My IQ has been increasing year by year.

Four or five days have passed since I casually drew that transition probability matrix in the old library.

The temperature at USTC has remained high for the past few days.

The sky was always a deep, almost white blue, with not a single cloud in sight.

The cicadas screech incessantly in the treetops, their calls almost never ceasing from morning till night, displaying a tenacious determination to burn summer to ashes. Chen Zhuo's life was as regular as a perfectly timed old pocket watch.

In the morning, I went to the second canteen to buy two meat buns and a cup of soy milk, and then headed straight to the foreign language reading room on the third floor of the old library.

A tacit understanding, almost like gears meshing, developed between him and Su Wei.

Su Wei seemed to see him as a reliable tool for providing solutions, while Chen Zhuo unceremoniously regarded her as the most useful living search machine at USTC. Each day, he only needed to leave a note on his desk, specifying the era and general field he needed to consult, and while he went to get a glass of water, those heavy, ancient documents would appear precisely on the corner of his desk. Chen Zhuo wasn't in a hurry.

He has been studying the foundations of algebraic topology and group theory from the 1950s to the 1970s.

He decided to temporarily set aside the latest cutting-edge journals and instead, little by little, trace back the historical development of mathematics and physics. He was searching for that logical feeling of how science is built up bit by bit.

In an era without the aid of large computers, how did the older generation of mathematicians build scientific fortresses on paper with only their pure intellect? The days slipped by amidst the rustling of pages and the whirring of ceiling fans.

evening.

The sun finally stopped its scorching heat and slowly sank behind the roof of the western teaching building.

Long shadows stretched across the campus, and the asphalt road, baked by the sun all day, still radiated waves of heat.

Chen Zhuo closed his notebook, pushed the several thick Russian books he had borrowed to the side of the table, and got up to pack his things.

Not far away by the window, Su Wei was still struggling with a bunch of complex actuarial data.

Since mastering the use of discrete matrices to reduce the dimensionality of continuous probability problems for those from other disciplines, she's been solving problems much more smoothly these past few days. It's even become a little more agreeable to Chen Zhuo's character designs. (Chen Zhuo: So it's just that they look agreeable? How sad~)

Chen Zhuo picked up the empty kettle.

Su Wei didn't even look up, just stared at the draft paper and hummed in response.

Chen Zhuo pushed open the door to the reading room and went down the stairs.

Even after leaving the library, the heat in the air was still somewhat stinging to the face.

Instead of going straight back to the dormitory building, he followed the path in front of the forest and turned towards a small shop next to the East District canteen.

Because it was summer vacation after the lockdown was lifted, there were very few people staying on campus, and the shelves in the convenience store were mostly empty.

The owner was a slightly overweight middle-aged man, shirtless, sitting on a bamboo recliner by the door, fanning himself with a palm leaf fan. On a small table next to him was a transistor radio, which was playing Shan Tianfang's "The White-Browed Hero".

"Boss, give me a bottle of soda."

Chen Zhuo walked over.

The boss didn't even lift his eyelids, but gestured with the palm-leaf fan in his hand towards the buzzing freezer next to him.

"Take it yourself, the screwdriver is tied to the handle."

Chen Zhuo walked over and opened the heavy freezer door.

He rummaged through a pile of popsicles and pulled out a glass bottle of Arctic Ocean soda. The orange liquid swayed inside, and a thin layer of white frost covered the bottle opening. He picked up the screwdriver attached to the wire and pried open the cap with a hiss.

A faint scent of oranges wafted out along with the cool air.

Chen Zhuo put a one-yuan coin on the freezer lid, took the soda and walked back.

When the chilled glass bottle comes into contact with the warm air outside, a layer of dense water droplets quickly condenses on its surface.

Water droplets gathered together, trickling down between his fingers and dripping onto the scalding pavement, where they evaporated instantly.

Chen Zhuo slowly took a sip.

It didn't really taste like oranges, mostly just carbonated, but one gulp and the icy coolness slid down my throat and into my stomach, washing away a lot of the stuffiness I felt after a long day in the library. Walking downstairs to the dormitory building, the dorm supervisor was sitting on a small stool by the entrance, picking green beans. Next to him was a basin already half full of beans. "Grandpa, enjoying the cool air?"

Chen Zhuo stopped and casually greeted him.

"Hey, Xiao Chen's back."

The building manager looked up with a smile.

"During this summer vacation, you're the only one in the whole building who keeps going to the teaching area every day."

"Study hard and make progress every day, I'm a model student, okay?"

Chen Zhuo smiled and replied.

The old man laughed heartily.

Chen Zhuo went up the stairs to the second floor.

Because it was a holiday, the entire floor was so quiet that you could hear your own footsteps.

Without Chu Ge's rapid-fire typing, without Wang Dayong's muttering as he memorized English vocabulary for the CET-4 exam, and without Lu Jia's neurotic flipping through books, the hallway now felt strangely empty.

Chen Zhuo pushed open the door, walked to his desk, and put down the kettle and the unfinished bottle of Beibingyang soda.

The desk was clean, except for a few ballpoint pens and a stack of draft paper he had compiled over the past few days, filled with algebraic structures and topological mappings he had extracted from old foreign journals. He didn't sit down to read, but instead pulled a towel from under the bed and went to the bathroom for a cold shower.

In summer, the tap water pipes are exposed to the sun all day, so the water is warm when it comes out, but it only becomes cold after a while.

Chen Zhuo closed his eyes, feeling the water flow down his back.

The abstract concepts of group theory and homological algebra that had been swirling in his mind all day became increasingly clear under the stimulation of the cold water. After showering, he changed into a clean, loose-fitting cotton short-sleeved shirt and knee-length shorts, casually dried his dripping hair with a towel, and left the bathroom. It was completely dark.

The streetlights outside the window lit up one by one, casting dappled shadows among the leaves with their dim yellow light.

Chen Zhuo pulled out a chair, sat down, and turned on the lamp on the table.

A warm yellow halo fell on the stack of draft paper.

He picked up his pen, his gaze falling on a set of homomorphic mappings that he had derived yesterday.

His extensive reading during this period solidified his underlying framework for discrete algebra.

Many physical and mathematical problems in the world are often described using continuous calculus, pursuing a smooth, seamless theoretical aesthetic. However, after reviewing so many manuscripts from predecessors, Chen Zhuo increasingly felt that when facing extremely complex multidimensional problems, continuity is often a beautiful trap. The more you try to find an accurate continuous solution, the more tightly you get entangled in those infinitesimals.

Conversely, if we can use an algebraic perspective to break down those continuous spaces and extract their discrete eigenvalues, many seemingly unsolvable problems will be easily solved. He stared at the paper, and the gears in his mind began to turn slowly and silently.

Just then, a piercing telephone ring suddenly broke out in the corridor.

"Ring ring ring ring ring one"

Those old-fashioned, red public 1C card phones hanging on the wall, with frighteningly loud volume.

Chen Zhuo paused for a moment.

During this hot summer vacation, there are probably hardly any mice left in the entire building.

Normally, when this phone rings, it's for people in the next few dorm rooms, but now none of them are here.

The bell rang stubbornly, over and over again.

Chen Zhuo put down his pen, pushed back his chair, and went outside. He walked to the telephone and picked up the receiver.

"Feed? Who?"

First came a burst of jarring static on the other end of the phone, like someone was banging on the receiver, followed by a chaotic background noise. You could hear someone shouting in the distance that the partial derivative was calculated incorrectly, along with the faint hum of an air conditioner and the sound of something heavy falling to the ground. "Hello? Is this the USTC Junior Class dormitory? Will anyone answer? Hello?"

A voice speaking at an extremely fast pace came through the receiver, carrying a sense of impatience, exhaustion, and barely suppressed excitement.

Chen Zhuo leaned against the wall and, upon hearing the voice, a faint smile appeared in his normally calm eyes.

"It's so late at night, if no one answers, are you talking to a ghost? Wang, you're so quiet!"

There was a sudden moment of silence on the other end of the phone.

Immediately afterwards, a deafening shout of victory erupted.

"Holy crap! Captain! It really is you! I thought your school was on holiday and the dorms were all locked down!"

Wang, who rarely spoke, spoke so loudly that Chen Zhuo had to move the receiver a little further away.

"I knew I had a good memory! I knew the dorm extension number you gave us by heart! They wouldn't believe me and insisted that it was unreachable!" "You do have a good memory."

Chen Zhuo switched hands to hold the receiver, speaking gently and slowly.

"Calling so late? What, the national team provides meals but not enough to eat? Planning to borrow money from me to buy instant noodles?"

"I wish I could just go hungry!"

Wang Huashao let out a long sigh on the other end of the phone, his voice filled with grief and indignation.

"Captain, you have no idea this place is uninhabitable! These national team coaches, they're practically a bunch of emotionless calculus machines!" "How so?"

"From 7:30 in the morning until 10:00 at night! It's all high-intensity theory classes and insane derivation problems!"

Wang, a man of few words, poured out his grievances in a rapid-fire manner, as if he wanted to vent all the grievances he had suffered over the past few days.

"This afternoon, they threw a continuous model of plasma hydrodynamics at us, which is all nonlinear partial differential equations! They also asked us to calculate analytical solutions under all sorts of bizarre boundary conditions." He swallowed hard, his voice sounding like he was about to cry.

"Captain, in my entire life, I have never seen so many intertwined score numbers. I feel like every time I close my eyes, all I see in my mind is an infinite number of tiny numbers holding hands and jumping rope." Chen Zhu listened to his vivid complaint.

He could almost picture the short, usually talkative Wang, scratching his head in despair, utterly hopeless, when forced to face a whole blackboard of partial differential equations. "Jumping rope is good; it can even train the cerebral cortex."

Chen Zhuo leaned against the wall and replied in a flat tone.

"Just don't let those infinitesimal quantities get tangled up in your head."

"Captain, you've changed. When you were in the provincial team, at least you would pretend to sympathize with us."

Wang, who rarely spoke, complained in a soft, whimpering voice.

"Are you having an incredibly comfortable time at HKUST right now? I heard that college students are all very relaxed. Is it true that as long as you don't fail any courses, no one cares about you, and you can go out and play whenever you want, and sleep whenever you want?" "I haven't been sleeping. I've been studying in the library these past few days."

"Damn, isn't that still more comfortable!"

Wang, who spoke little, sighed.

"You don't know, these past few days, top students from several provinces have been driven almost crazy. Last night, a guy from Northeast China kept shouting 'divergence is zero' in his sleep, scaring our whole dorm half to death." Chen Zhuo smiled and didn't reply.

Suddenly, a rustling sound of fighting came from the other end of the phone.

"Stop talking nonsense. You've almost burned through all the money in your IC card, and you haven't asked a single question about anything important."

A slightly low voice, tinged with obvious fatigue, rang out.

Immediately afterwards, Wang Huashao shouted from the other side, "Don't snatch it! I haven't finished speaking yet!" and then his voice was pushed away.

A series of short, rapid breaths came through the receiver.

"Chen Zhuo".

Zhou Kai.

Compared to Wang's quiet and boisterous manner, Zhou Kai's voice sounded much calmer, but even across the phone line hundreds of kilometers away, Chen Zhuo could still faintly hear the weariness emanating from his very bones. "Judging from the noise, he seems to be under a lot of pressure."

Chen Zhuo spoke up.

"He's alright, he's still breathing."

Zhou Kai gave a wry smile on the other end of the line.

"I just feel like my brain isn't working properly. The pace here is too fast, and the density of knowledge points is on a completely different level compared to the training camps in the province before." "Where are you stuck?"

Chen Zhuo asked very directly.

He knew Zhou Kai well; he had a proud streak and was definitely not the kind of person who would complain about a few tedious calculation problems.

What makes him feel like his mind is stuck is definitely some kind of mental impasse.

Zhou Kai was silent for a few seconds on the other end of the phone, seemingly reorganizing the jumbled formulas in his mind.

"It's the plasma model that Shuo Shao just mentioned. The instructors had us deal with a continuous fluid boundary problem in a complex electromagnetic field. They required 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."

Zhou Kai's voice carried a rare hint of frustration.

"Chen Zhuo, I'm not afraid of large amounts of computation. I can slowly derive even the most complex integrals. But once that continuous model is rolled out, if the boundary conditions change even slightly, the entire equation's trajectory becomes completely uncontrollable." He sighed.

"I spent four hours there this afternoon working on it and wrote six sheets of draft paper. The more I tried to get it precise, the tighter those continuous variables got tangled up in my head. It was like...like trying to find a thread in a tangled mess, the more I pulled, the tighter it got."

The motion-activated lights in the hallway suddenly went out because the two people hadn't made a sound for a long time.

Chen Zhuo stood in the darkness, listening to Zhou Kailu's heavy breathing coming through the receiver.

"Zhou Kai".

Chen Zhuo spoke, his voice exceptionally clear in the quiet corridor.

"Do you remember when we were training with the provincial team, Professor Wang had us build that light-controlled alarm device using those broken parts?" The person on the other end of the phone paused for a moment.

"Remember."

"At that time, we were initially thinking about how to calculate the perfect theoretical voltage and how to reduce the resistance error to zero."

Chen Zhuo spoke slowly and deliberately.

"But in the end, we found that the parts in reality simply did not support that perfect continuity theory, so we cut out the redundancy and directly used the most brutal mechanical closure to cut off time." Zhou Kai did not speak, but listened quietly.

"The problem you're facing now is the same as the one you faced back then."

Chen Zhuo looked up at the faint water stains on the corridor ceiling.

"The national team coaches ask you to find analytical solutions to test your mastery of continuous mathematical tools and push you to your limits. But if you really just want to solve the problem in the exam and get the points, you don't need to untie that knot at all."

"How can it be considered if it's not solved?"

Zhou Kai's voice was filled with doubt.

"Since the continuous variables are suffocating you, then cut them off."

Chen Zhuo's tone was so calm, as if he were stating a common sense statement.

"Don't worry about the continuous changes of the fluid in every infinitesimal time interval. Try to build a discrete grid and replace that irregular boundary with a finite number of discrete nodes." He stretched out his finger in the darkness and drew a few dots in the air.

"Then, reduce those complex partial differential equations to difference equations between adjacent grid points, and solve them using algebraic matrices." The other end of the phone suddenly went silent.

Only the faint hissing sound of electricity remained.

"Difference equations...discrete mesh..."

Zhou Kai repeated it to himself, his voice growing softer and softer, as if he were frantically processing something in his mind. "Yes."

Chen Zhuo continued.

"It cannot obtain an analytical solution that can be expressed by a beautiful function; it can only obtain a set of approximate data."

He smiled.

"But this data is enough to give you a foothold on a competition paper and get the score you deserve. More importantly, it can pull you out of that increasingly entangled quagmire of continuity. An exam is an exam; don't treat it like scientific research."

Zhou Kai took a deep breath on the other end of the phone.

"I see."

The heaviness and exhaustion that I felt seemed to be dispelled in that instant by a sudden burst of clarity in my mind.

"Chen Zhuo, have you encountered a similar problem here?"

Zhou Kai asked a question with some hesitation.

How do you have such a clear understanding of discretization?

Chen Zhuo looked at the dark window at the end of the corridor.

The old documents he'd seen in the library these past few days, the dozens of pages of continuous derivations written by mathematicians to prove a theorem, flashed through his mind. "No."

Chen Zhuoyu's words are gentle and understated.

"I've been studying at the library these past few days, and I've realized some of my old methods are too cumbersome. You guys are working your butts off over there, while I'm here just figuring out how to be lazy. It's so hot outside, and using my brain too much makes me sweat." "You rascal..."

Zhou Kai chuckled on the other end of the phone, his tense nerves visibly relaxing.

"Alright, I'm not going to talk to you anymore. While I'm still organized, I need to go back and redo those scraps of paper from this afternoon. Enough talk. Do you have any money left? If not, hang up now." "Hey, hey, don't hang up! I haven't even talked to He Gui yet!"

After a burst of static.

The voice in the receiver has changed.

There was neither Wang's quiet chatter nor the oppressive feeling of Zhou Kai's mental process.

There was only a steady breathing sound, devoid of any discernible emotional fluctuation.

"team leader."

He Gui's voice was muffled, and he enunciated each word very clearly.

"Yes, it's me."

Chen Zhuo responded.

"They're too noisy."

He Gui told a very true thing on the other end of the phone.

"It's the national team, how can we show that everyone is working hard if we don't make noise?"

Chen Zhuo continued, following his lead.

There was another three or four seconds of silence on the other end of the phone.

In the background noise, Wang Huashao seemed to be urging something, but He Gui stopped him.

"team leader."

He Gui called out again.

"I'm listening."

"We will win the gold medal."

When He Gui uttered those words, there was no passionate vow in his tone, nor any determined resolve to prove something. He spoke as if stating a given fact.

It's as natural as the sun rising as usual tomorrow morning, or water boiling at 100 degrees Celsius.

Chen Zhuo tightened his grip on the receiver slightly.

He recalled the slightly shy face he had first met He Gui, and the almost obsessive focus in his eyes when he stared at the multimeter during training. "I know."

Chen Zhuo's voice was very soft, but very clear.

"I believe in you."

"Um."

He Gui responded from the other end.

"Is the money in your card almost gone? I heard the notification sound."

Chen Zhuo heard a faint beeping sound coming from the receiver.

"There are only two cents left," He Gui said. "I'm hanging up."

"Okay, take care of yourself. Don't just focus on doing your homework. If you can't get any meat in the cafeteria, let Wang Huashao go. He's like a monkey, quick as a flash." Wang Huashao's muffled protest came from the other end of the phone, followed by...

With a click.

The call ended, leaving only a long, cold busy tone on the receiver.

Chen Zhuo slowly put the receiver back on the hang-up phone.

The corridor remained quiet.

The motion-activated light still didn't turn on. Chen Zhuo stood there for a while, and he could even feel the warmth from his palm lingering on the edge of the receiver during the call slowly dissipating. In this sweltering summer night, on this university campus drained of its youthful energy.

An invisible telephone line, spanning thousands of kilometers, briefly connected two completely different worlds. On one side was the most outstanding genius among his peers.

They were confined to an arena known as the national team, battling the most difficult formulas every day, struggling in the continuous quagmire of mathematics, for the honor of their country and for their own advancement to higher levels. They were anxious and exhausted, but their eyes burned with an inextinguishable flame.

On the other side was him.

Chen Zhuo turned around, stepping on the long shadows cast by the moonlight, and slowly walked back to dormitory 215.

Push open the door.

The room was just as it had been when he left.

The lamp cast a warm yellow light. On the glass bottle of Arctic Ocean soda on the table, water droplets had gathered into a small puddle, wetting a small piece of draft paper next to it. The stack of draft paper, filled with algebraic matrices, lay quietly on the table.

There was no coach's urging, no pressure from rankings, and no tedious, repetitive equations.

He had only a tranquil vacuum of physics and mathematics that belonged to him alone.

Chen Zhuo walked over and sat down in the chair.

He picked up his pen, his gaze falling once again on the draft paper.

The idea I just gave Zhou Kai—to break the continuous grid into discrete meshes—wasn't actually just some random test-taking trick he came up with.

That was the core conclusion he had drawn after repeatedly pondering and reflecting on it in the library these past few days.

A perfect solution for continuity is often a dead end in many complex real-world problems.

If one path is blocked, why not try another?

Chen Zhuo leaned back in his chair, picked up the half-finished bottle of Beibingyang soda, tilted his head back, and took a swig.

The soda wasn't very cold anymore, and most of the bubbles had dissipated. It flowed down my throat with a sweet, tangy orange flavor.

He put the empty bottle aside.

This phone call acted like a tiny catalyst, making his toolbox of discrete algebra clearer and more certain. The struggles Zhou Kai and his team faced in the mire reinforced his belief that his current approach of focusing on a solid foundation and avoiding blindly pursuing advanced continuity theories was correct. A knife, only when sharpened to be simple and pure enough, will cut things cleanly and efficiently.

Chen Zhuo put down his pen and turned off the light.

The dormitory was plunged into darkness, with only the moonlight filtering through the leaves outside the window, casting dappled light and shadow on the floor.

Chen Zhuo lay down on the bed, putting his hands behind his head.

I have to go to the library tomorrow.

He had almost finished reading the basic literature, and planned to ask Su Wei to help him find some recent years' core foreign journals to look at tomorrow. Chen Zhuo closed his eyes and turned over.

In this sweltering summer, being able to sleep peacefully without having to calculate those damn partial differential equations is truly a blissful thing.