expansions, and summation symbols with complex subscripts.
Smudges from an eraser were covered over with new equations, creating a dizzying, blurry white mess.
Li Jianming held an enamel mug. A few tightly curled tea leaves floated on the surface of the water.
He wasn’t drinking, his eyes fixed on an equation circled in red in the center of the board.
The door hinges creaked softly.
His student, Wu Tao, walked in, clutching a stack of A4 scratch paper with curled edges. Wu Tao had heavy, dark circles under his eyes, and his footsteps were sluggish.
"Teacher."
Wu Tao’s voice was low. He placed the scratch paper on the desk.
Li Jianming turned, his gaze shifting from the blackboard to the pile of paper.
"Still can’t prove the seventh lemma?"
Li Jianming asked, his voice a bit hoarse.
Wu Tao shook his head and sighed.
"Can’t close the loop."
Wu Tao flipped over the top sheet of scratch paper, pointing to a long line of calculations in the middle.
"After expanding the Laplace Matrix for the core node, once you get past the eighth order, the number of polynomial terms starts to explode."
Wu Tao rubbed the tired corners of his eyes and continued.
"Last night, I did as you suggested and tried to simplify it using traditional spectral graph theory, but I couldn’t find a general formula. The extra singular terms won’t cancel each other out. In the end, it just becomes a divergent infinite series."
Li Jianming walked back to his desk and set down his mug.
"How many terms did you check by hand?"
"I checked the first two hundred expanded terms," Wu Tao said. "There’s no pattern of convergence. It’s a total mess."
Li Jianming said nothing.
He knew Wu Tao had done his best.
This wasn’t a problem that could be solved by pulling an all-nighter. This was a wall in theoretical mathematics.
They were researching a pure mathematics conjecture on complex network topology. The foundational framework and preliminary validations had gone smoothly, but when it came to the core theoretical proof, they had hit a dead end.
Pure mathematical derivations allow for no ambiguity.
When engineering encounters an unsolvable problem, you can truncate, you can find an approximation.
Pure mathematics cannot.
The left and right sides of an equation must match perfectly. If a single link in the logical chain was missing, the half-a-cabinet’s worth of scratch paper they had filled would become a pile of waste.
Without a new algebraic isomorphic mapping to bypass this combinatorial maze, the conjecture would forever remain just a conjecture.
"Go get some sleep in the lounge next door."
Li Jianming looked at Wu Tao’s bloodshot eyes and waved his hand dismissively.
"Don’t you still have to work on the random walk model for your own dissertation? Go focus on that. Let’s set the seventh lemma aside for today. Brute-forcing it like this is just a waste of paper."
"But, Teacher Li, the proof is stuck right here..."
"Go rest."
Li Jianming cut him off. His tone was gentle, but it left no room for negotiation.
Wu Tao didn’t insist further, nodding as he exited the office.
Li Jianming was left alone in the room.
He pulled out his chair and sat down, reaching across his cluttered desk to pull out the autumn issue of *Discrete Mathematics*.
His thumb traced slowly over the rough cover.
Half a month ago, he had seen a short article in this journal.
The article was short, discussing node connectivity and matrix dimensionality reduction.
The author was listed as C. Zhuo, from his own university.
Li Jianming turned to the dog-eared page.
He read the few lines of the core proof steps from beginning to end once more.
Every time he read it, he felt his palms grow hot.
When faced with a similar polynomial explosion, this C. Zhuo hadn’t bothered to navigate the maze at all. Instead, they had constructed a discrete algebraic matrix out of thin air, slicing right through the infinitely recursive terms.
Then, using a non-linear compensation term, they had forcibly stitched the beginning and end of the logic together.
It was utterly clean.
’This was true mathematical beauty. No brute force, no getting bogged down in the mire. Just a change in perspective, drawing a closed loop in a higher dimension.’
At the time, Li Jianming had grabbed the journal and rushed straight to the Physics Building.
He had seen the name in the acknowledgements of a top-tier physics paper from Princeton and assumed C. Zhuo was some senior professor in the physics department who did interdisciplinary research.
He had gone to ask Alchemist for an introduction.
Alchemist had been sitting in an armchair, teacup in hand, beating around the bush in his usual, unhurried way.
Alchemist had said that Old Chen was a recluse who found people annoying. He also said that Old Chen was completely absorbed in tuning a model for the physics department’s national-level fluid dynamics project, and that he would arrange a meeting once the project was over.
Half a month had passed.
Li Jianming had forced himself to wait for half a month.
’We’re all scholars at the same university. Alchemist’s wind tunnel model is a key project, too. It would be bad form to interfere while they’re in a critical phase.’
But now, his derivation was completely and utterly stuck.
Li Jianming closed the journal and tucked it under his arm.
He couldn’t wait any longer.
How was Alchemist’s project progressing, anyway?
Had Old Chen helped him break the deadlock?
Li Jianming stood up and walked out of his office.
The air outside was muggy and still.
Li Jianming strode toward the Physics Building, though he felt a knot of uncertainty in his gut.
’If the physics department was still tearing their hair out, he probably wouldn’t even get to meet anyone.’
He walked through the red-brick entrance of the Physics Building. The first-floor lobby was quiet.
Instead of going straight upstairs, Li Jianming turned into a first-floor hallway. At the end was the physics department’s common lounge, where teachers and students usually gathered to get water and chat.
He wanted to test the waters first.
Before he reached the door, he heard voices from inside.
"Brother Zhang, your dark circles have finally faded a bit. You must have had a good catch-up sleep yesterday, huh?"

Comments

Loading...