After school that afternoon, Shen Qi brought a plastic bag full of drinks to a small classroom in the science building.
Including Shen Qi, twelve students had gathered in the classroom. They were the twelve strongest math students at Nangang Second High School, from different grades and classes. There were no girls, only boys.
They were the Nangang Second High School Math Olympiad team, representing the highest level of mathematics at their school.
It wasn't easy to make the team. Anyone who had never scored full marks on a math test was automatically disqualified.
There were twenty-eight science-track classes across the first, second, and third years. Shen Qi was the only student from his second-year Class 2 to make the school's Math Olympiad team. Zhang Wanbang had recommended him.
"Big shot, please have some tea."
"Big shot, please have some tea."
Shen Qi pulled out bottles of iced black tea, iced green tea, and lemon tea, then handed them out to the other eleven team members one by one.
Shen Qi's dad had taught him that when entering a new environment, no matter how impressive you were, you had to keep a low profile at first. Observe quietly, figure out the lay of the land, and only then start showing what you could do.
Shen Qi had known there was a mysterious team like this at school. They sometimes gathered in the science building, sometimes in the library. They had no fixed base, and were hard to track down.
That morning, Zhang Wanbang had told Shen Qi to report to the small classroom in the science building after school, to prepare for the High School Mathematics League that weekend.
This was Shen Qi's first time meeting the school Math Olympiad team as a whole. As a newcomer, he handed out tea first and observed quietly.
"What year and class are you in?" A chubby boy took the iced black tea from Shen Qi and asked.
"Second year, Class 2. I'm Shen Qi," he replied.
"Oh, Shen Qi. Second year." The chubby boy looked at the other students and asked, "You're all second-years. Do you know Shen Qi?"
"Not really." The second-year boys all shook their heads.
Everyone here had scored full marks in math. Shen Qi had been a poor student before his sudden rise over the past two months, so it was only natural that they didn't know him.
Shen Qi maintained an awkward but polite smile. "I'm a newbie, so I hope you senior brothers and fellow team members will look after me."
"Have a seat, Shen Qi." The chubby boy gestured for him to find a spot, then introduced himself. "I'm Meng Tianqiang, from Class 5 of the third year. I'm the captain of this team. Welcome aboard, Shen Qi."
"Big shot, please have another bottle of tea." Shen Qi took a bottle of oolong tea from the bag and handed it to Meng Tianqiang.
"No, no, I'm trying to lose weight." Meng Tianqiang waved it away.
Shen Qi unscrewed the oolong tea bottle and drank it himself.
Shen Qi's impression of the team was that no one had rejected him, but nobody was particularly enthusiastic about him either.
He'd observe a little longer before deciding.
Since it was a competition team, they had to have a coach.
Shen Qi noticed that the other team members were all reading or working on problems by themselves. Half an hour passed, but the coach still hadn't shown up.
Was the Math Olympiad team's training method really just getting everyone together to study on their own?
Shen Qi didn't dare ask too many questions and continued observing quietly.
Close to seven, someone entered the small classroom. He was a little old man, thin and slightly stooped.
"Hello, Teacher Cao!"
"Hello, Teacher Cao!"
Meng Tianqiang and the others greeted the old man one after another.
"Hello, Teacher Cao!" Shen Qi followed their lead. He didn't know the old man, but it couldn't hurt to call him Teacher Cao.
Though Cao Xin'an was old, his eyes were sharp. He glanced at Shen Qi. "New here? Recommended by Little Zhang?"
"Yes. I'm Shen Qi, a second-year student. I hope you'll guide me, Teacher Cao." Shen Qi guessed the old man was probably the team's coach, and that the "Little Zhang" he mentioned was Zhang Wanbang.
"Math depends on talent and insight. What's there to guide?" Cao Xin'an replied coolly.
Shen Qi fell silent. Why was Old Man Cao's coaching style exactly like Zhang Wanbang's? Had Zhang Wanbang been trained by him?
There was a small blackboard at the front of the classroom. Cao Xin'an went over, picked up a piece of chalk, and wrote a problem:
"Given that a is the only real root of f(x)=0, and a＞0, prove that f(x) is divisible by (x-a). If a is an imaginary root, prove that f(x) is divisible by (x+a)."
After writing the problem, Cao Xin'an said to Shen Qi, "New student, you have ten minutes to write out the proof. I'm going outside to smoke two cigarettes. If you haven't finished proving it by the time I come back, then go back where you came from." With that, he left to smoke outside the classroom.
Life was full of hurdles. Teacher Cao was testing his math ability. Shen Qi stood up, ready to solve the problem.
"Shen Qi, we all went through a test like this when we joined the team. Anyone without the ability gets eliminated." Meng Tianqiang spoke with the air of an old hand.
"I understand. Thanks for the warning, Captain Meng." Shen Qi walked to the blackboard and picked up the chalk, but didn't write anything right away. He fell into thought.
It made sense that he'd fallen into thought. Of course Teacher Cao's problem would be challenging. Meng Tianqiang watched Shen Qi's back. This new junior seemed clever enough, but unfortunately, he didn't have the ability to back it up.
This problem's way too simple. Is this really the level of our school's math team? Shen Qi thought to himself. That can't be right. If Little Zhang—Zhang Wanbang—was trained by Old Man Cao, then with their styles, he wouldn't come up with such a low-level test. I could train Chen Xiaoting hard for a while, and she'd be able to solve it in ten minutes.
A trap.
This had to be a trap.
Life was full of traps.
The world was a dangerous place.
Five minutes passed, and Shen Qi still hadn't written a single mathematical symbol. He stood in front of the blackboard, staring blankly.
A few second-year students whispered among themselves from their seats. "He's from Class 2, right?"
"Class 2's overall math level is average, just a little better than Class 3. Zhang Wanbang teaches both classes."
"Their top students aren't that impressive either. Huang Zikun is the best in their class at math, but even he couldn't get on the team."
"This Shen Qi probably just showed up in Class 2 recently. I think I vaguely remember him—didn't he get full marks in math on the last midterm?"
"Which of us here hasn't gotten full marks in math?"
The other team members put down their books and workbooks, and gathered around to watch Shen Qi. Their doubts about him kept growing. How had this guy gotten onto the team?
Just then, Shen Qi suddenly began writing furiously. Scritch, scratch, scratch. The chalk danced between his fingers, mathematical symbols leaping nimbly into place and combining into an offensive formation that launched a fierce proof against the statement on the blackboard.
The problem Cao Xin'an had given him concerned number theory.
Number theory was a branch of pure mathematics, and its origins could be traced back to Diophantine equations in ancient Greece.
The most famous work by the Greek mathematician Diophantus was Arithmetica. While reading it, Fermat, the "king of amateur mathematicians," wrote down a conjecture in the margin and added an explanation: "This conjecture is certainly true. I can write out a proof, but the margin is too small to contain it."
This was the source of the famous "Fermat's Last Theorem" in the history of mathematics. It wasn't proved until 1995, when the British mathematician Wiles established that it was true.
Qin Jiushao, one of the four great mathematicians of the Song dynasty, had also conducted extensive research into number theory. The "Jiushao Algorithm" featured in high school math textbooks came from Qin Jiushao.
Fermat was widely recognized in the Mathematics Community as the mathematician who had made the greatest contributions to number theory.
Shen Qi was solving the problem in Fermat's style. This was the main reason he had spent five minutes thinking without writing.
Of the three great figures—Diophantus, Qin Jiushao, and Fermat—Shen Qi had ultimately chosen Fermat.
Shen Qi finished the proof before Cao Xin'an came back into the classroom, then returned to his seat and sat down.
"To factor x^2-1 into two linear factors, first set
x^2-1=(x+a)(x-a)
Expand the right-hand side of the equation.
Then make the coefficients of the same powers of x on both sides equal..."
The rest of the team stared dumbfounded at the small blackboard, speechless for a long time. What on earth had this new guy written? They couldn't understand it!
Team captain Meng Tianqiang was in his final year of high school and had seen plenty. He was the first to understand Shen Qi's approach. "So you didn't use the Jiushao Algorithm to prove it, Shen Qi. You introduced a new method instead. The way you simplified the proof really opened my eyes. The stroke of genius was making the coefficients of the same powers equal."
"It's not all that new," Shen Qi explained. "This method of proof already existed in France in the mid-seventeenth century, while the Jiushao Algorithm appeared in the Southern Song in the thirteenth century. In fact, Qin Jiushao got involved in number theory four hundred years before Fermat. Maybe Fermat had read Qin Jiushao's Mathematical Treatise in Nine Sections. From the standpoint of mathematics itself, Fermat's theory was more incisive. Of course you could see farther standing on the shoulders of giants."
"Whoa, impressive, Shen Qi! You've already taught yourself Fermat's number theory." Meng Tianqiang immediately looked at Shen Qi in a new light. He turned to the other second-year students. "Hey, you're all second-years. Are you really saying you don't know each other?"
"Strangers at first, friends the next time!"
"We know each other now, don't we?"
"Class 2 has always produced talented students. Shen Qi's got what it takes. A late bloomer!"
"Now that Shen Qi's joined our team, we've got twelve people. The Golden Saints are all here!"
"Shen Qi, what's your star sign?"
The second-year boys immediately warmed up to Shen Qi, like long-lost brothers.
"Thanks for the kind words, guys. Let's hang out sometime." Shen Qi's quiet observations had given him a preliminary conclusion: Meng Tianqiang was the strongest in math among everyone in the classroom. The other ten were at most at Math Level 2, if he had to rate them.
"What's all the noise about?"
Suddenly, Cao Xin'an's voice rang out. He had returned to the classroom.
Everyone fell silent.
Cao Xin'an went over to the small blackboard and took one quick look. He'd already made his judgment.
His expression didn't change at all. Cao Xin'an looked at Shen Qi and asked, "What year of college have you taught yourself up to?"
Shen Qi thought for a moment before answering, "I've read a pretty wide range of books. If I had to compare it to college, I'd say somewhere between the second semester of sophomore year and the first semester of junior year."
Knock, knock.
Cao Xin'an tapped the blackboard. "Shen Qi, so what if you've taught yourself college-level material? Remember this: during the main round of the Mathematics League, you're not allowed to use methods beyond the scope of the high school curriculum. That's the same as cheating. What kind of bad habit is that? Did Zhang Wanbang teach you?"
"No, no, I came up with it myself. I did." Shen Qi definitely couldn't let his teacher Zhang Wanbang take the blame. If anyone had to take the blame, it was the system.
"You're full of yourself. Fix it!" Cao Xin'an shouted, then clasped his hands behind his back and left the classroom.
Shen Qi was dumbfounded. Cao Xin'an hadn't said a word about his proof. He'd just scolded him a few times and walked out. He was even more arrogant than Zhang Wanbang. Were all math teachers like this?
"Did I pass Teacher Cao's test, or not? Should I go home, or stay?" Shen Qi asked Meng Tianqiang.
Meng Tianqiang smiled. "Of course you should stay. Teacher Cao already told you not to use college-level knowledge when solving problems in the main round of the Mathematics League. Congratulations, Shen Qi! On behalf of Nangang Second High School's strongest Math Olympiad team, I'd like to extend you the warmest welcome! Come on, let's hear a round of applause!"
Clap, clap, clap.
The classroom erupted in applause. The entire team had officially welcomed Shen Qi.
"Big shot, please have some tea." A bespectacled first-year student handed Shen Qi a bottle of lemon tea.
"I bought this tea." Shen Qi accepted it.
"We didn't have time to buy any fresh tea, but we still had to make the ceremony happen. Senior Brother Shen Qi, could you teach me about Fermat's number theory sometime?" The first-year student looked eager to learn.
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