[Isaac Newton]: Everyone, why is there always a significant discrepancy between the speed of sound I calculate based on Boyle's Law and the results I actually measure in the gallery of the Royal Society?
[Galileo Galilei]: @Isaac Newton, what are your initial conditions? Have you considered the air's humidity, temperature, and even wind direction? If the error isn't large, could it be due to the precision of your instruments?
[Isaac Newton]: No, the value I calculated is 979 ft/s, but the measured value is 1142 ft/s. That's a full 16% difference! This absolutely cannot be explained away as mere 'error.' It's as if God has hidden some variable within the air...
Jiangcheng Seventh Middle School, Senior Year, Class (2).
Li Dong sat in the back of the classroom, looking at the group chat messages on his phone and shaking his head helplessly.
'These guys are way too into their roles...'
He stuffed his phone under a textbook and looked again at his math test, on which he had only scored an 87.
The test was out of 150 points, with 90 being a passing grade. Once again, he had failed to cross the passing threshold. A glorious defeat—my ass!
The phone under his textbook vibrated twice. It was a WeChat group he had joined a month ago called the "Cyan Dragon Study Group."
Back when he had just started his senior year, Li Dong had resolved to change his ways, feeling he couldn't keep slacking off.
To get into a decent university, he had searched all over the internet for study groups, hoping to find a few academic aces who could guide him and let him experience the atmosphere of striving for Qingbei.
Instead, he had stumbled into this group by mistake.
The group only had a dozen or so members, but their IDs were more impressive than the last, and their avatars more vintage than the next.
Besides the [Isaac Newton] and [Galileo Galilei] who had just spoken, the member list also included names like [Gauss], [Faraday], and even an [Einstein] who had been lurking for what felt like an eternity.
They were all the legendary figures from the black-and-white photos hanging in history books.
This wasn't a study group at all; it was clearly a large-scale rehabilitation center for people with eighth-grade syndrome.
He had originally thought the group would discuss things like predicting trends in past exam questions.
But what did he get instead?
They didn't spend all day discussing college entrance exam math problems. Instead, it was all wave-particle duality of light, the derivation of the mass-energy equivalence equation, the 3n+1 conjecture, and the like.
Li Dong recognized every word individually, but when strung together, they were complete gibberish to him.
'A bunch of posers.'
Li Dong was already in a bad mood today, and watching this group of people act out their roles so seriously only irritated him more.
Newton was here asking about the speed of sound. What was next? Was that Faraday guy going to put on a show and touch a live socket with his bare hands?
Just as he was about to leave the group, his eyes scanned over Newton's message again.
'Calculated value 979, measured 1142...'
Even though Li Dong was a slacker, he was still familiar with those two names.
Newton was the guy who sold apples with Jobs.
And Galileo, well, he was the guy who dropped things from a tall tower.
He'd learned about them in his textbooks.
'If you're all going to role-play, then I'll play along.'
Li Dong switched out of WeChat and opened "Douzhi AI."
He typed into the input box: "Why was there an error in Newton's calculation for the speed of sound? Why is the actual measured value higher than the calculated value?"
Just two seconds later, a large block of text popped up.
Li Dong glanced at it. It was filled with words he didn't understand at all, like "thermodynamics" and "adiabatic compression," but he couldn't be bothered to care. He just copied and pasted it.
[Senior Year Grind]: @Isaac Newton, you might have gotten one thing wrong. The propagation of sound in air is an adiabatic process, not an isothermal one. So, you need to include the adiabatic index in your calculation, or there will definitely be a discrepancy.
As soon as the message was sent, the group suddenly fell silent.
Galileo, who had been discussing with Newton whether wind speed was affecting the measurement, also went quiet.
One second, two seconds, ten seconds...
Li Dong felt a strange sense of unease.
'What's going on? Did the AI get it wrong?'
Just as Li Dong was about to retract the message and pretend nothing had happened, that Newton guy finally spoke up.
[Isaac Newton]: An adiabatic process? Do you mean to say, sir, that no heat is exchanged during this process?
[Isaac Newton]: How is that possible? Air is a fluid. Vibrations must be accompanied by compression and expansion. How could there be no heat conduction? Could you please elaborate, sir? What is this "adiabatic index"?
Li Dong looked at the screen and raised an eyebrow.
'Oh, so he's really getting into it, huh?'
He switched back to Douzhi AI and typed: "Explain the adiabatic index in detail and its application in calculating the speed of sound."
This time, however, the normally responsive AI lagged and then displayed a conspicuous red exclamation mark.
[Network connection timed out. Please try again.]
"Damn it!"
Li Dong cursed under his breath and quickly tried again several times.
This time, there was no error message, but the answer that appeared was full of complex calculus formulas and a jumble of Greek letters that looked like gibberish, things like gamma = C_p / C_v, and partial differential equations.
Li Dong tried a few more times, asking the AI for a simple explanation, but it started spouting nonsense, jumping from quantum mechanics to advanced theories in fluid dynamics.
You have to remember, this was early 2022, a time when AIs frequently hallucinated.
'This artificial idiot!'
Li Dong started to get anxious.
Meanwhile, in the group chat, Newton also seemed to be getting anxious.
[Isaac Newton]: @Senior Year Grind, Sir? Are you still there? If you could elaborate, I would be most grateful!
Li Dong had no interest in such verbal thanks, but the problem was, he was only halfway through his act. He couldn't just back down now, could he?
Li Dong gritted his teeth, his mind racing.
He tried his best to extract anything he could understand from the AI's answer.
Since he couldn't explain the complex principle, his only option was... to act profound!
[Senior Year Grind]: The mechanical velocity of sound propagation is far greater than the molecular velocity of heat transfer.
After sending that, he felt it wasn't quite enough. To cover up his own uncertainty, he added another line.
[Senior Year Grind]: Figure the rest out yourself. One must not become lazy in their studies.
After sending that message, Li Dong felt like a true educator.
The group fell silent once again.
Just as Li Dong was waiting for a response, he felt the light above him suddenly dim.
Li Dong stiffly raised his head and saw his math teacher, Old Yang, his face etched with disappointment.
Old Yang's voice wasn't loud, but the surrounding students could still hear him.
"You're on your phone day in and day out. You should reflect on why your math score is so terrible."
Old Yang shook his head and walked back to the teacher's desk, his hands clasped behind his back.
A few suppressed snickers came from the students around him.
Li Dong's face flushed bright red. The sense of superiority he'd felt from posturing in the group chat vanished in an instant.
Jiangcheng Seventh Middle School was, to be honest, a very average school.
The students' grades here were generally not very good. The college acceptance rate was frankly embarrassing; last year, only a little over 100 seniors met the minimum score for an undergraduate program, and over 70 of them were art students.
Here, the teachers had only one requirement for their students: just don't disturb others.
That was why Old Yang turned a blind eye to students bringing their phones to class.
After all, a student quietly reading a novel was much easier to manage than one who talked during class.
Li Dong watched Old Yang's retreating back, feeling a pang of guilt.
The truth was, Li Dong studied quite hard, often staying up late to grind through practice problems. But some things really just came down to talent.
He was the type who studied hard, but his grades remained stubbornly mediocre.
If he were at a top-tier high school, he might be able to get into an ordinary Tier 1 university by giving it his all.
But here at Seventh Middle School, his ceiling was probably an ordinary Tier 2 university, and even that would require him to work himself to death.
It was a matter of educational resources, and a matter of fate.
'Whatever, I'm not going to think about this anymore.'
Li Dong sighed, ready to put his phone away and take a good look at his test corrections.
Just then, the phone in his palm vibrated twice more.
He glanced at it subconsciously.
[Isaac Newton]: @Senior Year Grind, Sir, are you saying that the essence of heat conduction is the motion of molecules? And not caloric fluid?
Li Dong read the line and thought the guy was just way too deep into his character, still rambling on about "caloric fluid" at a time like this.
'I can't be bothered with you. Whatever, think what you want.'
He decided to ignore the group and focus on his studies.
Just as he was about to lock the screen,
[Isaac Newton]: Your idea is very novel. Although it subverts my previous understanding, my intuition tells me you are correct. I will verify it. Thank you for providing this line of thought.
Immediately after, a red packet suddenly appeared on the screen.
[Isaac Newton has sent you a direct red packet]
A red packet?
The instant the red packet appeared, Li Dong's finger had already tapped on it.
However, what he received wasn't a few yuan and jiao, but...
[You have received Isaac Newton's thanks.]
[Item Acquired: Concentration +1]
[Description: This is a token of gratitude from a titan of science.]
[When he thought, the world stood still. He was once so focused that he threw his pocket watch into boiling water instead of an egg.]
[Now you will experience this same Concentration, powerful enough to pierce through to the truth.]
[Duration: One hour (can be activated at any time)]
Li Dong froze. Before he could even react, a blue option box appeared out of thin air in front of him: [Use Now: Yes/No].
'For real?'
His finger lightly tapped "Yes."
A countdown timer immediately appeared before his eyes...
59:59
59:58, 59:57, 59:56...
Li Dong swallowed, looking back at the "Cyan Dragon Study Group" in disbelief.
[Isaac Newton]: I hope to receive your guidance again in the future.
A jolt of electricity shot up from the base of his spine to the top of his skull.
This...
Could it be that this group wasn't for role-playing?
Could it be that those people weren't just playing scientists, but were actual scientists?
So, a moment ago... did he really just lecture Newton, telling him "one must not become lazy in their studies"?
...
RRRRRING.
The class bell rang. Old Yang stood at the podium, frowning at the test papers in his hand.
"Our class did very poorly on this month's exam!"
His voice was tinged with exhaustion.
"The highest score in our class was only a 109! I honestly can't believe that not a single person managed to break 110!"
Most of the students below lowered their heads in shame.
"Especially the final bonus question, which involved derivatives and proving inequalities. Out of fifty students in the class, not a single person got it right!"
Old Yang sighed, then waved his hand in resignation.
"Alright, take out your papers. Let's start with the first multiple-choice question."
Given set A = {x | x² - 2x - 3
Normally, when Li Dong saw a problem like this, combining sets and function domains, his brain would just short-circuit.
His logical reasoning had always been weak, making these kinds of questions his worst nightmare.
But things were different now. He had Concentration +1.
The moment he saw the question, the world around him seemed to freeze. All background noise vanished.
All he could hear was Old Yang's voice, as if it were in slow motion.
"This question tests your understanding of set operations and the domain of logarithmic functions…"
As soon as he heard this, long-forgotten knowledge points in his mind flew toward him like iron filings drawn to a magnet.
He could even clearly recall that this topic was on page 12 of the Compulsory 1 textbook from the first semester of his first year. He had even accidentally left a ballpoint pen mark on the bottom-left corner of that page.
He also remembered a similar variation on page 24 of the *Five-Year Gaokao, Three-Year Simulation* workbook he'd done last month. He had gotten it wrong back then because he forgot that 'a' could be inclusive.
All the knowledge points arranged themselves in his mind. The process wasn't fast, but he genuinely understood the problem now!
x²−2x−3
Set B is x > a.
Since A ⊆ B, the interval (−1, 3) must fall completely within (a, +∞) on the number line.
Therefore, a ≤ −1.
While Old Yang was still at the blackboard drawing a number line to explain, Li Dong had already moved on to the next question.
It was a question about graphical transformations of trigonometric functions.
Li Dong had no idea how to solve this one. The knowledge points in his memory weren't enough to tackle it.
Normally, he would have gotten frustrated and skipped it, but not now.
Because he could quickly pinpoint the exact, crucial piece of knowledge he was missing.
He wasn't sure what "symmetrical about the origin" meant for the analytical expression of a sine function.
'Does it become an odd function, −sin(x)? Or does the phase simply become kπ?'
He quickly jotted it down in his error correction notebook.
Li Dong had never experienced a feeling like this before. Even for problems he couldn't solve, he could find a direction for his efforts.
'Is this how top students see the world?'
Before he knew it, the bell to end class rang.
"Alright, that's all for this class."
Old Yang never dragged out his lessons, which was one of the things his students liked most about him.
But Li Dong was wailing internally.
'Don't go!'
For the first time ever, he hated the sound of the bell.
He hadn't had enough. If only Old Yang would teach for another ten minutes... no, even five minutes would be great! He had just started to get a handle on an analytical geometry problem about deriving the eccentricity of an ellipse, but he hadn't fully grasped it yet.
He really wanted to rush up and stop Old Yang.
'Teacher, please, just give us a little more!'
But reason stopped him. If he dared to do that, he would be instantly ostracized by his classmates.
So, Li Dong just glanced at the countdown timer in the upper-right corner.
Fifteen minutes left!
'Can't waste it!'
He frantically started rummaging around for the blind spots he had marked in his correction notebook during class.
"Found it! Elective 2-2, page 34!"
Li Dong exclaimed in a low, excited voice.
Normally, his mind would wander after just a glance at such a tedious mathematical derivation. But now, every symbol seemed to be dancing for him, and every line of the formula showcased the beauty of logic.
'I have to figure this out! I have to master this topic right now!'
Just as he was completely engrossed in working through the formula, a large, chubby hand patted his shoulder.
"Dongzi! Stop pretending. Come on, I've got something cool to show you, a movie I just downloaded…"
Li Dong whipped his head around. A chubby-faced guy was holding up a phone, smiling slyly.
"Liu Liang!"
"Go watch it by yourself! I need to study!"
The air fell silent for two seconds.
Liu Liang stared at Li Dong as if he were an alien.
"No way, Dongzi. You're done for. You've caught the study bug!"
Li Dong ignored his teasing.
13:10
'Time is ticking away. Every second of this Concentration is priceless!'
"Don't bother me, I'm deriving a formula."
Li Dong once again immersed himself in the world of mathematics.
Seeing that he was actually studying, Liu Liang didn't pester him further. Besides, this wasn't the first time Li Dong had claimed he was going to study; he'd revert to his old self in three days, tops.
The surrounding noise was blocked out once more.
Li Dong seized the last ten-plus minutes. Facing one knowledge point after another, he took them down one by one, scoring a triple kill.
The geometric meaning of a derivative, the chain rule for composite functions, the method for identifying extreme points—all mastered!
At that moment, the blue countdown timer finally hit zero.
The math formulas that had seemed so friendly and lovely just a moment ago suddenly became hideous.
"It's… over already?"
He looked at the sunlight outside the window, feeling as if a lifetime had passed.
The efficiency of that short hour of studying was higher than his past week… no, his past month combined!
A never-before-seen light glinted in Li Dong's eyes.
'If I could maintain this state of Concentration… forget just a regular Tier 1 university, I'd even have a shot at Qingbei!'
Unfortunately, it was a one-time thing.
However…
He subconsciously pulled out his phone and looked at the WeChat group named "Cyan Dragon Study Group."
This was his only chance to change his fate!
The following English class was excruciating for Li Dong.
Li Dong's foundation in English was actually much better than his math; he could usually score around 110. But after experiencing that truth-piercing Concentration, his current learning efficiency made him feel like he was wasting his life.
He would memorize vocabulary only to forget it, then memorize it again. He could understand the grammar, but he'd still get the questions wrong.
This way of studying made him desperately miss the red packet sent by that guy named "Isaac Newton."
He finally managed to endure until school let out in the afternoon.
There were two hours until the evening self-study session, time for the day students to go home for dinner.
Li Dong was a boarding student, so he didn't need to go home. He hastily ate some rice in the cafeteria and returned to the classroom to ponder a serious question: how could he swindle… oh, no, get another red packet from those legendary scientists?
He even tried playing red packet games with the group members.
But the chat group prompted him: [This activity has been detected as unrelated to "academic discussion." Please adopt a proper attitude toward learning.]
Just as he was staring blankly at the screen, feeling at a complete loss, his phone suddenly vibrated.
A new message popped up.
Li Dong quickly tapped it open.
[Isaac Newton]: Following the line of reasoning you suggested, Your Excellency, I just conducted an experiment in my laboratory.
I found a discarded bronze cannon barrel, bored into it forcefully with a dull drill bit, and immersed the entire apparatus in water.
If heat were a substance, then the amount of bronze shavings produced would be finite, and the heat released should also be finite.
But! Guess what happened, Your Excellency?
Li Dong could feel Newton's excitement.
[Isaac Newton]: The water boiled! As long as I keep drilling, the water keeps boiling!
Heat is generated ceaselessly! This proves that heat is not some kind of fluid substance at all, but a form of motion! The vigorous motion of molecules!
Thank you for your guidance, Your Excellency. The fog that has puzzled me for years has finally lifted today!
Reading this series of messages, the corner of Li Dong's mouth twitched.
'Isn't this the experiment that the Earl of Lennford or Joule did?'
'Newton, are you stealing the thunder from your successors?'
However, the instant Newton sent that last message, lines of semi-transparent text appeared above his phone screen:
[System Announcement: Inspired by you, group member "Isaac Newton" has developed the embryonic form of the "kinetic theory of heat" 150 years ahead of schedule.]
[The technology tree of Parallel Universe #1666 is deviating…]
[Congratulations. As the "mentor" who triggered this butterfly effect, your Group Leader authority has been unlocked.]
[Attribute Panel opened.]
Before Li Dong could react, a transparent panel appeared before his eyes:
Host: Li Dong
Identity: Cyan Dragon Study Group Leader (Probationary)
[Core Attributes]
Concentration: 0 (The average level for a normal person. The slightest disturbance will break your focus.)
Logic: 0 (Your cerebral convolutions might be a bit smooth. A slightly roundabout problem can easily throw you off.)
Memory: 0.1 (Your only praiseworthy attribute. You can probably remember the name of the prettiest girl in the class next door, but that's about it.)
[Special Reward]
For altering the course of history, you have received a feedback reward: Concentration +0.1
...
Li Dong was completely stunned by words like "parallel universe," "tech tree deviation," and "butterfly effect."
He never imagined that just by casually showing off, he'd actually caused a parallel universe's tech tree to deviate.
'This feeling... it's like I'm God, casually plucking a string and making the whole world tremble.'
Li Dong swallowed and shifted his gaze to his attribute panel.
[Concentration: 0.1]
'Wait, what the hell is 0.1?'
Li Dong wore a constipated expression. Attributes with decimals? How was he supposed to work with that?
Suddenly, a flash of insight struck him.
'Wait!'
'The effect of that red packet Newton just sent was [Concentration +1].'
'If that red packet represented Newton's Concentration, then…'
'Newton is 1, and I'm 0.1…'
Li Dong started chuckling foolishly.
'That's Newton we're talking about! The legend who casually invented Calculus just to calculate planetary orbits!'
'Even if I only have one-tenth of his… here at Jiangcheng Seventh Middle School, wouldn't I just dominate?'
Still excited, Li Dong turned his attention back to the group chat interface.
'Um... I already kicked open the door to thermodynamics for you. Isn't there some other show of appreciation?'
Li Dong stared at the screen, waiting for a long time.
The group was silent.
Forget a red packet; there wasn't even a sticker.
'This Newton… he's not one of those scumbags who uses you and then tosses you aside, is he?'
Just as Li Dong was about to proactively ask for a red packet, someone in the group finally spoke.
[James Joule]: @Isaac Newton, Sir! Your experiment is absolutely astounding! I followed your line of thinking, using a paddle wheel to stir water in a bucket and measuring the change in water temperature. The results perfectly verified that heat is the motion of fine particles!
[James Joule]: In this process, mechanical work was converted into heat! It's simply a work of God! By the way, a chemist here, a Mr. Dalton, seems to have mentioned a concept called the "atom." I believe that's what you meant by molecule, correct?
[James Joule]: Thank you so much, Sir Newton! If it weren't for you, I don't know how much longer I would have wandered, lost in the erroneous "caloric theory"!
Looking at these lines of text, Li Dong was taken aback for a moment.
'Joule?'
'He's another legend—a man who, like Newton, has a unit of measurement named after him.'
Newton's reply came quickly.
[Isaac Newton]: @James Joule, no, you are thanking the wrong person. I was merely guided by another.
[Isaac Newton]: The one who truly discovered all this is @Cramming for Exams. He is the one who showed me the correct path. You should be thanking him.
'Look at that! Just look at that!'
'That's the magnanimity of a true master! Unlike certain advisors who, for the sake of... ahem…'
Since these great minds wanted to thank him, Li Dong certainly wasn't going to be modest.
'No need to be so formal. Since we're all so familiar with each other, how about sending a red packet to show your appreciation?'
[System Notification: This behavior has been detected as unrelated to "academic discussion." Please adopt a proper attitude toward learning.]
'Damn it!'
Li Dong fumed helplessly, but he quickly calmed down.
'Asking for a red packet directly didn't work, so I'll have to try another way.'
'If I can't get a material reward, I'll just have to fleece them for some knowledge!'
'This group is filled with the most brilliant minds in human history. If I could get them to give me some pointers on my studies…'
With this thought, Li Dong immediately took action.
[Cramming for Exams]: It was nothing, really, not worth mentioning. However… I've run into a small problem recently.
[Cramming for Exams]: I have a nephew who is about to take a very important exam, but he's a bit slow and has always struggled with math. I was just trying to explain a problem to him, and after a long time, it still wasn't clicking.
[Cramming for Exams]: I was wondering if any of you have some good study methods that could help my poor, slow nephew?
Li Dong's persona as a master couldn't possibly be ignorant of high school math, so he would ask on behalf of his "nephew"!
The trick worked like a charm. Newton replied quickly.
[Isaac Newton]: Since he is your nephew, his aptitude cannot be too poor. Why don't you post the problem for us to see?
Li Dong was overjoyed.
'Getting Newton to be my tutor? Can any of those cram schools even compare?'
Li Dong quickly flipped open his math test paper and found the final, killer problem that had stumped the entire class.
[Given the function f(x) = e^x - ax - 1 (where a is a constant). If f(x) ≥ 0 holds true for any x ≥ 0, find the range of values for the real number a.]
Li Dong replaced the "e" in the problem with "the base of the natural logarithm" and swapped the term "derivative," which Newton might not understand, for "fluxions," a concept from Newton's era that he would comprehend. Then, he sent it.
[Cramming for Exams]: This is the problem. How does one determine the bounds of the constant in this fluxion?
Less than two seconds after the message was sent…
[Isaac Newton]: The answer is a ≤ 1.
Li Dong waited a bit. He was still expecting Newton's derivation process.
A minute passed, but Newton said nothing more.
Li Dong grew a little anxious and continued to ask.
[Cramming for Exams]: Um… could you be a little more detailed? My nephew is a bit slow; he won't understand just by looking at the answer. Is there a specific derivation process?
[Isaac Newton]: ???
[Isaac Newton]: Process? Isn't it self-evident? What process is needed?
Li Dong suddenly realized he'd made a mistake.
He was asking Newton!
Who was Newton?
He was the monster among geniuses who, in his twenties, went back to his rural home to escape a plague and, out of sheer boredom, casually invented Calculus, discovered universal gravitation, and developed spectrum analysis!
This was like asking Bolt to teach you how to run. Bolt would just say, "You hear the gunshot, and then WHOOSH, you just dash to the finish line, right?"
A mere mortal could never learn that way!
Just as Li Dong thought his "fleecing" operation was about to end in failure, the man named Joule appeared again.
[James Joule]: Ahem… Um, Sir Newton, you may be overestimating the thinking speed of an ordinary person.
[James Joule]: @Cramming for Exams, I can deeply sympathize with the problem your nephew is facing. I am of dull aptitude myself, so I understand the pain of your brain just not getting it.
Li Dong's eyes lit up.
'That's right! Joule!'
'Joule came from a family of brewers. He hadn't received much formal higher education; he taught himself mathematics to solve physics problems.'
'This kind of self-taught master must have a study method that works for him!'
So Li Dong hurriedly typed in the group.
[Cramming for Exams]: Mr. Joule! You're too modest! I was wondering if you had any insights you could share?
[James Joule]: If not for your insights, I wouldn't have been able to so quickly determine that heat is the motion of molecules. Since your nephew is having trouble with his studies, I will share my own learning method.
[James Joule]: Although these clumsy methods are not worth mentioning in front of Sir Newton, for someone with a weak foundation, they might help build a solid base.
Then he sent a document to the group.
Li Dong immediately opened it, and the contents of the document appeared in his mind.
The first point was Breakdown and Mastery.
This meant breaking down concepts into the smallest possible units. Master one unit at a time: memorize definitions, derive formulas, and solve ten practice problems of the same type with perfect accuracy before moving on to the next concept.
The second point was Review and Quantify Errors.
Generally, people make mistakes for three reasons: they forgot the formula, they miscalculated, or they had no idea how to approach it. Therefore, if you get the same type of problem wrong twice, you must stop and relearn that entire unit from the beginning, which brings you back to the first point.
The third point was Connect and Transfer Methods.
The science subjects are all interconnected. While studying, you should often think about whether a method can be applied to other subjects.
For example, finding the maximum or minimum value in math is the same process used in physics kinematics.
The conservation principles in chemistry are the same as the conservation of energy in physics.
Once you open up your mind, you'll naturally find clues to solving those difficult problems you couldn't do before.
In truth, this method wasn't complicated. It wasn't that the average person couldn't think of it, but very few could actually follow through.
It was like a multiple-choice question.
If hard work isn't guaranteed to pay off, would you still persevere without hesitation? Most people would probably give up halfway.
But if someone told you that as long as you follow their method, you are guaranteed to succeed, far more people would be willing to grit their teeth and persevere.
Now, with Joule's endorsement, Li Dong had made up his mind. He would follow this method step by step.
With this method, plus the attribute boosts he could get at any time…
Li Dong felt like he was about to take off.
Just as Li Dong had finished thanking Joule and said he would have his nephew try it…
The bell for evening self-study rang.
The classroom door was pushed open, and Old Yang walked in, carrying the stack of test papers he hadn't finished going over.
"Everyone, quiet down!"
"Take out your test papers. We're picking up where we left off this afternoon!"
"And Li Dong, stop hiding your phone under your book. You think I can't see it?"
Li Dong quickly stuffed his phone into his pocket.
The whole class erupted in laughter.
...
At the front of the class, the chalk in Old Yang's hand tapped against the blackboard. TAP, TAP.
"Problem 18, solid geometry. This was a freebie! How many times have I gone over this? Establish a three-dimensional Cartesian coordinate system! Find the normal vector! Why can't you all remember? Huh? On a simple question like this, over a dozen of you still didn't get any points?"
He was lecturing with great enthusiasm, but the eyes of at least half the students below were glazed over.
Only a few students in the front rows were still taking notes.
As for the students in the back rows...
Old Yang's gaze fell on Li Dong's seat.
Old Yang had always had a pretty good impression of Li Dong.
The kid wasn't the sharpest, the type for whom it was hard to get things to 'click,' no matter how you taught him. But his saving grace was his diligence.
But today, Li Dong was acting exceptionally strange.
Since the start of class, the kid had been doing God knows what, constantly scribbling all over his test paper. You might think he was correcting his mistakes, but Old Yang was only on problem 18, and Li Dong was already working on the final bonus question.
'Has he just completely given up?'
Old Yang sighed to himself.
In an environment like Seventh Middle School, once a student gives up on themself, there's nothing a teacher can do to pull them back.
Old Yang shook his head and went back to explaining the test questions.
However, what Old Yang didn't know was that the Li Dong he saw as having given up on himself...
...was, at that very moment, frantically berating himself thanks to his Concentration +0.1.
'You idiot...'
Li Dong stared at the steps he'd taken to solve the problem, wishing he could go back in time and slap himself twice.
'The need for monotonicity analysis was so obvious. Why did I take the logarithm of both sides? Was I just trying to make things harder for myself?'
It felt like a Challenger-tier player looking back at their Bronze-league gameplay—it was nothing but mistakes.
He still couldn't see the answer at a glance like those academic aces, but he could clearly identify his mistakes and see the correct path forward.
While Old Yang was going over the test, Li Dong had already reviewed all the problems he'd gotten wrong at the beginning of the exam.
The thrill of solving the problems was so intense he couldn't stop.
'This feeling... It's not as good as that freak Newton's Concentration +1, but for a failure like me, it's more than enough!'
Li Dong gloated internally and turned his gaze to the final bonus question on the test.
[Given the function f(x) = eˣ − ax − 1 (where a is a constant). If f(x) ≥ 0 for all x ≥ 0, find the range of values for the real number a.]
Newton had already provided the answer to this question: a ≤ 1.
But he hadn't shown the derivation.
In the past, Li Dong definitely wouldn't have been able to derive the answer on his own.
But now, riding this wave of intense focus, he suddenly remembered the "Deconstruction + Basic Looping" method from the study guide Joule had shared.
'Deconstruct the problem... Holds true for all x... which means the minimum value must be greater than or equal to 0...'
'Find the minimum value... take the derivative... f′(x) = eˣ − a...'
In less than five minutes, Li Dong was staring at the final derived result on his scratch paper, a ≤ 1. He was completely stunned.
'I... solved it? Just like that?'
He patted his cheeks in disbelief.
This test might have been made by the school and wasn't especially difficult, but this was still a bonus question.
'I solved it just like that?'
'Was it just easier because I was working backward from the answer? Or is this +0.1 Concentration really this powerful?'
Li Dong felt terrifyingly capable.
'Deconstruction + Basic Looping...'
Li Dong muttered the phrase to himself and began rummaging through his school bag.
He'd always considered "dihedral angle" problems in solid geometry his weak spot. Since Joule said to break problems down into their smallest components, he'd start by practicing how to find the "normal vector."
'Book Two... Where did Book Two go...'
He was so excited that his movements were a little too rough as he searched.
The noise was particularly jarring in the quiet classroom.
At the front of the room, Old Yang finally lost his patience.
He had just asked if anyone had solved the bonus question, but not a single student had volunteered to answer.
And then there was Li Dong, making all that noise and causing a scene.
"Li Dong!"
The furious shout made the entire class jump. Everyone's head snapped toward Li Dong in the back row.
Li Dong, who had his head buried in his bag looking for a book, instinctively looked up with a bewildered expression.
"Huh? Here!"
"Li Dong, if you feel you've already completely mastered this problem and don't need my lecture, then come up here and show everyone how it's done."
"If you haven't solved it, then stop messing with your bag and pay attention!"
Old Yang pointed to the blackboard behind him.
He was just trying to get Li Dong to pay attention; he didn't actually expect him to come to the board and solve the problem.
The surrounding students all ducked their heads, afraid Old Yang would turn his fury on them next.
Liu Liang, in the next seat, nudged Li Dong with his elbow and whispered.
"Dongzi, you're toast. Old Yang's making an example out of you."
But thanks to his enhanced Concentration, Li Dong's thought process had become incredibly... linear.
His brain was still contemplating a better way to apply Joule's study method.
His interpretation of Old Yang's tirade went something like this:
Information received: The teacher is calling me.
Directive analyzed: Go to the blackboard and solve the problem.
Operation executed: Okay, I'll go solve it.
As for Old Yang's true intentions and the difficulty of the question... all of that was filtered out by the +0.1 Concentration.
"Oh, okay."
Li Dong agreed, then stood up and started walking to the front of the class.
He walked up to the blackboard as if in a daze.
Seeing that he had actually come up, Old Yang was momentarily stunned. He then turned to address the class in a grave tone.
"Class, I know this question is difficult. But it's been a while now, and not one of you has even tried to think it through. You're all just waiting for me to give you the answer..."
He was still speaking when he noticed the students looking as if they'd seen a ghost. He was just about to turn and see what was happening.
But then he saw Li Dong walk past him, coming down from the blackboard.
Old Yang was dumbfounded. 'What on earth is with Li Dong today?' he thought. 'He seems completely out of it. Did he just come up here to immediately go back down?'
Just as he was about to give Li Dong a proper scolding, he heard a student in the front row exclaim.
"Oh, so that's how you do it!"
"'That's how you do what'?"
Startled, Old Yang instinctively followed the student's gaze to the blackboard behind him.
[If a ≤ 1, then f'(x) = e^x - a ≥ 1 - a ≥ 0. The function is monotonically increasing, and the minimum value f(0) = 0, which satisfies the condition.]
[If a > 1, the local minimum is f(ln a) = a - a ln a - 1. Since this value is always less than 0 when a > 1, it does not satisfy the condition.]
[Final Conclusion: a ≤ 1]
Old Yang's eyes widened as he stared at the solution on the blackboard.
This... How is this possible?
Had it even been a full minute between Li Dong walking up to the board and walking back down?
After his initial shock, Old Yang quickly regained his composure, but his brow furrowed even more deeply.
He checked the work from top to bottom.
It was all correct.
But Li Dong had skipped many steps. On an actual exam, he would've definitely lost points for that. But for someone who understood the problem, those steps were trivial; they would fill in the gaps mentally.
Li Dong's derivation, therefore, looked more like a set of guiding notes than a full solution.
This kind of abbreviated solution might be plausible coming from an academic ace, but from Li Dong—a student who regularly failed math—it was utterly unbelievable.
Therefore, Old Yang felt no sense of pride. Instead, he was even more disappointed.
'No wonder the kid was on his phone all afternoon,' he thought. 'He must have found the original question online and memorized the answer!'
Old Yang was bitterly disappointed, frustrated that his student wasn't living up to his potential.
'So what if he failed this one monthly exam? Does he really need to resort to this to save face? He's only fooling himself!'
"Fine. Well written," Old Yang said, nodding expressionlessly at Li Dong, who had returned to his seat.
He didn't intend to put Li Dong on the spot in front of the whole class.
But the other students knew Li Dong's usual standard. There was no way he could have solved that problem so quickly.
Whispers began to spread among some of the students.
"He must have looked up the answer online."
"Definitely. I saw him on his phone just a minute ago."
Only one person, a girl in the front row, was sizing up Li Dong with a look of shocked suspicion.
Her name was Misha. She was the academic representative for their class and had scored a 109 on this very test.
She hadn't been able to solve this problem, so she had secretly looked it up on her phone. The standard online solution used the parameter separation method, which was a very complicated process.
But the method Li Dong had written on the board...
...was completely different from the online answer!
'Did he come up with that himself?' Misha chewed on her pen, a flicker of curiosity in her beautiful, fox-like eyes.
Just then, Old Yang, after a moment's hesitation at the front of the room, called out to Li Dong again.
"Li Dong, come back up here for a second."
Li Dong stood up, looking confused.
"Teacher Yang?"
"Since you have such a good grasp of this problem, it must mean you have a profound understanding of derivatives and inequalities." Old Yang picked up an eraser and, with a couple of quick swipes, cleared a space on the board.
"As it happens, I have a variation of that problem right here. The difficulty is close to that of a bonus question on the actual college entrance exam."
As he spoke, he wrote a new problem on the board:
[Given the function f(x) = e^x - a ln(ex), if f(x) ≥ 0 holds true for all x in the interval (0, +∞), find the maximum value of a.]
After he finished writing, Old Yang handed the chalk to Li Dong.
He wasn't deliberately trying to make things difficult for Li Dong. It was just that this kind of vanity, once indulged, was bound to happen again.
He didn't want this once-diligent student to start down the path of cheating just for a bit of ridiculous pride.
He even held on to a tiny, almost impossible shred of hope.
'But what if he can actually solve it?'
"Go on, Li Dong. Give it a try."
Li Dong looked at the problem on the blackboard with a strange expression.
He turned to look at Old Yang, a hint of confusion on his face.
"Teacher Yang."
"Hm? What is it? Find it too difficult?"
Old Yang sighed internally. 'So he can't do it after all?' Just as he was about to give Li Dong an easy way out...
"No," Li Dong said, pointing to the blackboard.
"This problem is essentially the same as the last one. How about you give me a different one?"
He genuinely wanted a problem he didn't know how to solve so he could master a new concept.
Old Yang was left speechless. Even his good temper was starting to fray.
"Then by all means, solve it and show me!"
...
Old Yang's full name was Yang Shengguo, and he was already thirty-eight this year.
Watching Li Dong's chalk fly across the blackboard, he suddenly felt a sense of unreality.
In that instant, it was as if he saw his younger self.
Back then, he had been studying for his bachelor's and master's degrees at Beijing Normal University. Full of vigor and ambition, he was on a natural path to pursue his doctorate and walk the road of scientific research.
But at the critical moment of publication, his research findings were stolen by the very mentor he respected and published under someone else's name.
He felt wronged. He was young and hot-headed, unwilling to bow down, so he confronted his mentor and caused a huge scene.
As a result, not only were his hopes of a Ph.D. dashed, but he was effectively blacklisted from that circle, unable to find even a decent job.
His heart had grown cold by then, so he returned to his hometown of Jiangcheng and became a math teacher at the ordinary, public Seventh Middle School.
In the first few years, he had also wanted to teach these kids well. He wanted to teach them knowledge, but more than that, he wanted to teach them how to be good people.
He wanted to teach them how not to be taken advantage of, and how, if they ever became teachers themselves, to never exploit their own students.
But reality was never as rosy as one imagined.
Every place has its own rules. The top-quality students were all snatched up by the prestigious private schools and key public high schools.
The students who came to Seventh Middle School were, for the most part, ordinary people with average abilities. Some were still trying hard but couldn't find the right method, stuck in mediocre limbo. Others had already given up completely, planning to just coast their way to a high school diploma.
Watching them, Yang Shengguo's passion slowly cooled.
'Just teaching is enough. As long as I can face my conscience and share what I know... as for whether the students listen or learn anything, that's up to fate.'
He had thought this was all his life would amount to—just watching over his thermos of goji berry tea, slowly growing old here.
Until today.
Li Dong, the student who usually couldn't even touch the passing line, had given him a sudden shock—and a long-overdue surprise.
At this moment, Li Dong's eyes were fixed solely on the problem on the blackboard.
He was incredibly focused now. The complex function graphs before his eyes were breaking down, one by one, into their smallest components.
'No need to brute-force the derivative's zero point...'
'For a problem with this structure, the key is to observe its form.'
'Since the problem requires the inequality to hold true for all values, I just need to find the critical point where the graphs of the functions on both sides are tangent. That will give me the limit for the constant *a*.'
He found that Joule's "decomposition method" was incredibly useful. Once you saw through the core Logic, the rest was just grunt work.
Although, this grunt work was a bit demanding.
He was actually still struggling a bit. First, his Concentration was only at 0.1, so it was easy for his mind to wander during high-intensity mental calculations.
Second, his logical reasoning was still at 0, the level of an ordinary person. If he hadn't already done a problem with the same core principle, he might not have been able to solve this one so quickly.
Thankfully, his natural Memory was 0.1, which saved him from having to look up formulas in a book.
Li Dong picked up the chalk. Facing the modified problem Old Yang had given him, he didn't perform any complex derivative calculations, nor did he draw any coordinate axes.
"Solution: The original equation is equivalent to e^x ≥ a ln(ex)."
Li Dong's hand paused for half a second.
Then, he directly skipped the entire process of constructing functions, taking second derivatives, and discussing extreme points—a process that would have filled half a draft notebook for an average student.
Two fundamental tangent line inequality models appeared in his mind.
He wrote two lines of extremely concise derivation on the blackboard:
"Using tangent line scaling, we know: e^x ≥ ex and x ≥ ln x + 1."
"Therefore: e^x ≥ ex = e(x) ≥ e(ln x + 1) = e(ln x + ln e) = e ln(ex)."
When this chain of inequalities appeared on the blackboard, the pen in Misha's hand CLATTERED onto her desk.
"Is this… double scaling?"
Misha's face was filled with disbelief.
Old Yang was also stunned. That leap showed real depth. Without a massive amount of practice and extremely high mathematical intuition, no one would dare to write it like that.
But he could see that the logical chain within it was flawless.
"From the inequality chain above, the equality holds if and only if x=1."
"Thus, a_max = e."
The chalk made a final, crisp sound against the blackboard.
"Um… Teacher Yang, I'm done."
The classroom was so quiet you could hear a pin drop.
The students looked at each other in confusion. They couldn't really understand the solution on the board and had no idea if it was correct.
So they could only turn their gazes to Old Yang.
A few students in the front row, including Misha, were frantically verifying the solution in their notebooks.
"How… how did he get to this step?"
A student mumbled under their breath.
"Where's the differentiation process? Why did he just use a greater-than-or-equal-to sign?"
"Yeah, isn't that taking too much of a shortcut?"
Old Yang stood where he was, staring at the solution on the board, and said nothing for a long time.
After a long while, he let out a deep sigh, as if expelling years of pent-up frustration.
'Looks like… I can't just coast and wait to die anymore.'
His voice was so soft that no one heard him.
Old Yang didn't rush to judge whether the answer was right or wrong.
For the vast majority of students in Class 2 of the third year, this "isomorphic scaling method" was a competition-level technique. There was no need to delve deep into it.
It was better for them to secure their fundamental points rather than waste time on this technique.
"Li Dong, you…"
Just as Old Yang was about to speak, a knock suddenly came from the classroom door.
KNOCK KNOCK KNOCK.
The door was pushed open, and a somewhat weary face peeked in.
"Teacher Yang, sorry to interrupt. I just need to make a quick announcement."
Old Yang nodded toward the door.
"Go ahead, Teacher Jiang."
Teacher Jiang addressed the students below the podium.
"Everyone, sorry for the interruption."
"The city just sent out a notice. Next month, there's a Commercial Physics Cup competition, which is a qualifier for the provincial preliminaries."
"The school has been allocated a few spots. Any students interested in signing up? There's no training; just think of it as practice."
The class fell silent, everyone burying their heads even lower.
Teacher Jiang was used to this. These tasks to fill quotas weren't common at Seventh Middle School, but they weren't rare either.
Students from their school usually went just to fill seats. They weren't really qualified to truly participate.
"If anyone wants to sign up, come find me in my office next Monday."
After speaking, he gave Old Yang a wry blink.
The meaning was clear: *Nothing I can do. We're short on people.*
Yang Shengguo nodded and watched Teacher Jiang leave.
After this brief interlude, the classroom returned to silence.
Yang Shengguo turned around and gave Li Dong a deep look, his tone much softer than before.
"Alright, Li Dong, you can go back to your seat."
Being stared at by Old Yang made Li Dong's skin crawl. He couldn't shake the feeling that there was something strange about the look in his teacher's eyes.
"Oh."
Once Li Dong was back in his seat, Old Yang pointed to the blackboard and said,
"Li Dong's solution to this problem is… completely correct."
"Furthermore, his approach was very clever, using the scaling method. It seems he's put in a lot of hard work on his own time."
Old Yang paused, then changed his tone.
"However, this method requires a very high level of logical thinking and is prone to errors. Everyone should proceed according to their own abilities."
"In the college entrance exams, these types of problems are usually bonus questions. We should still focus on securing the points we're supposed to get and not bite off more than we can chew."
Although Old Yang was trying to cool things down, the way the students looked at Li Dong had already changed.
Surprise, suspicion, jealousy… a mix of all kinds of emotions.
"Didn't Li Dong fail math? How did he suddenly…"
"Did he just memorize the solution to this hard problem to show off?"
"Probably. Why else would he not even calculate the derivative?"
In the front row, Misha bit her lip, still furiously scribbling derivations in her notebook.
Even using the approach Li Dong had provided, she had only just managed to verify the validity of the first inequality.
'Those steps he skipped… was it really because they were too simple for him?'
Misha glanced back at Li Dong, a faint sense of defeat creeping into her heart.
…
The bell for the end of evening self-study finally rang.
It was Friday, so boarding students could leave school and go home.
Many parents were waiting for their children at the school gate.
Li Dong walked toward the bus stop with his backpack on, Liu Liang silently following beside him.
Just as they were about to get on the bus, Liu Liang suddenly spoke up. "Dongzi."
"Hm?" Li Dong stopped walking.
Liu Liang looked at him, his expression complex. Half-joking, half-serious, he said,
"Did you really get hooked on studying?"
Li Dong could hear the trace of dejection in his tone.
During your teenage years, when a friend you always messed around with suddenly starts trying hard, that sense of panic from being left behind is unavoidable.
Li Dong turned around and said with sincerity,
"Liangzi, I think we need to start being responsible for our future."
"I want to give it my all, if only to make my mom worry a little less."
Liu Liang was stunned for a moment, then broke into a grin to hide the loneliness in his eyes.
"Look at you, all enlightened now. Go on, go on, future top student."
After saying goodbye to Liu Liang, Li Dong got on the number 302 bus home.
It was already past ten at night, and the bus was empty.
Li Dong sat in a window seat.
Outside the window, the nightscape of Jiangcheng receded before his eyes.
The skyscrapers in the city center were brightly lit. The price of a single square meter there was equivalent to his family's entire monthly income, assuming they didn't eat or drink.
The bus slowly pulled away from the commercial district. The lights grew sparser, and the surrounding buildings became low and dilapidated.
Li Dong's hand tightly gripped the phone in his pocket. It held the key to changing his destiny.
The bus stopped at the entrance to his old residential complex.
Li Dong climbed the six flights of stairs with his backpack on. Before he even opened the door, he could hear his mom, Li Qin, talking on the phone inside.
"…Alright, alright, thank you for the trouble."
"Ah, as long as it helps him improve his grades, that's all that matters. Besides, it's much cheaper than hiring a professional tutor… Okay, tomorrow then. Thank you so much."
Li Dong pushed the door open and went inside.
Li Qin hung up the phone and saw her son had returned.
"Xiaodong, you're back! Are you hungry? I can heat up some food for you."
"I'm not hungry." Li Dong changed his shoes and looked at his mother.
"Mom, who were you on the phone with just now?"
Li Qin poured him a glass of water and said with a smile,
"Oh, I have something to tell you."
"One of my colleagues has a kid who goes to Jiangcheng University of Technology. He's a junior in the math department."
"I heard his grades are pretty good, so I asked him to come over on weekends to tutor you."
Afraid her son would resist, Li Qin quickly added,
"He's a university student, so he's cheaper. We can afford it."
Li Dong froze.
Jiangcheng University of Technology was a local Tier 2 university. A math major from a Tier 2 university… well, those who know, know.
'A student from a Tier 2 university's math department is going to tutor me?'
Li Dong subconsciously touched his phone.
Who were his "teachers" now?
They were Isaac Newton and James Joule—some of the most brilliant stars in human history!
It felt like he was enjoying a gourmet feast, but his mom, afraid he was hungry, had specially hired someone to give him a couple of cold steamed buns.
He really wanted to refuse, but seeing his mother's excitement,
he couldn't turn down her good intentions.
Ever since his father passed away, his mother had shouldered the burden of their family all by herself.
Now, she was pinching pennies to hire a tutor for him. If he refused, it would make her feel like she hadn't provided him with the best learning conditions.
So, Li Dong nodded and said,
"Okay."
"Don't worry, Mom. I actually really love the feeling of studying now."
Hearing this, Li Qin's face blossomed into a wide smile.
"Yes! That's the spirit!"
...
Jiangcheng University of Technology.
It used to be a junior college. A few years ago, it merged with several vocational schools and was upgraded to a four-year university.
Although it now bore the name of a University of Technology, locals still called it the polytechnic college, and its prestige was nothing to write home about.
Women's Dorm 306.
Lu Yao was in front of the mirror, shaping her eyebrows.
In the reflection, her skin was fair and her features delicate. A little touch-up was all it took to make her look exceptionally radiant.
Her roommate came in from the balcony, carrying a washbasin. Seeing the scene, she immediately started teasing.
"Well, well, Miss Lu. Heading out for a date? Did that heartthrob from the Civil Engineering department finally win you over?"
Lu Yao shot her an annoyed glance.
"What date? I'm going to a tutoring session."
"Tutoring?" Her roommate looked skeptical. "You're putting on makeup for a tutoring session? Who are you trying to kid?"
Lu Yao pursed her lips and didn't explain.
The reason was actually quite simple.
At a polytechnic university with a severe gender imbalance, especially in the mathematics department where she was one of only two girls in her class, boys were constantly sizing them up.
And what girl doesn't like to hear a few compliments?
Over time, wearing makeup whenever she went out had become standard procedure for Lu Yao.
There was no way she could explain this bit of vanity to a girl from another department.
After finishing her makeup, Lu Yao changed into a cream-colored trench coat, grabbed her bag, and left the campus.
She casually flagged down a taxi.
"Driver, to Junzi Road in the old district."
Sitting in the back seat, Lu Yao watched the scenery fly by and let out a soft sigh.
This tutoring job was really just her repaying a favor.
Fifty yuan an hour for tutoring… in this day and age, that kind of money meant you could only afford McDonald's if you went on a discount day, let alone for one-on-one high school math tutoring.
Besides, she wasn't exactly free. Although her third-year courseload wasn't heavy, she was already preparing for the graduate school entrance exam to get into a different university.
She hadn't chosen to study for the exam on her own because she knew herself. With her lack of self-control and independent study skills, getting in would be nearly impossible.
That was why she had been busy looking for a test prep agency recently.
But she had no choice. The student who needed tutoring was Aunt Li Qin's son.
Her own mother had made a huge mistake at work and was almost fired. It was all thanks to Aunt Li Qin running around and pulling strings that the issue was resolved.
Lu Yao didn't even want to accept any money, but her mother had insisted.
"You have to take it, but not too much. Aunt Li can't afford a high price. But if you don't take anything, knowing her personality, she would never let you go."
'I heard Aunt Li's son only scored in the 80s on his last test. So, if I just go over the basic formulas and review the key points from the first few required books, that should be enough.'
Lu Yao mentally mapped out her teaching plan for the day.
The car soon stopped at the entrance of an old residential complex.
Lu Yao paid and got out. Looking at the red brick buildings in front of her, she couldn't help but feel a little creeped out.
If there were no streetlights at night, she would never dare to come here alone.
Following the location from her WeChat message, she found the right apartment building.
Sixth floor.
No elevator.
Lu Yao was out of breath by the time she reached the top.
Standing at the door of 602, she took a moment to catch her breath before knocking.
KNOCK KNOCK…
"Who is it?"
A boy's voice came from inside—clear, crisp, and quite pleasant to the ear.
"I'm Lu Yao. Aunt Li sent me for the tutoring session."
CLICK. The security door swung open.
A boy in a gray T-shirt stood there. He was quite tall, and though a bit thin, he had a very clean-cut look about him.
"Lu Yao? Come on in."
Li Dong stepped aside to let her pass.
What Lu Yao didn't know was that just a moment before she knocked, this clean-cut young man had been in a state of extreme excitement, furiously working through practice problems.
Ever since receiving Joule's guidance yesterday, it was as if Li Dong had unlocked a whole new world.
He had stayed up until three in the morning solving problems. The feeling of concepts flooding his mind, impossible to push away, was countless times more satisfying than instantly headshotting an opponent in a video game.
This made Li Dong realize the terrifying power of 0.1 Concentration.
Of course, Li Dong's own innate 0.1 Memory also allowed him to absorb the material that much faster.
He had woken up automatically at six this morning and immediately started devouring his books again.
Using Joule's "deconstruction + foundational loop" method, in just one night and one morning, he had reviewed almost all the math concepts from his three years of high school.
Formulas that once looked like hieroglyphics were now understandable at a glance. After doing just a couple of problems, he could extrapolate the underlying principles.
He was even starting to feel that high school math was a bit… too easy.
Just as Lu Yao was walking in, Li Dong's phone screen was displaying: *New Introduction to Mathematical Analysis* by Zhang Zhusheng.
He was looking up university-level mathematics.
"You don't have to change your shoes. We're not that formal here."
Li Dong scratched his head, looking a little awkward.
He had never had a private tutor before and had no idea what the procedure was. Was he supposed to introduce himself? He blurted out傻乎乎的.
"Hi, Lu Yao. I'm Li Dong, your... uh, the one you're tutoring."
Seeing how nervous he was, Lu Yao couldn't help but let out a laugh, and the prim-and-proper teacher persona she had been prepared to adopt vanished.
"Easy there, kiddo. Don't be so nervous. I don't bite."
As she spoke, she walked naturally into the living room.
The old wooden table in the living room was piled high with math textbooks from all three years of high school, along with several open workbooks, creating a bit of a mess.
And in the middle of that pile of books, a phone screen was still lit up.
Lu Yao had excellent eyesight and caught a glimpse of the screen's contents.
*New Introduction to Mathematical Analysis*?
Lu Yao paused for a second, then a sense of exasperation washed over her.
'Kids these days. Their foundation isn't even solid, so why are they so eager to aim for the stars?'
He had only scored in the 80s and probably hadn't even mastered trigonometric functions or solid geometry, yet here he was, looking at Zhang Zhusheng's *New Introduction to Mathematical Analysis*?
Wasn't this a classic case of one's reach exceeding one's grasp?
'Looks like I'll have to give him a good talking-to. You have to learn to walk before you can run.'
Lu Yao secretly made up her mind.
When Li Dong saw Lu Yao staring at his phone, he panicked and quickly walked over to lock the screen and put it away.
The feeling was as awkward as getting caught watching porn by your parents.
After all, for a failing student like him to be looking at something like that... if word got out, people would laugh their heads off.
He quickly pulled over a chair.
"Lu Yao, have a seat. I'll go get you a glass of water."
"Don't worry about it. Let's just get started."
Lu Yao waved her hand dismissively, sat down with a professional air, and took a pen out of her bag.
"Aunt Li told me your results on the last monthly exam weren't ideal. Let me see your test paper first."
"I want to analyze the types of mistakes you made to see where your weak points are. Then we can work on strengthening them."
Lu Yao was very familiar with this routine.
Li Dong hesitated.
He really wanted to say:
'Actually, I understand all the problems I got wrong. Why don't you teach me some Calculus instead?'
But looking at her serious and responsible expression, he didn't have the guts to say it out loud.
"Oh, okay."
Li Dong obediently handed over his monthly exam paper.
Lu Yao took the paper and glanced at the score.
87.
Yep, that looked about right.
...
Lu Yao held the test paper and looked at Li Dong again, sighing softly in her heart.
'This kid doesn't have the face of a top student; he has the face of someone who'd get into puppy love.'
'Boys like him usually sit in the back of the classroom. They're good at basketball, but their grades are a complete disaster.'
'If his grades were better, he'd probably have priority in the dating pool at college.'
Lu Yao teased herself inwardly, then picked up her red pen and went straight to the glaring red X's.
"Look at this multiple-choice question on the concept of sets."
Lu Yao pointed to the third question.
"The answer should have been A, asking for the intersection. You chose B, which means you obviously missed the case of the empty set."
"This kind of mistake stems from not having a solid grasp of the basic concepts, and it's one many students make…"
Just as Lu Yao was about to expand on the three elements of a set for Li Dong, she stopped.
She had noticed the notes written next to the problem, and her voice died in her throat.
[If A∩B=∅, then Δ
The handwriting was a bit messy, but the line of reasoning was perfect. There were no superfluous steps, and the case-by-case analysis neatly avoided every trap in the problem.
"Huh?"
Lu Yao looked up at Li Dong.
"Are these notes you took when your teacher went over the test?"
Li Dong had been thinking about the different descriptions of the definition of a limit in *New Introduction to Mathematical Analysis*. He was startled by the question and took a moment to register it.
"Uh… I guess you could say that."
Lu Yao nodded.
"Well, you took very good notes. It seems you were paying attention in class after all."
She continued looking down the page.
The next incorrect problem was on trigonometric functions.
Li Dong's work was a complete mess; he'd even used the wrong formula.
But Lu Yao had learned her lesson. This time, she looked at the notes beside it first.
Sure enough.
Next to the wrong answer was a simple circle with a few auxiliary lines accurately dividing the angles.
[Using unit circle symmetry, point P(x, y) symmetric about the origin ⇒ P'(-x, -y)]
…
The correct answer had been derived in just three steps.
"This…"
The more Lu Yao looked, the more she felt something was off.
Although she was a student at a second-tier university, she was still a formally trained math major. She had an eye for these things.
This kind of problem-solving approach was definitely not something a student who usually scored in the 80s could come up with on their own.
There was only one explanation—he had an excellent teacher.
"Hey, kiddo, what school do you go to?" Lu Yao couldn't help but ask.
Li Dong didn't understand why she was suddenly asking this, but he answered honestly, "Jiangcheng Seventh Middle School."
"Seventh Middle School?"
Lu Yao frowned slightly.
She was well aware of Seventh Middle School's reputation in Jiangcheng. It was known for its hands-off approach, with average students and a faculty that was said to be rather laid-back.
'Are the teachers at Seventh Middle School really this dedicated now?'
Lu Yao muttered to herself.
The notes on this test paper hit the nail on the head every single time. Some of the approaches were even more clever and concise than the standard answers in the official study guides.
This level of teaching would be considered mind-blowing even at Jiangcheng Sixth Middle School, the best in the city.
She couldn't help but sigh as she spoke to Li Dong.
"You have a great teacher. You'd better not let him down."
Lu Yao continued to flip through the test. After looking through the first few sections, her impression of Li Dong had improved significantly.
'This kid isn't a lost cause. At the very least, his attitude toward corrections and the quality of his notes show that he wants to learn.'
That is, until she flipped to the very last page.
The bonus question section.
As expected, the kid hadn't answered it. But now, in the blank space, was a hand-written variation of the problem.
[Given the function f(x) = e^x - a ln(ex), if f(x) ≥ 0 holds true for all x in (0, +∞), find the maximum value of a.]
Lu Yao's eyebrows shot up.
"Isn't this an isomorphic structure? Your teacher actually covers this kind of problem with you?"
The difficulty of this question was already approaching math competition level.
To solve it using conventional methods, you would need to construct two new functions, perform differentiation twice, and in the middle of all that, deal with an extreme value substitution involving an implicit zero. The amount of calculation was staggering.
Even she would need over ten minutes and a full sheet of scratch paper to solve it.
She instinctively looked at the solution process on the paper, preparing to see how this "note" was written.
However, the very first line of the solution stunned her.
There was no function construction.
No second derivative.
[Using tangent line inequality: e^x ≥ ex…]
[The original equation simplifies to…]
[Therefore, a_max = e]
The entire process was just five short lines!
Lu Yao rubbed her eyes. She wasn't seeing things. How did it just jump straight to the conclusion?
'What the hell kind of logical leap is this?'
'Is it missing something important?'
She quickly grabbed her scratch paper and traced the logic.
First step, correct.
Second step, substitution with a composite function, correct.
Third step, verification of the equality condition, holds true at x=1, correct!
"Hiss—"
Lu Yao sucked in a sharp breath of James Joules.
This solution method was nothing like high school math. It utilized function convexity and the tangent line inequality to launch a "dimensional-reduction attack" on the problem.
Forget a regular high school teacher; even her own university professor wouldn't have thought to use this method to solve this problem.
Lu Yao looked up, her expression complex as she stared at the young man before her.
"Li Dong."
"Yeah, what is it?" Li Dong, who was taking a sip of water, was startled by her sharp tone.
"This solution…" Lu Yao pointed to the last problem, her voice a bit dry.
"Did your teacher explain how he came up with this method? Or did you just copy what he wrote on the board?"
Li Dong blinked, a little embarrassed.
"Um… Lu Yao, the teacher didn't actually go over this one."
"He didn't?" Lu Yao didn't quite understand.
"Yeah, it was a variation the teacher wrote down in class. I just tried to work it out myself."
Li Dong did his best to make his tone sound sincere.
"I figured it'd be too much trouble to brute-force it, so I wondered if I could use an inequality to take a shortcut. I didn't expect it to actually work."
Lu Yao was speechless.
Seeing Li Dong's "I was just trying to save some effort" expression, Lu Yao couldn't help but feel a pang of disappointment.
'You're a slacker who scored an 87, and you're telling me that, just to be lazy, you casually derived a brilliant solution that even *I* couldn't think of?'
'That's just too unbelievable!'
Lu Yao stared into Li Dong's eyes, trying to discern whether he was lying.
But his gaze was too sincere—so sincere it made her feel like she would be a bad person for doubting him.
Yet, her rational mind told her it was impossible.
'He's faking it!'
The three words exploded in her mind.
'He must have looked up the answer somewhere, or the teacher explained it, and now he's claiming he figured it out himself.'
'Boys these days… They'll say anything for a bit of pathetic vanity.'
She did not like dishonest students.
And when she thought about Aunt Li working so hard, even begging people to find him a tutor, a sour taste filled her mouth.
But she had made a promise, so she had no choice but to bite the bullet and continue.
"Fine. Since you can derive it yourself, that means I don't need to explain this problem to you."
"Let's get back to the fundamentals."
Lu Yao did her best to drag the kid back onto the "correct" path.
For the remainder of the session, Lu Yao began to painstakingly explain the basic concepts where students in the 80-90 score range most easily lose points.
From solving quadratic inequalities, to setting up coordinate systems in simple solid geometry, to the summation formulas for sequences.
She explained everything concisely.
Li Dong listened attentively at first, but he soon grew bored of reviewing concepts he had already thoroughly mastered.
As she spoke, his gaze began to drift, and his mind flew back to *New Introduction to Mathematical Analysis*.
"Li Dong, pay attention!" Lu Yao rapped her knuckles on the table.
"Eighty percent of the college entrance exam is basic questions. You have to know this stuff inside and out!"
Li Dong snapped back to attention and asked tentatively,
"Um… Lu Yao, I already know the basics. Could you maybe teach me a little about Calculus?"
Although he felt he could understand it by reading the book himself, he suspected that a formal university education might offer a different perspective than his own unorthodox, self-taught approach.
Hearing this, Lu Yao sighed inwardly.
But in order to raise his score—or at least keep him from failing his next exam—Lu Yao refused him without hesitation.
"Calculus won't provide any substantial help for your upcoming college entrance exam. Your number one priority right now is to ensure you don't lose any points on the fundamental questions."
And so it went. One person gritting her teeth and teaching by the book, the other gritting his teeth and listening while his mind was filled with higher mathematics.
An awkward and very long hour finally crawled by.
"Alright."
Lu Yao closed the test paper.
"That's all for today's tutoring session."
She glanced at her phone. It had been about an hour, but she had no desire to continue. Besides, judging by Li Dong's condition, he seemed listless as well.
"Huh? We're done?" Li Dong was still thinking about *New Introduction to Mathematical Analysis* and didn't register her words at first.
"Yeah, I have something to do, so I have to head back to campus."
Lu Yao gathered her things, stood up, and offered a polite but distant smile.
"You can spend the rest of the time reviewing on your own. Don't bite off more than you can chew. Focus on solidifying your foundation first."
"Also…"
She paused and said in a meaningful tone,
"It's not easy for Aunt Li to earn money…"
With that, Lu Yao grabbed her bag and walked out of the room without a backward glance.
Li Dong sat in his chair, utterly bewildered.
'Why do I get the feeling… that she's angry?'
…
After leaving, Lu Yao felt deeply conflicted.
She wondered, should she say something to Aunt Li?
But if she told her directly, she was afraid she would hurt Aunt Li's feelings…
Lu Yao was caught in a dilemma.
Meanwhile, the source of her dilemma, Li Dong, was excitedly scribbling integral signs on a piece of scratch paper.
'So this is the Newton-Leibniz formula… It's so beautiful!'
'If I apply this to calculating the work done by a variable force in physics…'
The young man's eyes were filled with a pure thirst for knowledge.
He was completely unaware that he had just been labeled as someone who was overly ambitious and out of touch with reality.
