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Chapter 19: Chapter 19: You Should Apologize to Him

Jiangcheng University of Technology, Women’s Dorm 306.

”Jeez, Wang Hao! How many times do I have to tell you? I have to study! It’s not that I’m ignoring you, but why are you so clingy? If you’re that bored, go write my paper for my elective course!”

A young woman on the balcony was letting loose on the person on the other end of the line.

After hanging up on her boyfriend, she heaved a long sigh and turned to Lu Yao, who was packing her books.

”Yaoyao, that Teacher Yang from the grad school prep center you mentioned... is he still taking new students?”

As soon as she said this, the other two roommates in the dorm quietly perked up their ears.

Ever since Lu Yao had casually mentioned that the grad school exam tutor she found was a master’s graduate from Beijing Normal University’s mathematics department, the atmosphere in the dorm had grown delicate.

Everyone was already on edge during their junior year. Some were prepping for the grad school entrance exams, some for the civil service exams, and others were job hunting. Anxiety was in the air.

And when you’re all in one dorm room, if one person starts grinding like their life depends on it, the others can’t help but feel a strange sense of guilt.

That anxious feeling of ’Everyone else is working so hard, am I a total failure?’ was somehow even worse than a breakup.

It had been fine when everyone was slacking off together. But now, not only was Lu Yao studying for the grad school exams, but her tutor was a master’s graduate from one of the nation’s top universities. This just cranked up their anxiety.

Lu Yao spoke as she stuffed several grad school math review books into her bag.

”I’m not sure if he’s still taking people, but I can ask for you today.”

She paused for a moment, then added as if remembering something.

”But after today, he probably won’t be tutoring me for a little while.”

”Huh? What happened? Is there a family emergency?” her roommate asked, surprised.

Lu Yao shook her head, her tone tinged with unconcealable envy.

”No, Teacher Yang said there’s a senior in his class who’s competing in the Huaxuan Cup Applied Physics Competition next week.”

”He needs to make time to tutor that student. After all, physics and math go hand-in-hand.”

”He’s so responsible. He’s willing to postpone a high-paying tutoring gig like mine just to help one of his own students.”

Lu Yao sighed.

”I really envy the students in his class. If I’d had a teacher like him back in high school, maybe advanced math wouldn’t be such a struggle for me now.”

”The Huaxuan Cup?” Her roommate looked blank for a second.

”Yep. It’s a commercial competition, but it’s highly prestigious in the field,” Lu Yao explained. ”The final round is said to be even harder than the Ossai semifinals. Anyone competing in it is probably a top-seeded student from their school.”

With that, Lu Yao shouldered her bag, pushed open the door, and left.

...

Forty minutes later, in a small classroom at the prep center.

Yang Shengguo seemed to be in pretty good spirits.

”You’re here? Then let’s get right to it.”

Unlike tutors from other centers, Old Yang didn’t like to make small talk or serve up motivational platitudes to pad the session time.

He still abided by the old saying: A teacher’s duty is to pass on the way, impart knowledge, and resolve doubts.

Even when just earning some extra cash, he had to be worth the money.

”Lu Yao, after these past few sessions, I’ve realized your foundation is actually quite good.”

”For an average university, you’d be perfectly fine studying on your own. But since your target is Jinling University, there are some things I must be direct about.”

Old Yang opened Lu Yao’s workbook and pointed to several proof problems related to the Mean Value Theorem.

”There’s a flaw in your logical approach to Calculus. You rely too much on formulas and pre-established conclusions. As soon as a problem’s conditions are even slightly obscure, you don’t know how to construct an auxiliary function.”

”For example, when converting between Lagrange’s and Cauchy’s Mean Value Theorems, you always apply the formulas mechanically.”

Lu Yao lowered her head, her face flushing slightly.

It was true. This had always been her weak spot. Her problem-solving skills were based entirely on the intuition she’d built up by grinding through mountains of practice questions. The moment she saw a new problem type, she was lost.

”To give you a more intuitive understanding of the art of ’construction,’ I have a problem for you.”

As he spoke, Old Yang took out a blank sheet of paper and wrote down an expression.

”For a junior math major like you, solving this problem should be no trouble at all.”

”But I don’t want to see you use conventional differentiation to brute-force it. I want to see how you think.”

After he finished writing, Old Yang pushed the paper in front of Lu Yao.

Given the function f(x) = e^x - a ln(ex), if f(x) ≥ 0 for all x in (0, +∞), find the maximum value of a.

Looking at the problem, Lu Yao froze.

This... Isn’t this...

Seeing her stunned reaction, Old Yang smiled. ”What’s wrong? Think it’s too easy?”

Lu Yao snapped out of it, a strange expression on her face.

Although she had complained at length about Li Dong after getting home, her science-major compulsiveness had driven her to study that ”isomorphic scaling” solution on her own time.

Even though she had been certain at the time that there was no way Li Dong had come up with it, she had to admit the solution was brilliant.

So, she picked up her pen.

No constructing a complex difference function, no taking the second derivative.

Using tangent line inequality: e^x ≥ ex...

Equality holds if and only if x = 1...

a_max = e

In less than a minute, without even using any scratch paper, Lu Yao had written down the entire solution.

Sitting across from her, Old Yang’s hand, holding his thermos, froze in mid-air.

”This...”

’Well, I’ll be,’ Old Yang thought to himself.

’How did I run into another monster?’

’Last time it was that freak Li Dong, and now Lu Yao has evolved too?’

’Even though junior math majors have a strong foundation, wasn’t her reaction speed and line of reasoning a little too fast?’

”Lu Yao, you...” Old Yang’s voice carried a hint of surprise.

”How did you figure it out so quickly? That isomorphic scaling approach... usually only someone with extensive competition training would see that instantly. Can you walk me through your thought process?”

Hearing Old Yang’s praise, Lu Yao felt her cheeks grow hot.

Normally, she would have been ecstatic to receive such a compliment.

But right now, she just felt awkward.

”Teacher Yang, actually... I’ve seen this problem before.”

”You’ve seen it?”

Old Yang was puzzled.

”This problem is a variation on a classic model, but I only came up with the specific numbers a few days ago in class. It was just something I jotted on the board. Where could you have seen it?”

”You wrote it yourself?”

Lu Yao exclaimed.

”It can’t be that much of a coincidence, can it?”

”What’s a coincidence?”

Lu Yao asked tentatively.

”Teacher Yang... are you, by any chance, a teacher at Jiangcheng Seventh Middle School?”

Old Yang nodded. ”I am. Have I never mentioned it?”

”Oh my god...” Lu Yao put a hand to her forehead, a wry smile on her face.

”What is it? What’s wrong with being a teacher at Seventh Middle School?” Old Yang was completely baffled by her reaction.

Lu Yao then explained how her mother had asked her to tutor a high school senior from Seventh Middle School.

”...so that’s the story. I saw this exact problem, and this solution, on his test paper.”

As she spoke about it, Lu Yao started to get worked up again.

”The most infuriating part is that the student only scored in the 80s on his math exam—his fundamentals aren’t even solid! Yet he had the nerve to tell me he derived the solution himself just because he was trying to be lazy.”

”Kids these days are so arrogant.”

”It was obviously the gem you taught in class. It would’ve been one thing to just copy it, but he had to take all the credit for himself.”

The more Lu Yao spoke, the more sense her own theory made.

However, she failed to notice the increasingly priceless expression on Old Yang’s face.

Only after Lu Yao had finished did Old Yang speak, his voice slow and his tone complex.

”Lu Yao, that student you were tutoring... his name wouldn’t happen to be Li Dong, would it?”

Lu Yao froze.

”Yes, yes! That’s him, Li Dong! Teacher Yang, is he a handful for you in class, too?”

Old Yang leaned back in his chair and shook his head.

”It really is a small world...”

”What is it, Teacher Yang?” Lu Yao sensed that something was off.

Old Yang sat up straight. His smile vanished, and his expression turned serious.

”Lu Yao, I think you’ve truly misunderstood him.”

”Huh?”

”I may have written the problem on the blackboard, but that solution...”

”...the one using tangent line inequality? He really did derive that himself, right there in class.”

”And it took him less than a minute.”

Lu Yao suddenly felt like the world had been turned upside down.

”How is that possible?! Didn’t he... didn’t he only score in the 80s on his math exam?”

”Grades represent the past, not the present.”

Old Yang cut her off.

”Li Dong has changed dramatically. He even scored a 360 on a Physics Ossai practice exam.”

”Lu Yao, I think the next time you see him, you should apologize. Or at the very least, reintroduce yourself to your junior.”

Lu Yao sat frozen in her chair, the image of the boy’s clear, sincere eyes flashing in her mind, along with the words she had scoffed at: ”I was just messing around and gave it a try.”

’So... it turns out *I’m* the clown?’

...

Time flew by, and in the blink of an eye, it was the weekend again.

For a high school senior, the weekend just meant doing practice tests in a different location.

Li Dong was hunched over his desk.

’The differential form of Maxwell’s Equations...’

Li Dong twirled a pen in his hand, his brow deeply furrowed.

’Gauss’s Law, ∇·E = ρ/ε₀... This isn’t just a formula, it’s a description of the divergence of the source field.’

With the boost from [Physical Perception] and his core attributes, these once-dry Greek letters seemed to come alive before his eyes.

But even so, truly mastering and integrating this university-level knowledge in such a short time was still incredibly mentally taxing.

CLICK.

His bedroom door was pushed open.

Li Qin walked in, carrying a plate of apples that she had peeled and cut into small pieces.

”Xiaodong, take a break. Have some fruit.”

Li Qin looked at the book-covered desk, her eyes filled with pride and relief.

”Mom, I’m not tired.”

Li Dong casually speared a slice of apple, popped it in his mouth, and mumbled.

Li Qin set the plate down and hesitated for a moment before speaking.

”Oh, right, Xiaodong. I have something to tell you. Lu Yao is coming over tomorrow to tutor you in math.”

COUGH COUGH...

Li Dong nearly choked on the apple.

He whipped his head around, his face a mask of horror.

”Who? Lu Yao?”

Li Dong remembered the older girl who had been so inexplicably disappointed in him.

”Mom, can we... not have her come over?”

he asked, his face twisting into a pained expression.

”What kind of nonsense is that!” Li Qin’s expression turned stern.

”Lu Yao is a university student, and you scored so poorly on your last monthly math exam. How can you say you don’t need tutoring?”

”But...”

’Women are so much trouble.’

’And then there’s Misha at school, who’s been like a ghost lately, always turning around to stare at me for no reason.’

’This is impossible! I can’t live like this!’

”Mom, really, my math has improved a lot. I really don’t need...”

Just as Li Dong was about to argue his case, the phone in Li Qin’s pocket suddenly rang.

She took it out, and her expression changed slightly when she saw the caller.

”Oh, Supervisor Liu... Yes, yes, I’ll be right over. Okay, on my way.”

Hanging up, Li Qin looked at her son with an apologetic expression.

”Xiaodong, they need me at the supermarket for an emergency inventory count. I have to go right now. You’ll have to make your own dinner tonight, okay?”

She was already heading for the door as she spoke, but she turned back to add one last instruction.

”When Lu Yao comes tomorrow, you be sure to learn from her properly. And fix your attitude! Don’t let her think we have no manners!”

SLAM!

The door shut.

Li Dong was left standing there, utterly dumbfounded, the half-eaten slice of apple still in his hand.

’Seriously... All I want to do is study Maxwell’s Equations in peace. Why is that so hard?’