Takes a James Joule of Breath

Lu Yao held the test paper and looked at Li Dong again, letting out a soft sigh inwardly.

This junior's face clearly did not look like that of a top student. If anything, he had the face of someone prone to puppy love.

Boys like him usually sat in the back rows at school, played decent basketball, and had grades that were hard to put into words.

If his grades were better, he'd probably get priority when choosing a girlfriend in college.

Remember the launch website domain ??????????.??????

Lu Yao teased him in her mind, then picked up her red pen and looked directly at the bright red crosses.

"Look at this multiple-choice question, the concept of sets."

Lu Yao pointed at the third question.

"This one should have been A. It asks for the intersection, but you chose B. You obviously overlooked the case of the empty set."

"This kind of mistake means your basic concepts aren't solid. It's also something many students tend to get wrong..."

Just as Lu Yao was about to explain the three elements of a set to Li Dong,

she saw the notes beside the question, and her voice abruptly stopped.

The handwriting was somewhat messy, but the line of thought was completely correct. There were no unnecessary steps, and the case analysis in particular had neatly avoided every trap in the problem.

"Huh?"

Lu Yao looked up at Li Dong.

"Did you write these notes when the teacher went over the test?"

Li Dong had been thinking about several descriptions of the definition of limits in New Lectures on Mathematical Analysis. Hearing her question, he froze for a moment before coming back to himself.

"Ah... more or less."

Lu Yao nodded.

"Mm, these are very well written. Looks like you did listen in class."

She continued reading.

The next wrong question involved trigonometric functions.

Li Dong had made a complete mess of it, even using the formulas incorrectly.

But Lu Yao had learned her lesson this time. She first looked at the notes beside it.

Sure enough.

Beside the wrong question, there was only a circle, with several auxiliary lines accurately dividing the angles.

[Use the symmetry of the unit circle. Point P(x,y) is symmetric about the origin? P'(-x,-y)]

In just three steps, the correct answer had been derived.

"This..."

The more Lu Yao read, the more something felt off.

Although she attended an ordinary second-tier university, she was still a properly trained mathematics major. She had an eye for these things.

This kind of problem-solving approach was absolutely not something a student who usually scored in the eighties could come up with on his own.

The only explanation was—his teacher taught well.

"Junior, which school are you from?" Lu Yao could not help asking.

Li Dong did not understand why she had suddenly asked, but he answered honestly, "Jiangcheng No. 7 High School."

"No. 7?"

Lu Yao frowned slightly.

Naturally, she knew Jiangcheng No. 7 High School's reputation. It was famously hands-off, with average students and supposedly rather laid-back teachers.

"Are No. 7's teachers this conscientious now?"

Lu Yao muttered to herself.

Every note on this test cut right to the heart of the matter. Some approaches were even more ingenious and concise than the standard answers in supplementary textbooks.

Teaching at this level would have been astonishing even at Jiangcheng No. 6 High School, the best school in the city.

She could not help sighing to Li Dong.

"You have a good teacher. Don't let him down."

Lu Yao kept flipping through the test. After reviewing the earlier questions, her impression of Li Dong had improved considerably.

This junior was not beyond saving. At the very least, the care he had put into correcting his work and the quality of these notes showed that he wanted to learn.

Until she reached the final page of the test.

The bonus question section.

Sure enough, this junior had not done this question. But in the blank space, there was a copied variation of it.

Lu Yao raised her eyebrows.

"Isn't this a structural substitution problem? Your teacher actually taught you this kind of question?"

The difficulty of this problem had already reached the threshold of competition mathematics.

Using the conventional method, one would need to construct two new functions and differentiate twice. It also involved substituting implicit critical points along the way, resulting in an astonishing amount of calculation.

Even if she did it herself, it would take more than ten minutes and fill an entire sheet of scratch paper.

She instinctively looked at the solution process on the test, ready to see how these "notes" had been written.

However, the first line of calculations made her freeze.

No constructed functions.

No second derivative.

[Use tangent-line bounds: e^x≥ex...]

[The original expression simplifies to...]

The entire process was only five short lines!

Lu Yao rubbed her eyes. She was not seeing things, so how had it reached the conclusion directly?

"What the hell kind of leap is this?"

"Wasn't something important missing?"

She hurriedly followed that line of reasoning on her scratch paper.

The first step was right.

The second step, composite function substitution, was right.

The third step, verification of the equality condition—it held at x=1. Right!

"Hiss."

Lu Yao took a James Joule of breath.

This solution did not resemble high school mathematics thinking at all. It used the convexity and concavity of functions, along with tangent-line inequalities, to deal a direct "dimensionality reduction strike" to the function.

Forget an ordinary high school teacher—even her own major-course professor would not have thought of solving this problem that way.

Lu Yao raised her head and looked at this junior with a complicated expression.

"Li Dong."

"Yeah, I'm here." Li Dong had been drinking from his cup and jumped at her sudden call.

"This solution..." Lu Yao pointed at the last problem, her voice slightly dry.

"Did your teacher explain how he came up with it? Or did you just copy it down from the blackboard?"

Li Dong blinked and said somewhat embarrassedly,

"Well... Sister Lu Yao, the teacher didn't explain this question."

"He didn't?" Lu Yao did not quite understand.

"Mm, this was a variation the teacher wrote during class. I tried working it out myself."

Li Dong tried his best to make his tone sound sincere.

"I thought brute-force calculation would be too troublesome, so I wondered whether I could take a shortcut with bounds. I didn't expect it to actually work."

Lu Yao: "..."

Looking at Li Dong's expression of I only did it to save effort, Lu Yao could not help feeling disappointed.

You were a struggling student who scored eighty-seven in math, and you were telling her that, just to save effort, you had casually derived a brilliant solution that even she would never have thought of?

That was way too fake!

Lu Yao stared into Li Dong's eyes, trying to tell whether he was lying.

But Li Dong's gaze was too sincere—so sincere that she felt like a bad person for doubting him.

Yet reason told her it was impossible.

He was putting on an act!

Those three words exploded in Lu Yao's mind at once.

He must have looked up the answer somewhere, or perhaps the teacher had told him, and he was claiming he had derived it himself.

Boys these days would say anything for that pathetic little bit of vanity.

She did not like dishonest students.

And when she thought of how hard Auntie Li worked to earn money, even begging people everywhere to tutor him, she felt even worse.

"Fine."

Lu Yao closed the test paper, her tone becoming much colder.

"Since you can solve this problem, that means your foundation is better than I imagined. Let's end today's test analysis here."

She glanced at her phone. It had not even been an hour, but she no longer wanted to continue.

"Huh? We're done already?" Li Dong was confused.

He had still been waiting for Lu Yao to teach him some calculus. Even an explanation of epsilon-delta language would have been fine.

"Mm, I have something to do, so I need to go back to school first."

Lu Yao packed up her things, stood, and gave him a polite but distant smile.

"Review the rest on your own. Don't bite off more than you can chew. Build a solid foundation first."

"And..."

She paused, then said earnestly,

"Auntie Li doesn't have an easy time earning money..."

With that, Lu Yao picked up her bag and left the room without looking back.

Li Dong sat in his chair, completely baffled.

"Why does it feel like... she got angry?"

"Did I say something wrong?"

Jiangcheng University of Technology.

Room 306 of the women's dormitory was in an uproar.

"Jungle king, CPDD! Carry me!"

On the bed by the door, one girl was playing Honor of Kings.

Meanwhile, another girl in pajamas was on the phone, her voice full of grievance.

"Wang Hao! I told you, we're done! Completely done! You actually wouldn't go check in for me? What do you mean, you're a guy and can't help me choose an elective course on my behalf? That's your excuse? You don't love me at all!"

The entire dorm room was a noisy mess.

"Creak."

The dorm door was pushed open, and Lu Yao walked in with a less-than-pleasant expression.

The girl playing games took off one earbud.

"Oh, Yaoyao, you're back so soon? Didn't you say you were going to tutor all day?"

"Don't mention it."

Lu Yao dropped into her chair.

"What happened? Did he piss you off?" Her roommate leaned over curiously.

"Was that kid too dumb to teach?"

"It would've been better if he were dumb!"

Lu Yao shook her head helplessly.

"You have no idea. High school students these days are way too pretentious!"

"How was he pretentious?"

"Tell me, someone who scored in the eighties in math and couldn't even grasp basic set concepts actually brought me a competition-level problem and said he solved it himself!"

The more Lu Yao spoke, the angrier she became.

"And he said it in such a humblebragging way too: 'I just wanted to save some effort, so I tried it casually. I didn't expect it to work.'"

"Listen to that. Is that even something a human would say?"

Her roommates were not math majors, so they did not really understand the gap between competition problems and an eighty-something score, but they understood her emotions.

"Damn, that arrogant?" the girl playing games said with a laugh.

"Are post-00s kids all this confident now?"

"Exactly!" another roommate chimed in.

"He probably wanted to show off in front of a pretty senior like you. Boys at that age care about saving face and want to get your attention."

Lu Yao sighed, feeling irritated and conflicted.

She wondered whether she should tell Auntie Li.

But if she said it outright, she was afraid Auntie Li would be hurt...

Lu Yao was caught in a dilemma.

Meanwhile, in an old residential complex several kilometers away.

Li Dong, who had been branded as vain, excitedly sketched integral signs across his scratch paper.

"So this is the Newton–Leibniz Formula... It's so beautiful!"

"If I apply this to work done by variable forces in physics..."

The young man's eyes were filled with nothing but a thirst for knowledge.

He clearly had no idea he had already been labeled a show-off.