I'm Just Looking, Not Saying Anything

As a homeroom teacher, Zhang Wanbang was confused. Was this really Shen Qi, the gamer and useless underachiever?

As a math teacher, Zhang Wanbang was delighted, because his student was discussing Cayley and Weierstrass with him.

Their discussion lasted about ten minutes. For the most part, Zhang Wanbang asked questions and Shen Qi answered.

"We generally consider Cayley the founder of matrix theory. One of Cayley's corollaries says that the product of two matrices can be zero even if neither matrix is zero, provided at least one of them is indefinite. Shen Qi, do you think this corollary is correct?"

"Actually, Cayley was wrong. The corollary is incorrect; both matrices have to be indefinite. I only know the result, Teacher Zhang. If you want me to prove it, I'm not good enough."

"Weierstrass was the first to obtain the canonical form of the pencil A+λB. Shen Qi, how do you understand the canonical form of this pencil?"

"Here, A and B don't have to be symmetric, but they satisfy the condition that the determinant of A+λB isn't identically zero."

"Correct. Now, its inverse theorem came from Sylvester and was proved by Weierstrass. If I remember right, the Advanced Algebra textbooks from our day gave just one sentence about this inverse theorem. Do you know what it says?"

"I... I don't know!"

"This inverse theorem says that if the determinant of A+λB has the same elementary divisors as the determinant of A′+λB′, then a pair of linear transformations can be found that simultaneously transform A into A′ and B into B′. Shen Qi, how do you understand this inverse theorem?"

"I... I can't understand it..."

"Advanced Algebra really is too abstract for a high school student, but I'm glad you've taught yourself to this level, Shen Qi."

"Cayley and Weierstrass, matrix algebra and all kinds of determinants—it's hard to explain them to you in just a few words." Zhang Wanbang casually pulled out a sheet of A4 paper, wrote down several lines of mathematical symbols, and handed it to Shen Qi. "Do as much as you can. Come see me in the office at this time tomorrow."

Shen Qi took the paper and saw that it had five math problems on it. It seemed Teacher Zhang wanted to test him further.

"Okay, see you tomorrow, Teacher Zhang." Shen Qi said goodbye to Zhang Wanbang and left the teachers' office.

Back in the classroom of Class 2, Grade 11, Shen Qi began tackling the problems Zhang Wanbang had set.

The first problem was to prove the Cauchy–Schwarz inequality: XXXXXX (a mathematical expression that some phones could not display), and give the conditions for equality.

The problem wasn't too difficult. It was an introductory proof problem in Advanced Algebra, testing the concept of inner product spaces.

Shen Qi quickly completed the proof and wrote it out on the paper.

System: "Host solved the problem successfully. Reward: 2 Academic Ace Points."

"Oh, nice, 2 Academic Ace Points." Shen Qi couldn't earn Academic Ace Points by doing high school math problems anymore, but he could earn them by doing university-level math.

At the same time, the Chinese teacher came into the classroom. It was time for Chinese class.

Shen Qi focused entirely on solving Zhang Wanbang's math problems and didn't pay attention to the Chinese lesson. A person's energy was limited, after all; it was hard to focus on two things at once.

Zhang Wanbang's second problem was to solve a system of linear equations. It required combining Gaussian elimination with the properties of augmented matrices, and was somewhat more difficult.

Shen Qi ran into some obstacles while solving it. Performing elementary transformations on a system of linear equations was equivalent to performing row operations on its augmented matrix.

System of equations → augmented matrix

Augmented matrix → system of equations

Eliminate the x1 term in the first equation

Then the third row of the augmented matrix was transformed

Add four times the second equation to the third to eliminate the x2 term in the third equation, obtaining a system in echelon form

Then the augmented matrix also had to be transformed into...

"My eyes are going cross-eyed..." Shen Qi kept switching back and forth between the system of linear equations and its corresponding augmented matrix until he started questioning his life.

Shen Qi gritted his teeth and forced his way through the problem. The process was agonizing, but once he finally got past the hurdle, the sense of achievement was twice as sweet.

After spending the entire Chinese lesson on it and burning through countless brain cells, Shen Qi finally solved Zhang Wanbang's second problem.

"Host solved the problem successfully. Reward: 5 Academic Ace Points."

He could have earned 1 Academic Ace Point from Chinese class, but since Shen Qi hadn't paid attention, the lesson contributed nothing to his score.

It didn't really matter, anyway. Shen Qi had solved two math problems during Chinese class and earned 7 Academic Ace Points.

"Solving two math problems is the same as sitting through seven Chinese lessons. Doing 200 university math problems... Never mind. I'll take a break first." During recess, Shen Qi took Advanced Algebra out of his schoolbag and reviewed the major coursework of math students.

First-year math majors had three required foundational courses: Advanced Algebra, Mathematical Analysis, and Analytic Geometry.

Of these, Analytic Geometry was relatively the easiest. It could be understood as the three-dimensional version of high school plane analytic geometry.

In terms of abstraction, Advanced Algebra was the hardest. In terms of computation, Mathematical Analysis was the hardest.

As for later branches, such as Real Analysis, Functional Analysis, topology, Partial Differential Equations, Differential Geometry, and Algebraic Geometry, those with the ability could study them, while those without it would fail.

"Hey, Shen Qi, what book are you reading?" His deskmate, Chen Xiaoting, noticed that Shen Qi was reading a strange book.

"Advanced Algebra." Shen Qi closed the book and pushed it across Chen Xiaoting's desk.

Chen Xiaoting saw the cover and was stunned. "Advanced Algebra, a full-time university math textbook... Is this a college textbook?"

"Yep." Shen Qi nodded.

"I'm just looking, not saying anything." Chen Xiaoting flipped through a few pages, then handed Advanced Algebra back to Shen Qi. "Is this Advanced Algebra your secret to getting perfect scores?"

"No. This book won't directly help improve your high school math grades."

"Then why are you studying it?"

"Advanced Algebra offers a kind of abstract logical thinking. You could say it's useful—it's very useful. You could also say it's useless—it's completely worthless." Faced with the vastness of mathematics, Shen Qi was still an apprentice. He couldn't explain the ultimate meaning of math either; he was exploring it in his own way.

"Sounds so profound, but it has nothing to do with me. I only got 85 on this math test. I really regret going into the science track." Chen Xiaoting's grades in math, physics, chemistry, and biology were all average at best. She made up some points with Chinese and English, barely keeping her total score in the middle of the pack.

Just then, the school broadcast began playing the exercise music. It was time for the morning exercises.

"Come on, let's go exercise." Shen Qi stood up and asked Chen Xiaoting to go downstairs with him.

Chen Xiaoting awkwardly smiled, one hand over her lower abdomen. "I'm not feeling well, so I'm skipping the exercises today."

Oh, she was on her period. She really shouldn't exercise; jumping around could cause problems. Shen Qi had heard all kinds of things about periods, and high schoolers knew about this stuff. "Then get some rest. Let me know if you need anything."

"It's really not that bad. You should go do the exercises." Chen Xiaoting's face turned red. How could a girl tell a boy what she needed?

Within minutes, over a thousand students had assembled on the school field, lined up by class.

Nangang Second High School had a long history. It had been founded during the Republic of China era by patriotic revolutionaries. The principal strictly upheld the school's basic principles: "Build strong bodies, develop students in a balanced way, educate without discrimination, and treat everyone equally." The school had no advanced or regular classes. Strengthening students' physical fitness and teaching positive values were the principal's promises to society.

After the ninth set of broadcast exercises ended, Shen Qi stayed on the field. Next up was physical education.

For most boys, PE class was the happiest time of the day, a rare break from their heavy workload.

The principal of Nangang Second High School had kept his promise to "build strong bodies and develop students in a balanced way." PE classes would continue through the first semester of senior year, while some other high schools had already abolished them during the second year of high school.