I was a top student in America.

Upon hearing what Mr. Miller said, David didn't delay and immediately pulled out Li Ao's paper from the pile of test papers and handed it over.

A yellow note with the proof was stuck to the corner, and a big question mark was drawn in red next to the last question.

While Professor Miller and Professor Jensen were looking at the papers, David casually mentioned the gossip he had just found out:

"Speaking of which, this Leo is quite famous in our summer camp. He got perfect scores on his application for AMC12, AIME, and USAMO, but his school is just an ordinary public high school in the South Side of Chicago."

"There are also posts on the forum about his interview with the Chicago Tribune, saying that he is not only a key player on the basketball team, but also has to work odd jobs, and he still manages to study for fifteen or sixteen hours a day. I guess he had already gone through the IMO practice questions several times before he came here."

After collecting the papers yesterday, David, out of curiosity, flipped through the registration materials and casually searched for the newcomer's name on the student forum.

Ms. Miller remembered the name; she made a special mark next to this file when she was organizing the list a few days ago.

"It's truly remarkable to maintain this level of study intensity. However, once you reach the black belt level, simply doing a lot of practice problems isn't enough."

Professor Jensen casually chimed in, his eyes already fixed on the proof steps in the exam paper.

The professor knew very well that the students who could get into the national math competition summer camp were not lacking in hard work.

You might get a high score on the USAMO by doing tons of practice questions, but that will only get you to red or blue belt level.

The goal of the black belt group is to reach the national team. To stand out here, one must rely on pure problem-solving intuition and mathematical talent.

In particular, the questions in this diagnostic test were carefully selected by the coaching team, and the difficulty level was evident.

Therefore, when Professor Jensen heard that a freshman had submitted his paper early with a very high accuracy rate, his first reaction was: We've encountered some promising students this year.

He didn't care at all about the gimmick of "studying for sixteen hours a day".

As you scan the page downwards, the solution becomes immediately clear.

Just as David said, the proofs for the first five questions were flawless, even quite neat and beautifully written, without a single superfluous word.

Two questions did not use the conventional solution from the reference answer; the steps were much simpler, but the core deduction was not omitted at all.

It's truly remarkable that this level of quality could be produced in less than an hour and a half.

Even Professor Jensen, who rarely praises others, muttered something unusual:

"Well written."

But when he saw the last question, he frowned.

After scrutinizing him for more than ten seconds, a hint of surprise flashed in his eyes.

The scaling approach to this problem seems to be derived from some kind of weighted Hermite-Hadamard form.

Professor Jensen didn't say anything. He simply took a pencil from the pen holder, grabbed a piece of scrap paper, and started calculating in front of Professor Miller and David.

The draft paper rustled as he looked increasingly focused.

David stood there, somewhat stunned.

It's just a diagnostic test, why did the tutor have to do the calculations himself when looking at the paper?

But having studied under Professor Jensen for over three years, he knew his mentor's temperament all too well, and speaking up now would only invite trouble.

He could only stand there and wait patiently.

A few minutes later, Professor Jensen finally put down his pen, his tone unusually excited.

"He didn't get this question wrong. His process was a bit roundabout and different from the standard answer, but the logic was completely sound. I even suspect that he deliberately followed this line of thought to answer the question."

"This question deserves full marks."

Hearing his mentor say that, David felt a pang of jealousy.

Looking back, when I used to ask my supervisor for advice on research ideas or draft papers, he always had that indifferent poker face, at most managing to say, "Keep it up."

He had always thought that the professor was just naturally like that.

"So it's because my writing is simply not good enough for him?"

David was startled by his own thought, quickly shook his head to banish it, and forcefully steered the conversation back on track:

"Professor, is he using a new method?"

Professor Jensen tapped his draft paper and explained:

"You didn't look closely enough. He transformed the discrete weights back into piecewise integral averages, creating a new inequality chain under a weighted Hermite-Hadamard two-sided estimation."

"Although the proof is a bit complicated, using this conclusion to calculate extreme value inequalities is both simple and accurate."

"To put it bluntly, he spent 90% of the first part proving this lemma, and this problem is just a special case of his lemma."

"This kid's way of thinking, hmm, it's kind of interesting."

After hearing this, David was speechless.

He studied mathematics and knew all too well how tedious it was to reconstruct such weighted inequalities into a chain of proofs.

This is not only quite abstract, but also has a frightening number of mathematical details. Just the derivation of the weight allocation and boundary conditions alone can lead a group of undergraduate math students into a dead end.

This kind of abstract thinking ability cannot be developed by simply spending time practicing; it relies purely on talent.

Just as I was pondering this, the professor spoke again.

"Change his score to full marks. Put him and Benjamin on the watchlist. They're talented and hardworking; these are the people our summer camp should focus on developing."

"Understood." David took notes.

After reporting the matter, he didn't stay any longer and turned to leave.

Just as he reached the door, Professor Jensen suddenly spoke up:

"Wait a minute. I remember there's a workshop on mathematical analysis at UIUC tomorrow afternoon. Send an email to Leo and Benjamin to audit it, and see how his intuition is for analyzing problems."

"Okay, I'll go back and send out the notice right away," David replied, pushing open the door and leaving the office.

No sooner had David left than Professor Jensen got up and sat down at his computer.

He didn't rush to grade the remaining placement papers. Instead, he logged back into the summer camp registration system and, following David's earlier words, clicked on the interview post about Li Ao in the forum.

……

Li Ao didn't go to the library tonight.

He stayed in the dormitory alone and continued to study the book "Principles of Mathematical Analysis".

Suppose that a sequence of functions converges uniformly on a closed interval, and each function is continuous...

He stared at an example problem for a while, and soon a proof idea came to him.

"Uniform convergence requires first controlling the error between fn and f, and then using the continuity of a certain fn to control the difference caused by the change of the independent variable."

Having determined the direction, he picked up a pen and soon finished writing down the steps for ε control and triangle inequality decomposition on the draft paper.

System prompts will light up at appropriate times:

[Under intense study conditions... Intelligence +0.1]

Just as I finished proving the problem, the dormitory door was pushed open with a "bang".

Kevin, Taylor, and Ethan, three young men, squeezed in excitedly, each clutching a few sheets of A4 paper covered in formulas.

"Leo!" Taylor slammed the paper on Li Ao's desk, his face beaming with excitement. "We got the answer key for the placement test! Benjamin and Natalia wrote it on the whiteboard in the discussion room."

Li Ao was not surprised by this.

He knew that his roommates had gone to the math building's common discussion room that night to participate in a problem-solving review session organized by the students themselves.

There's a long-standing tradition in American high school competitions that top students always come up with unofficial solutions after exams.

Every year after the initial assessment, the discussion room is always packed with new students checking their answers.

Benjamin said that this year's questions were generally difficult, and he estimated that not many people would get full marks.

Taylor continued, "The three of us just checked the answers. Kevin did well and should be in the top few."

"Based on previous years' cutoff scores, Ethan and I are roughly on the average, so we shouldn't have to attend evening tutoring sessions this time."

"This answer was put together by Benjamin and Natalia, so it should be pretty reliable." Kevin nodded in agreement, while Ethan looked at Li Ao with anticipation.

Li Ao listened to them chattering away.

Although he doesn't usually check answers, he still reached out and picked up the papers and glanced at them.

After reading it, he nodded: "The first few questions were similar to my approach. For the last question, they used a different method than me, but this solution is simpler and clearer, so there's no problem."

Hearing Li Ao's certainty, the three boys in the dormitory cheered again.

With this academic genius in charge for the next month, I feel like I've got a lifeline for problem-solving and discussion classes.

Even Taylor felt that she could still be saved at this summer camp.

With the preliminary tests now complete, the summer camp's intensive lectures, endless practice materials, and high-intensity discussion sessions have finally begun.

……