I was a top student in America.

It was just past nine o'clock on a Saturday morning at the end of January.

In the workshop classroom at Whitney Young High School, Li Ao was writing down a few key steps on a piece of scrap paper, explaining a difficult algebraic inequality problem to Sam next to him.

"Let's make a substitution first." Li Ao lightly tapped the paper with the tip of his pen. "Let x, y, and z be the reciprocals of a, b, and c, respectively. Since abc equals 1, then xyz must also equal 1. In this way, the left side of the inequality can be directly transformed into the symmetrical form of x squared divided by (y+z).

"Next, we directly scale this symmetrical fractional form that applies Cauchy's inequality." He drew a line on the paper, "and immediately we can see that it is greater than or equal to the square of (x+y+z) divided by twice (x+y+z), which is half of (x+y+z)."

"Finally, we'll conclude with the AM-GM inequality. Since xyz equals 1, then x + y + z is naturally greater than or equal to 3 times the cube root of xyz. The lower bound is exactly 3/2. Q.E.D."

Ever since he won first place in the state at ICTM, Li Ao has become the focus of private discussion among students from various schools in the North District of the training camp.

Even when Green was on the podium, he would often use his drafts as examples to broaden the thinking of the people below.

In addition, he doesn't put on airs in the classroom, and he'll answer almost any question anyone brings him.

After a few times, people like Jimmy and Sam had long since willingly started calling him "Leo" and following him around.

In the eyes of these proud and ambitious competition students, the title of "Number One in the Northern District Competition Circle," which Matthew had worn for a long time, had quietly changed hands after several head-to-head competitions.

"Got it, I'll try to deduce it myself following this line of thought." Sam took the draft paper and examined it closely, making two light dots on the substitution equations with the tip of his pen, muttering to himself.

Li Ao casually put the pen on the table, leaned back in his chair, and stretched.

His gaze swept past the desks in front of him and around the classroom.

As the competition drew near, the classroom was filled with a suffocating anxiety.

A girl in the front row had spread out a whole table of scratch paper and was frantically making corrections; two boys next to her were huddled together, their brows furrowed as they looked at the answers; and in the corner, someone was staring blankly at a notebook full of densely written mistakes.

After entering January, Green's teaching pace went up rapidly, with the number of questions he threw at students increasing exponentially every day, and the specially provided internal lecture notes had already reached the third volume.

Unfortunately, there are less than two weeks left until the AMC 12 exam that will sweep across the United States in early February.

The oppressive feeling of the countdown was so intense that everyone was almost suffocating.

Li Ao withdrew his gaze and looked back at the draft paper in front of him.

Compared to the frantic efforts of those around him, he simply twirled his pen calmly, his thoughts drifting back to a complex weighted inequality.

Around 11 a.m., after Green finished explaining the first round, he assigned free practice.

When the lunch break bell rang, Li Ao pressed his aching right wrist and rotated it, finally lifting his head from his notebook.

Forcing a new conclusion out of thin air is not as easy as it seems.

After finishing the second half of the AP Calculus textbook, he set his sights on a classic theorem in convex function integration—the Hermite-Hadamard Inequality.

If f is convex on [a, b], then f((a+b)/2)≤ 1/(ba)∫_a^bf(x)dx≤(f(a)+f(b))/2.

Using geometric intuition, this inequality is not difficult to understand—the mean of the integral is tightly sandwiched between the "midpoint function value" and the "endpoint mean".

But after flipping through several analytical reference books he had borrowed from the public library, he discovered that there was still much to be done with this stuff.

If we introduce a weight function w(x) into the integral, can the squeeze at both ends be tightened more?

Just do it.

He started with the symmetric weight function, which is the easiest to learn, assuming that it is symmetric about the midpoint of the interval.

In existing literature, most weighted versions only perform one-sided estimations, and the results that refine both ends simultaneously are incomplete.

As he continued down this line, he became increasingly certain that there was definitely an even tighter and more elegant two-sided inequality hidden within.

The outline of the conclusion has already taken shape in my mind: under the condition of a specific symmetric weight function, the weighted integral can be locked by a more stringent upper and lower bound than the original theorem.

Once this is rigorously proven, it will be of great benefit to everything from convex function approximation, error estimation of numerical integrals, and expectation calculation in statistics.

After pondering it for half a month, progress was stuck on the specific boundary conditions of the weight function.

The framework has been built, but it's just one final step away from being a perfect fit.

He didn't go to such lengths to work on basic pure mathematical derivations because he was bored.

Instead, after mastering both AP Calculus and AMC 12 mock exams, he discovered that his intelligence attribute on the panel had stopped increasing.

For nearly a week, he gritted his teeth and did eight full AMC 12 mock exams, but his IQ score only jumped once, a meager increase of 0.1.

Compared to the initial frequency of jumping three or four times a day, it's a precipitous drop.

It turns out that the strategy of mindlessly practicing old questions to gain experience has reached its peak.

To improve further, one must explore the blind spots that high school competitions do not cover.

Fortunately, the surge in attributes triggered by the derivation of a new academic conclusion during the previous state competition gave him inspiration.

The system clearly acknowledges this "independent originality," even if the conclusions are not universally applicable and only hold true under specific conditions.

So recently he decisively switched tracks, from passively solving problems to actively deriving solutions.

This is currently the only way to break through the 110 mark in intelligence.

Looks like I'll have to go to the public library on 61st Street again after school next Monday to try my luck and see if I can find any more advanced analytical works.

That still didn't work, so on Wednesday I simply rode my bike straight to Hyde Park and spent an afternoon at the Regenstein Library at the University of Chicago.

Anyway, there's only a little over a week left until the AMC12 exam. Green will most likely cancel the intensive course next weekend so everyone can adjust on their own. Saturday will be a good time to tackle the exam.

Li Ao shifted his gaze from the draft paper, and with a thought, the system panel quietly appeared in his field of vision.

【Intelligence: 109.7】

"Just one last step," Li Ao muttered to himself, staring at the fluctuating numbers.

He had a strong intuition that as long as he could thoroughly solve the two-sided proof of this weighted inequality, his intelligence attribute would surely surpass the 110-point mark.

At that time, the fifth exclusive term will also be unlocked. He has been looking forward to the qualitative change that this level might bring for far too long.

……

Monday's basketball training session, warm-up has just ended.

Jamal's loud voice suddenly came from behind, abruptly cutting off the weighted deduction path that Li Ao was still practicing in his mind.

"Leo, are you going to play in the first playoff game next week?"

"Of course I'll fight! I can't afford to mess things up at a time like this!"

Li Ao turned around and answered without hesitation.

Since the last "stand mobilization meeting," Mrs. Paterson's logistical support has become increasingly expedited.

Coach Durant even gave him a special privilege, like a get-out-of-jail-free card: in order to ensure his energy for academic competitions, Li Ao could freely allocate his training time and even "take a break as needed" in non-critical games.

Even with his privileges, Li Ao never missed a single tough battle.

Even though he occasionally missed training for the workshop, his threat on the court did not diminish. On the contrary, with his increasingly consistent three-point shooting, he fought his way from the bottom of the bench at the beginning of the season to the starting lineup.

Now, the title of "Wyndham sharpshooter" has become a key point that coaches at schools across the South District must highlight on their tactical boards.

Wyndham High School also took advantage of this momentum to make it into the playoffs' top 16 for the first time in 30 years.

If we win the crucial round of 16 next week, it will be the first time in the school's more than 30-year history that we have made it into the quarterfinals.

This is enough to ensure that the names of this year's team members are neatly inscribed in the school's sports hall of honor.

Upon receiving Li Ao's affirmative reply, Jamal's eyes lit up instantly, and he excitedly slapped Li Ao on the shoulder: "Brother Leo, with you saying that, we're in luck!"

With next week set to be a game that will rewrite team history, the entire team, from Coach Durant to the fringe players on the bench, is burning with determination.

At this critical juncture, as long as we can ensure that everyone is ready to fight, the tension in everyone's hearts will not dissipate.

Seeing Jamal's excitement, Li Ao was somewhat infected by it.

Basketball was just a stepping stone for him in college, but to say that he was indifferent to "leading the team to the quarterfinals and making history" would be too self-deceptive.

"Beep—!"

The whistle blew sharply across the arena, and Durant clapped his hands to call the team to gather at center circle.

Jamal sprinted onto the court while gesturing wildly and showing off something to Jaylen beside him.

After a period of intense tactical positioning training, it was time for the break between sets.

The team members, carrying plastic water bottles, collapsed haphazardly on the sidelines, panting heavily.

Durant was a little further away, pulling Tayshaun along and gesturing at the whiteboard, but it was impossible to hear what he was saying.

"If we really beat them next week, where will we go to celebrate?"

"Do you even need to ask? You have to go to that 'Iron Bar' bar in the basement on 51st Street. Malik said he can get a few fake adult IDs on Friday. As long as the doorman doesn't stare at the photos too intently, you're guaranteed to get in."

Amidst the lively discussion, Jay Chou, wearing a white towel on his head, squatted in a corner, gulping down water from a water bottle.

Only after seeing Li Ao sit down on the bench did he wipe his face and ask loudly, "Leo, where do you think would be a good place to go?"

It was only after studying with Li Ao for a while that Jay Chou truly witnessed what it meant to be outmatched.

Li Ao only gave him one or two example problems each day, not requiring him to understand the logic, but just to memorize the various tricks. Surprisingly, he actually got a "B" in the final exam for the first time ever.

From that moment on, Jay Chou was completely convinced.

Whether in the stadium, the corridor, or the cafeteria, everyone greets Li Ao whenever they see him.

When I encounter a problem I don't understand, I'll shamelessly go up and ask.

"That's right, Leo. Next week, as long as you're on the perimeter, their defense won't be able to relax. Where do you want to celebrate? We'll be there to keep you company."

Malik had just returned from the coach's office and took over the conversation with a smile.

Since the gym intervened and handled Todd's situation, the two have unexpectedly gotten along well.

Li Ao didn't hesitate for even half a second when faced with this sudden question.

He pulled the towel from around his neck and casually wiped the sweat from his chin: "You guys decide. I'm still thinking about a math problem."

The moment the words were spoken, the area around the bench fell silent.

Several people froze in their water bottle-holding postures, unable to recover for a long time.

Jamal was the first to laugh out loud: "Leo, your efficiency is really leaving no room for anyone else..."

He started laughing in anger halfway through his sentence.

Jaylen, standing next to him, didn't say anything, but simply covered his face with a towel and nodded in deep agreement.

Nobody mentioned going anywhere to have fun anymore.

Li Ao lowered his gaze, staring at the sweat dripping onto the wooden floor in front of his toes, his mind clear.

The weighted squeezing path that I had been struggling to push forward for so long suddenly gave me a new idea after just a couple of quick mental steps.

For him, being able to secretly solve a math problem amidst the noise of the stadium is much more enjoyable than spending a night partying in a crowded underground nightclub on 51st Street.