My IQ Increases Year by Year

The ceiling fan overhead had been turned to its third setting without anyone noticing.

The spinning blades made a faint clicking sound, rustling the sheets of scratch paper on the desk.

Chen Zhuo reached over, grabbed a nearby empty cup to weigh down the corner of the paper, and went back to the Theoretical Physics Tutorial in his hands.

In late May in Huizhou, a sticky humidity had begun to creep into the air.

The campus lockdown had been going on for quite a while now. The initial tension had long since been eroded by the day-in, day-out monotony.

The students on the Keda campus were like frogs in slowly warming water. Besides eating and sleeping, all they did was hope for some definite news about the end of the lockdown to come over the campus broadcast.

Yet, Room 215 was strangely quiet.

Chen Zhuo held a black fountain pen, writing methodically on a sheet of scratch paper.

He first had to process the book’s original Russian text in his head, then reproduce, line by line, the derivation steps the author had habitually omitted.

It was surprisingly strenuous work.

The book was filled with page after page of partial differential equations and endless integral symbols.

Chen Zhuo didn’t hate these formulas, but he couldn’t say he liked them, either. To him, it was like taking a perfectly straight, flat road and insisting on paving it with fine cobblestones.

He was used to the point-to-point nature of discrete algebra, to its clean, single-step elegance.

In contrast, this current method—using infinitesimals to fill every tiny gap in pursuit of a smooth transition—felt tedious to him.

But he said nothing. He just gripped his pen and continued to reproduce the book’s omitted derivations, line by line, on his scratch paper.

His handwriting was steady, the integral symbols arranged neatly on the scratch paper. When he came to a step that required approximation with a higher-order infinitesimal, he paused. He stared at the equation for two seconds, then dutifully followed the book’s logic and wrote it out.

"Goddamn it..."

A frustrated sigh came from the side.

Wang Dayong sat at his own desk, hands buried in his already messy hair. He shoved the Advanced Mathematics problem book away from him and collapsed back into his chair like a deflated ball.

"Is there something wrong with this last major problem on real analysis?"

He stared at the ceiling and ran a hand through his hair in frustration.

"I’ve been at it for over an hour. The more I try to bound it, the bigger the error term gets."

The pen in Chen Zhuo’s hand paused. He had just finished deriving a continuous field integral from Landau’s text, and his mind still felt a little fuzzy from the effort.

He picked up his cup, took a sip of water, and turned to look at Wang Dayong across from him.

"Where are you stuck?"

"An asymptotic integral in a high-dimensional space."

Wang Dayong pushed the thick problem book over, along with his scratch paper, and pointed to a long string of equations.

"First, I tried using the Lebesgue dominated convergence theorem to move the limit inside the integral, but the boundary conditions weren’t satisfied. So then I started brute-forcing the bounds, using epsilon-delta arguments to pin down the upper and lower limits. But this higher-order error term just won’t converge. I’ve filled half a page with inequalities. It’s a complete mess."

Chen Zhuo took the scratch paper.

The page was covered in all sorts of inequalities using absolute values and nested integral symbols.

Wang Dayong’s fundamentals were solid; every step of his analysis was logically airtight. But it was precisely because his approach was so orthodox that he’d become ensnared in an endless net of continuity.

Chen Zhuo glanced at it for only a moment before setting the scratch paper aside. His gaze returned to the original problem.

Instead of picking up a pen to help Wang Dayong rewrite the inequalities, he simply tapped a finger on the integrand in the question.

"Why are you insisting on integrating it as a continuous volume?"

Chen Zhuo’s voice was calm.

Wang Dayong froze.

"But it’s a domain of integration, isn’t it? It’s fundamentally a continuous manifold."

"On the surface, yes."

Chen Zhuo pointed to the string of symmetrical constraints following the function.

"But look at its boundaries. In this particular high-dimensional space, the essence of this integral isn’t to find a smooth volume."

Chen Zhuo picked up a pen and drew several dots in a blank space. He then connected them with straight lines, forming a simple grid.

"Don’t bother with the continuous integral. It’s too convoluted."

Chen Zhuo said as he drew.

"Map the space it describes directly onto a discrete lattice model. Those complex constraints are actually just the connections between the vertices in this graph theory model."

Wang Dayong leaned in. He looked at the dots, his brow still furrowed.

"And after making it discrete?"

"Write out its adjacency matrix."

Next to the grid, Chen Zhuo wrote a simple algebraic symbol for a matrix.

"Once you’ve constructed this matrix, the asymptotic value of that headache-inducing high-dimensional integral becomes, in a mathematical sense, completely equivalent to the trace of this matrix raised to the nth power."

Wang Dayong’s eyes flew wide.

"The trace of the matrix to the nth power..."

Wang Dayong muttered to himself, his mind racing.

"Is equal to the sum of its eigenvalues raised to the nth power... And as n approaches infinity—which is what the asymptotic limit is—all the other eigenvalues become negligible. The final result depends only on the largest, dominant eigenvalue!"

In that instant, an analysis problem that would have required half a page of painstaking bounding and countless infinitesimals to approximate was transformed into a simple linear algebra calculation: just find the eigenvalues.