Studying math is a joy!
The library was fairly busy that afternoon. After lunch, Qi Hao finally managed, with some difficulty, to secure a spot in the corner of the third-floor science reading room.
It was an excellent seat.
The light was good, there was no noise from his roommates hammering away at their keyboards, and no howling songs from the dorm next door. It was the perfect haven for grinding through problems.
He unzipped his backpack and pulled out Demidovich's Problems in Mathematical Analysis, a stack of fresh A4 scratch paper, and two gel pens full of ink, arranging them neatly on the desk.
"I won't get greedy today. I'll tear through twenty problems to warm up."
Qi Hao took a deep breath and awakened the system in his mind.
[Reverse Analysis · Problems activated!] [Remaining talent duration: 47 hours, 59 minutes, 59 seconds.] [Foundation Recasting Quest activated!] [Remaining quest duration: 47 hours, 59 minutes, 59 seconds.] [Notice: The timer only runs while the host is fully focused on solving problems. It automatically stops when problem-solving is interrupted. Go forth, tovarisch, and crush every fortress of truth beneath the brute force of problem-grinding tactics!]
The countdown system was downright generous. As long as he didn't dawdle, 48 hours of pure problem-solving time would be enough for him to strip a layer off Demidovich.
Qi Hao spun his pen, his eyes blazing as he zeroed in on the first problem.
Find the limit: lim_{x→0}[√(1+tanx)-√(1+sinx)]/ x^3
Before, his first reaction to a hellish problem like this, with trigonometric functions nested under square roots, would definitely have been to tear at his hair and then use L'Hôpital's rule.
After all, L'Hôpital's rule was forever the GOAT! When in doubt, just use L'Hôpital!
But now, his intuition told him to use Taylor's formula!
With a sweeping motion, Qi Hao put pen to scratch paper and began writing.
Rationalize the numerator and smash those annoying square roots, then ruthlessly expand tan x and sin x to the third order using the Maclaurin formula!
Next came the denominator. As x approached zero, the limit inside the parentheses was a supremely satisfying 2.
Scratch, scratch, scratch!
His pen made its final stroke, and the answer appeared on the page.
It was 1/4.
The instant he finished that final stroke, the entire chain of problem-solving logic clicked completely into place in Qi Hao's mind.
[Congratulations, you have successfully solved a problem. Mathematical logic reconstruction in progress...]
Immediately afterward, Qi Hao felt a shock deep in his mind. Then the half-understood concepts that had been a tangled mess in his head-the control of remainders in Taylor expansions and the principle of matching orders when substituting equivalent infinitesimals-fell neatly into line, as if someone were directing them.
The core logic connecting them, which Qi Hao had previously needed to piece together consciously, suddenly meshed on its own, forming a new network of knowledge!
Qi Hao even had the feeling that if he were given ten more limits of the same type right now, he wouldn't need to think at all. He could produce the answers in seconds through muscle memory alone!
The feeling of integrating all that knowledge was even more exhilarating than chugging an entire bottle of ice-cold gamer fuel in the middle of summer.
Sure enough, success was addictive.
"Ah... that feels good."
Qi Hao stared at the thick volume of Demidovich on the desk, the look in his eyes completely transformed.
The problem book that had once made his scalp tingle just from opening it was now a whole golden experience dungeon in his eyes!
Every problem was an experience monster waiting to be slain, and he, Qi Hao, was the badass wielding Taylor expansions and treading equivalent infinitesimals underfoot, ready to steamroll his way to the end!
"Next problem."
Qi Hao turned the page in one crisp motion, without even lifting his eyelids.
The second problem concerned partial derivatives of a multivariable function.
Before, the sight of that mass of partial derivative symbols alone would have sent him drawing diagrams on scratch paper for ages to sort out the relationships. But now, his newly reconstructed mathematical logic seemed to come with built-in navigation, and the solution path quickly emerged in his mind.
His pen touched the paper, and he finished it in one smooth flow.
The third problem, the fourth, the fifth...
He went through scratch paper at a visible pace, turning aside sheet after sheet packed with calculations.
Those once-repulsive composite and trigonometric functions seemed to grow pleasing to the eye under his relentless, high-intensity work.
As his pen wrote down the final simplified result, Qi Hao let out a long breath and had the system stop the timer.
He had finally ground through twenty Demidovich problems, and the sky outside had darkened.
Dragging his utterly drained body out through the library doors, Qi Hao felt the cool night breeze and pulled out the phone he had kept silent all afternoon. Only then did he notice two unread messages on the screen, both from Wang Jun.
"Godfather, bring me a flatbread on your way back!"
"Your dad's starving to death, get back here!"
He checked the time. It was almost eight in the evening.
Qi Hao made a detour to the second cafeteria. After hesitating at the counter, he ordered two beef flatbreads to go and bought himself a serving of pork ribs over rice before slowly making his way back to the dorm.
The moment he pushed open the dorm room door, a flurry of mouse clicks and keyboard taps reached him, accompanied by Wang Jun's raspy voice: "Jungler, come gank!"
Qi Hao looked inside and saw Wang Jun fighting away in a game with his headset on, half an oily flatbread stuck between his lips.
"Aren't you already eating?" Qi Hao shook the plastic bag in his hand. "Do you still want the two beef flatbreads I brought? If not, I'll save them for breakfast tomorrow."
At the words "beef flatbreads," Wang Jun didn't even turn his head. Eyes fixed on the screen, he called out indistinctly through his mouthful, "Yes, yes, yes! Of course I do! Chen Yuan brought me a layered flatbread when he came back earlier. That honest kid didn't even think to bring me another one. One wasn't nearly enough!"
When the match ended, Wang Jun turned around and took the bag Qi Hao handed him, muttering as he did, "You didn't answer the messages I sent this afternoon. I thought you were busy hanging out with some junior girl. Don't tell me you spent the whole afternoon at the library?"
Qi Hao pulled out his chair, set the pork ribs and rice on the desk, and sat down heavily. "Yeah."
Wang Jun's hand stopped as he reached for a flatbread. "You really stayed at the library for over four hours?!"
"Yeah, I didn't finish the problems." Qi Hao took a bite of rice, looking rather helpless.
A freshman who could sit in the library for over four hours straight in the afternoon without budging had a level of focus most people didn't possess.
Chen Yuan, who was sitting nearby reading, also looked over at Qi Hao curiously.
"Are you crazy? You spent over four hours doing problems? Didn't you find it boring?" Wang Jun took a bite of his beef flatbread, his face full of incomprehension.
He really hadn't found it boring.
For the old Qi Hao-or rather, for ninety-nine percent of ordinary students in the world-studying math was undoubtedly a long, drawn-out punishment.
But that afternoon, Qi Hao had experienced a thrill unlike anything he had ever felt before.
Compared to the dopamine that came from mastering truth, the little numerical thrills in games were downright dull.
Listening to his roommate's exclamation, Qi Hao happily ate his meal.
You don't have a system, so you wouldn't understand. Studying math is a joy!