"You have no idea. The top students from several provinces have been driven crazy these past few days. Last night, this guy from the Northeast was yelling ’zero divergence’ in his sleep. Scared the hell out of everyone in our dorm."
Chen Zhuo chuckled but didn’t reply.
A rustling sound of a struggle suddenly came from the other end of the line.
"Stop wasting time with small talk! You’re about to burn through all the money on the IC card, and you haven’t even asked the important question."
A slightly deep voice, tinged with obvious exhaustion, spoke up.
Immediately after, Wang Huashao could be heard yelling, "Hey, don’t grab it! I’m not done yet!" before his voice faded into the distance.
A series of short breaths came through the receiver.
"Chen Zhuo."
It was Zhou Kai.
Compared to Wang Huashao’s boisterous energy, Zhou Kai’s voice sounded much calmer. But even through hundreds of kilometers of telephone line, Chen Zhuo could still faintly detect the bone-deep exhaustion seeping through.
"Sounds like they’re really working you to the bone over there," Chen Zhuo said.
"It’s manageable. I’m still breathing."
Zhou Kai gave a bitter laugh on the other end.
"I just feel like my brain’s seizing up. The pace here is too fast. The density of the material is on a completely different level from when we were at the provincial training camp."
"Where are you stuck?"
Chen Zhuo asked directly.
He knew Zhou Kai. The guy had a proud streak and wasn’t the type to complain over a few tedious calculations.
For him to feel like his brain was seizing up, he must have hit some kind of conceptual impasse.
Zhou Kai fell silent for a few seconds, as if mentally reorganizing the jumble of formulas in his head.
"It’s that plasma model Wang Huashao just mentioned. The coaches asked us to solve a boundary problem for a continuous fluid in a complex electromagnetic field. They want us not only to write out the complete set of partial differential equations, but also to find an approximate analytical solution under several extremely irregular boundary conditions."
There was a rare hint of frustration in Zhou Kai’s voice.
"Chen Zhuo, I’m not afraid of heavy calculations. I can work through even the most complex integrals step by step. But once you lay out that continuous model, the slightest change in the boundary conditions sends the whole equation spiraling out of control."
He sighed.
"I spent four hours on it this afternoon and filled up six sheets of scratch paper. The more I tried to find an exact solution, the more tangled up I got in the continuous variables. It was like... like trying to find the end of a thread in a tangled mess—the more you pull, the tighter the knot gets."
Because they had been silent for so long, the voice-activated light in the hallway CLICKED off.
Chen Zhuo stood in the darkness, listening to Zhou Kai’s slightly heavy breathing through the receiver.
"Zhou Kai."
Chen Zhuo spoke, his voice especially clear in the quiet hallway.
"Do you remember back at the provincial team’s training camp, when Professor Wang had us build that light-controlled alarm with those junk parts?"
There was a pause on the other end of the line.
"I remember."
"Back then, we were all obsessed with calculating the perfect theoretical voltage and reducing the resistor’s margin of error to zero," Chen Zhuo said unhurriedly.
"But in the end, we realized the real-world parts couldn’t support that kind of perfect, continuous theory. So we cut out the redundancies and just used a crude mechanical closure to force a discrete trigger."
Zhou Kai didn’t speak, listening quietly.
"The problem you’re facing now is the same as that one."
Chen Zhuo tilted his head back, looking at the faint water stains on the hallway ceiling.
"Those national team coaches are asking you to find an analytical solution to test your mastery of continuous mathematics tools. They’re pushing you to your limits. But if your real goal is just to solve this problem on the exam and get the points, you don’t need to untie that knot at all."
"If I don’t untie it, how do I solve it?" Zhou Kai’s voice was filled with confusion.
"If the continuous variables are suffocating you, then cut them."
Chen Zhuo’s tone was as flat as if he were stating a common fact.
"Stop worrying about the continuous changes of the fluid in every infinitesimal time interval. Try building a discrete grid. Replace that irregular boundary with a finite number of discrete nodes."
He stretched out his fingers in the darkness, drawing a few points in the empty air.
"Then, degenerate those complex partial differential equations into difference equations between adjacent grid points. Solve it using an algebraic matrix."
The other end of the line suddenly went quiet.
Only the faint hiss of static remained.
"Difference equations... discrete grid..."
Zhou Kai muttered the words to himself, his voice growing quieter and quieter, as if some frantic conversion was happening in his mind.
"Right," Chen Zhuo continued.
"It won’t give you a neat analytical solution that can be expressed with a pretty function. All it will give you is a pile of approximate data."
He chuckled.
"But that pile of data is enough to put you on solid ground on a competition paper and get you the points you deserve. More importantly, it will pull you out of that ever-tightening quagmire of continuity. An exam is an exam. Don’t treat it like scientific research."
The sound of Zhou Kai taking a deep breath came from the other end of the line.
"I get it."
The heaviness and exhaustion that had weighed him down seemed to have been washed away in an instant by this sudden breakthrough in his thinking.
"Chen Zhuo, have you... run into a similar problem on your end?" Zhou Kai asked hesitantly.
"How do you have such a thorough understanding of discretization?"
Chen Zhuo gazed at the pitch-black window at the end of the hallway.
The old papers he had read in the library these past few days, the dozens of pages of continuous derivations written by mathematicians to prove a single theorem, flashed through his mind.

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