For the next four or five days, life at USTC felt like it was on repeat.

As dawn breaks, the temperature rises and cicadas begin to sing; as darkness falls, the temperature drops slightly, and the cycle repeats itself.

Chen Zhuo's daily routine remains a straight line between the cafeteria and the old library.

He didn't change his routine or work day and night like a madman who had discovered a treasure just because he found a perfect entry point in that book, "Discrete Mathematics." Those two pages of half-finished matrix derivation drafts would be laid out on the table by the window every day without fail.

But he spends no more than an hour and a half on it each day.

For the remaining seven or eight hours, he continued to peruse the brand-new foreign mathematics journals that Su Wei had found for him, eagerly absorbing cutting-edge mathematical thinking and perfecting the vast and complex algebra toolbox in his mind.

Doing academic research is like making soup.

If you force the heat to be too high before it's ready, the soup will often taste bitter.

Now that the algebraic framework for the proof of the lower bound in graph theory has been established, the rest is like carving a small piece of wood—gently scraping away a little bit of wood shavings each day with a carving knife. There's no need to rush.

Once all the logical gaps are filled, the thing will naturally be complete.

That afternoon, the sun outside was so scorching it felt like it was burning.

The old ceiling fans in the reading room whirred and spun, barely stirring the stuffy air.

Chen Zhuo finished reading the last chapter of the "Journal of Combinatorial Theory" in his hand, closed the book, leaned back in his chair, and stretched languidly. He had been sitting for a while, and his bones made a few soft cracking sounds.

He picked up the kettle on the table and shook it; it was empty.

Standing up, Chen Zhuo picked up the water bottle and walked towards the water dispenser at the end of the corridor.

As he passed by Su Wei's desk, he slowed his pace slightly and his gaze fell on her desk.

Su Wei wasn't in her seat; she probably went to the restroom or to find a book.

Her desk was still occupied by a tall stack of draft paper and heavy professional books.

Next to it was a pen refill tied together with an old rubber band.

The transparent plastic tubes, with dried blue marks on the metal nibs at the bottom, were neatly bundled together, about twenty in total. Each one had been squeezed dry, not a single drop of ink remaining.

The book "Probability Theory and Mathematical Statistics" is stuck on the chapter on continuous-time stochastic processes.

Chen Zhuo couldn't help but take another look, and then his eyebrows twitched slightly.

The two pages, densely covered with calculus symbols, were covered with marks that Su Wei had roughly crossed out with a red pen.

Those lengthy integral formulas used to calculate continuous expected values ​​were mercilessly marked with large red crosses by her. And in the blank spaces of the pages, and even in the crevices of the edges, were matrices that she had rewritten in blue pen.

She not only used the Markov chain transition matrix that Chen Zhuo taught her to solve the deadlock she had been stuck on that day, but she also used this discrete algebra tool to reconstruct and forcibly calculate all the examples and exercises involving continuous time series in this entire chapter.

As Chen Zhuo was reading, Su Wei pushed open the door to the reading room and walked in.

She was holding a washed, damp towel and casually wiping the sweat from her face.

Seeing Chen Zhuo standing next to her table staring at her, she stopped and draped a towel over the back of her chair.

"What are you looking at? Did I calculate the formula wrong?"

Su Wei's voice remained clear and crisp, with a slight huskiness, without the slightest hint of awkwardness.

"You calculated it correctly."

Chen Zhuo pointed to the textbook that had been altered beyond recognition and made a gentle joke.

"I'm just a little upset. A few days ago, I just felt that your tools weren't quite right, so I lent you a kitchen knife. But you, not only did you use it to chop vegetables, you also chopped up the cutting board, the stove, and even the kitchen door frame."

Su Wei glanced at her masterpiece following his finger, her expression calm.

"A useful tool should be used more often."

She pulled out a chair and sat down, casually pulling a new refill from the pen holder and skillfully unscrewing the pen barrel to replace it.

"Since you said that breaking down the continuous timeline into a discrete state halves the computational load and increases the fault tolerance, why should I bother calculating infinitesimals? Why insist on going through the trouble of finding a workaround?"

Chen Zhuo looked at her matter-of-fact expression and nodded helplessly.

"That's true, but some continuous problems are designed to test your understanding of the boundaries of calculus. If you forcibly transform them into discrete matrices, although you can eventually get an approximate numerical solution, there will be a loss in theoretical accuracy."

"I don't need absolute precision."

Su Wei raised her head, her eyes very open and honest, even carrying a kind of coldness unique to actuaries.

"The financial market is essentially a collection of human nature. No formula can calculate it with 100% precision. If I go to take the actuarial exam or work on risk control models in the future, what my boss wants is not for me to write a beautiful calculus function, but for me to provide a risk prediction with an error within a controllable range in the shortest amount of time." She reached out and tapped the matrix on the draft paper.

"This tool can help me finish the exam 20 minutes faster than others and make fewer mistakes when calculating the flow of huge sums of money. That's enough. As for whether the theory is beautiful or not, that's something for you math and physics students to worry about. I'm just an ordinary person. I only care about whether it's easy to use."

Chen Zhuo stood there, looking at the girl with short hair and wearing a faded white T-shirt, and couldn't help but gasp.

This kind of pure, almost greedy pragmatism is not annoying at all; on the contrary, it exudes a wild, burgeoning vitality.

"Good."

Chen Zhuo picked up his water bottle and smiled.

"Keep chopping your cutting board, just remember not to dull the blade. There's a spot where the initial value you set for the eigenvalue transition probability is a bit conservative. You can try increasing it a little more, which can improve the calculation speed by about five percent."

Leaving behind this casual remark, Chen Zhuo picked up the water bottle and headed towards the water dispenser.

When Chen Zhuo returned with the water, Su Wei was already working on the matrix again on the draft paper, just as he had instructed. Neither of them spoke again, and the reading room returned to its familiar quiet as they each studied.

The sunlight outside the window gradually slants westward.

Chen Zhuo returned to his seat, opened his notebook, and took out the two pages of draft paper on graph theory proofs.

Today, it's time to wrap things up.

Only one step remains.

At the end of the paper, the original author used four full pages to classify and discuss the topological graphs in extreme cases in order to prove the stability of a certain lower bound. Chen Zhuo looked at the huge algebraic eigenvalue mapping that had already taken shape on the draft paper and picked up his pen.

No need for separate discussion.

In the world of algebra, all extreme cases eventually converge to the boundary constraints of the largest eigenvalue of a matrix.

The pen tip moved smoothly across the paper.

Clear and fluid algebraic expressions flowed from his hand, like clear spring water washing away the silt covering stones, revealing the hardest, most original texture beneath. As he wrote the last inequality and drew a small black square in the lower right corner to signify the end of the proof, the sky outside darkened. One by one, the streetlights on campus lit up.

Chen Zhuo put down his pen, picked up the two and a half pages of draft paper, and reviewed them from beginning to end, word for word.

The logical loop is perfect, with no leaps or far-fetched lemmas.

The cumbersome proof of more than thirty pages was completely deconstructed into a five-page structure that can be perfectly autonomous within an algebraic framework.

He let out a long breath, flattened the paper, and tucked it into his notebook.

"Is the wooden board ready?"

Su Wei's voice drifted over from across the room. She was tidying up the stationery on the table, crumpling up the few sheets of waste paper she had collected that day. Chen Zhuo looked up, tightened the cap on his water-based pen, and made a soft clicking sound.

"Um."

He nodded calmly.

"We've hammered in the last nail."

"That sounds like a pretty big project."

Su Wei picked up the kettle.

"Are we going to read those new books again tomorrow?"

"I'm not watching anymore."

Chen Zhuo slung the shoulder bag over his shoulder.

"While you're reading these next few days, could you also keep an eye out for 'The Journal of Graph Theory' or a few other core journals? You don't need to specifically look for them, just read whatever comes to mind." "Okay."

The two walked out of the reading room one after the other.

At the top of the stairs, the two naturally parted ways.

Su Wei walked south back to the girls' dormitory, while Chen Zhuo walked along the forest path towards the boys' dormitory building.

The breeze is quite cool tonight, and it feels very comfortable on my skin.

Back in dormitory 215, I pushed open the door and found the room completely dark.

Chen Zhuo turned on the light.

He walked to his desk, put down his shoulder bag, and pulled out the few sheets of draft paper filled with derivations.

Next comes the real physical work.

Chen Zhuo bent down and pressed the power button on the computer under the table.

Chen Zhuo pulled out a chair and sat down, skillfully opening an early English document processing software.

Typesetting software in 2002 was far less intelligent and user-friendly than it is today.

Especially when dealing with pages full of English letters, complex mathematical symbols, and massive discrete algebra matrices, it's simply inhumane. There are no formulas generated with a single click, and no intelligent alignment for formatting.

Chen Zhuo pulled the keyboard in front of him.

Accompanied by the crisp sound of keystrokes, lines of English summaries and introductions appeared on the blue screen with white text.

Typing this text was no challenge for him. His vocabulary and English proficiency, accumulated over his past and present lives, were more than enough for him to describe his arguments with precise academic language. The dormitory was quiet, save for the whirring of the ceiling fan and the rhythmic tapping of Chen Zhuo's fingers on the keyboard. Chen Zhuo was very focused.

He wanted to ensure that the spacing between every symbol and the alignment of every equation on these five pages achieved a visual balance.

At least Chen Zhuo himself seemed very comfortable.

Time passed by, second by second.

The night outside the window grew deeper and deeper, and occasionally a few barks could be heard from the residential area in the distance.

When Chen Zhuo typed the last line of the proof and added the period representing QED, he stopped typing. He rubbed his neck, picked up the kettle on the table, took a sip of water, and then, holding the mouse, meticulously checked the formatting, line by line, from the first line. The matrix alignment was perfect.

No subscripts were omitted.

The logical deduction was exactly the same as the one on the draft paper.

Chen Zhuo nodded in satisfaction, moved the mouse, and clicked the save button in the upper left corner.

Then, he bent down and pressed the switch on the printer next to the main unit.

Chen Zhuo pressed the print shortcut on the computer.

Soon, the printer swallowed a blank A4 sheet of paper. The first page, filled with pure English letters and complex algebraic matrices, slowly slid out of the output tray. Five pages were printed in no time.

Chen Zhuo reached out and picked them up from the tray.

The black ink was clearly printed on the paper, and the layout was so neat that it looked as if it had been torn directly from a top-tier journal.

Chen Zhu tapped the five pages on the table to align the edges.

A lengthy and tedious enumeration spanning over thirty pages.

A clean and concise five-page reconstruction of discrete algebra.

Chen Zhuo opened the drawer and pulled out an international airmail envelope with red and white stripes along the edges.

Picking up a black ballpoint pen, Chen Zhuo wrote down an address in English in the recipient's section on the front of the envelope.

That was the overseas address of the editorial office of *Discrete Mathematics*. He had memorized it a few days earlier while browsing through the journal in the reading room. In the sender's section, he simply wrote a few pinyin characters: ChenZhus, along with the mailing address of Huazhong University of Science and Technology. After writing the address, he stuffed the five pages into the envelope, tore off the tape, and neatly sealed it.

After doing all this, Chen Zhuo glanced at the clock on the wall.

It's almost 1 a.m.

Turn off the computer and printer.

Wash up, turn off the lights, and go to bed.

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