Jeong Myeong-uk looked around at the students.
“Jeon Sang-cheol, where are you?”
Jeon Sang-cheol rose hesitantly to his feet.
“You solved it well using the factorization identity. How did you think of that approach?”
“W-well...”
Jeon Sang-cheol's voice trailed off. He sounded uncertain.
“Did you learn it at an academy?”
“W-well... I came across it briefly a long time ago.”
“A long time ago?”
“The moment I saw the hint, I remembered it.”
“Good.”
Hearing that private academies still taught such formulas, Jeong Myeong-uk realized he had underestimated them.
“Hmm. Still, your solution was appropriate. For something you learned so long ago, you seem to have remembered all of it.”
Jeon Sang-cheol's face brightened at the teacher's praise.
Jeong Myeong-uk turned his attention to the other students.
“Go Hyeon-seong and Son Cha-hee!”
The two students stood up.
“You both wrote down the answer, but... what happened here?”
“We were told to memorize it at an academy a long time ago...”
“It's impressive that you memorized such a complicated formula. But there's something strange about your working.”
“I couldn't remember the steps.”
Go Hyeon-seong answered as though it were no great matter, while Son Cha-hee remained silent. Being able to write down an answer only because they had memorized the formula was practically the same as admitting that they could not solve the problem.
In truth, Son Cha-hee had not remembered the formula at first. But when Jeon Sang-cheol announced that he had solved the problem, she realized it was something she had learned at an academy long ago. After that, she had racked her brains until, almost miraculously, she recalled it.
Once she had written down a rough version of the formula, it was not difficult to work backward and reconstruct the original equation to verify it. Repeating the process, she had managed to piece together the correct answer perfectly.
In any case, after calling on the three students, Jeong Myeong-uk began writing out the solution on the board.
“To derive the quadratic formula...”
It was an extremely familiar expression found in middle school textbooks. After writing down its derivation, Jeong Myeong-uk added a familiar factorization identity for cubic expressions.
“If you compare these two expressions until you've practically stared a hole through the paper...”
Tap, tap.
The sound of chalk against the blackboard filled the room.
The classrooms and laboratories for other subjects used large whiteboards and markers. The mathematics classroom, however, still had an old-fashioned green blackboard and white chalk. Apparently, the sound of chalk was supposed to wake students up and help them concentrate.
“The key to solving a cubic equation is eliminating the quadratic term. Once you understand that, anyone can solve it. You can work out that key idea from the factorization identity above. Now, if we substitute for x like this...”
The equation unfolded into a neat solution.
Watching it happen, one could almost believe that mathematics was a form of magic.
“Oh, that wasn't so difficult after all.”
The students began grumbling as they watched.
Jeong Myeong-uk smiled.
It was easy to examine and understand a solution that someone else had already discovered. But even with the simplest problem, being the first to venture down an unexplored path was extraordinarily difficult.
A genius was not someone who followed a road another person had paved. A genius was someone who carved out a new road.
Just like Tartaglia, who had first solved the cubic equation five hundred years ago.
The bell rang, marking the end of class.
“That's all for today.”
Jeong Myeong-uk gathered the answer sheets and was about to leave when Son Cha-hee hurriedly stopped him.
“Sir! You said four students solved it, didn't you?”
“Yes. What about it?”
“You haven't mentioned one of them.”
“Ah!”
Jeong Myeong-uk swept his gaze over the students.
“We've run out of time. But that student solved not only the cubic equation but also the quartic equation properly. That was the only student who solved both problems perfectly.”
Son Cha-hee stared blankly at Jeong Myeong-uk's retreating figure.
She had never imagined that anyone would actually manage to solve the problem properly. What was more, the student was neither her, the top-ranked student in the class, nor Jeon Sang-cheol, who ranked second. She could not even begin to guess who it was.
She vaguely remembered something she had heard at an academy years ago. Hadn't they said that the formula for the roots of a quartic equation varied depending on the conditions, was far more complicated than the cubic formula, and involved calculations that were an absolute nightmare?
In fact, these days, no academy taught students the formulas for solving cubic and quartic equations.
'Someone actually solved that?'
As Son Cha-hee stood there in disbelief, she noticed Kang Woo leisurely getting up from his seat at the very back.
'It couldn't be Kang Woo... could it?'
And yet, for some inexplicable reason, she could not shake the feeling that it had been him.
* * *
On the third floor of Building B was the faculty office shared by the teachers responsible for first-year subjects.
The teachers returned there after finishing all their classes for the day.
“Everyone! Could we have a short meeting?”
Kim Yun-taek, the first-year grade coordinator, called the teachers together. In no time, more than ten of them had gathered in the meeting room.
After checking who was present, Kim Yun-taek began.
“You've all taught your first classes today. What did you think?”
“The students were definitely more advanced than last year's.”
The teachers' assessments were much the same.
Kim Yun-taek was pleased to hear that this year's students were as capable as expected. It was unusual for the favorable impression created during the entrance examinations to hold up through the first day of lessons.
He handed out the materials he had prepared.
“These are the results of yesterday's diagnostic assessment. I've given everyone the list of the top twenty students, along with the results for the remaining students in your respective classes. As expected, Lee Min-chan and Son Cha-hee, who distinguished themselves in the entrance examination, have performed exceptionally well. The two are vying for first and second place, with a considerable gap separating them from the other students.”
Cha Do-do frowned slightly as she examined the materials.
Once again, Son Cha-hee had fallen a little behind Lee Min-chan. Worse, the breakdown of her results was not particularly encouraging. She had scored lower than him in mathematics, though she had outperformed him in chemistry and biology. She had also fallen behind on the written-response questions and made up ground on the multiple-choice sections.
In the long run, if students who excelled in mathematics and physics were considered the strongest, Son Cha-hee appeared to have a difficult road ahead of her.
No wonder Kim Yun-taek, Lee Min-chan's homeroom teacher, looked so pleased.
“A student's genius reveals itself in mathematics, particularly in written-response mathematics problems. Wouldn't you agree?”
Kim Yun-taek looked to the other teachers for agreement.
The first to agree was Jeong Myeong-uk, the mathematics teacher.
“This year's students are very capable. I could tell that much when I graded the diagnostic assessment.”
“Exactly. Lee Min-chan also did well on the written-response physics problems.”
Cha Do-do frowned slightly at the mention of Lee Min-chan.
She looked through the diagnostic assessment results for her own class. As expected, Son Cha-hee had the highest score.
But the moment she found the name of Kang Woo, the student she had thought so peculiar and difficult to understand, her face twisted.
His name was at the very bottom of the list.
'Of course his score is terrible. He just guessed his way through the multiple-choice questions.'
She had expected a poor score after seeing the artwork on his answer sheet, but this was a little too much. Moreover, he had left every written-response question blank except for the final problems in physics and Earth science. His mathematics written-response section was practically a blank sheet.
At this point, he had obviously done it on purpose.
'It's not as though I can perform an exorcism on a boy that age...'
Cha Do-do decided she would have to give Kang Woo a stern talking-to.
Beside her, the Earth science teacher, Kim Seon-ho, asked a question.
“By the way, how did Kang Woo and Choi Dae-woo do?”
“Kang Woo? He's at the very bottom of our class. And Choi Dae-woo is... this student is well below the middle too.”
“Ah, I see.”
“Are you interested in them?”
“Because they solved the last written-response question.”
Kim Seon-ho smiled and turned his attention back to the score sheet.
Just then, Jeong Myeong-uk, who was sitting some distance away, joined their conversation.
“Kang Woo?”
“Do you know him?”
“Ah, I taught his class today...”
Cha Do-do had a dreadful feeling that Kang Woo must have caused trouble. Her face tensed, and she tried to offer an explanation as naturally as possible.
“That student is a little unusual. He says he's never attended a private academy...”
“I know. In today's lesson, I gave them a test with an unusual problem that required quite a bit of calculation...”
“And?”
Everyone's attention turned to Jeong Myeong-uk.
“Kang Woo was the only student who solved the entire thing.”
“What about Cha-hee?”
Cha Do-do asked hurriedly.
“Son Cha-hee effectively failed to solve it. She barely managed to write down an answer she'd memorized. Most of the other students couldn't even begin.”
Jeong Myeong-uk's explanation brought Cha Do-do's own lesson to mind. Hadn't Son Cha-hee's group won thanks to Kang Woo's performance?
Why did Kang Woo's abilities seem to fluctuate so wildly?
While she struggled with her confusion, Kim Seon-ho smiled.
“I suspect Kang Woo's actual abilities are well above average.”
“I got that impression too, though I haven't confirmed it yet.”
Jeong Myeong-uk agreed.
Kim Yun-taek, who had been listening, joined in.
“Kang Woo... Is that the student we met in the cafeteria yesterday at lunch?”
“Yes, that's him.”
Kim Yun-taek remembered the discussion he had had with Cha Do-do about the written-response problems.
After looking at Kang Woo's diagnostic assessment results, he had dismissed him as nothing special and lost interest. Yet now the mathematics teacher was bringing him up again.
Come to think of it, hadn't they said Kang Woo had solved the final physics problem?
It was a shame that the boy was not in his class, but if an outstanding student had enrolled, that was something to welcome.
'Assuming he really is an outstanding student, of course...'
If Kang Woo was interested in physics, there was a good chance he would choose it for his research project. Kim Yun-taek found himself wanting to become the boy's supervising teacher and mentor him.
The fact that Kang Woo belonged to Cha Do-do's class made the prospect even more appealing.
'After all, there's no doubt Lee Min-chan is better than Son Cha-hee...'
Still, Kang Woo's diagnostic assessment results bothered him. So did the fact that he had never attended an academy and had entered through the special admissions track for socially disadvantaged students. There was a risk that he might end up taking on a troublesome student instead.
Then an idea occurred to him: a way to showcase Lee Min-chan while finding out what Kang Woo was truly capable of.
Having made up his mind, Kim Yun-taek spoke again.
“We're holding another diagnostic assessment before the official enrollment, aren't we?”
“That's right. In previous years, there have been students who worked harder and improved their scores considerably on the second assessment.”
Jeong Myeong-uk answered.
Kim Yun-taek presented the proposal he had been waiting to make.
“Why don't we hold the diagnostic assessment and have the students undertake a research project as well?”
“A research project? Wouldn't that place too much pressure on them...?”
“There's nothing wrong with putting them to work right from the start. That way, they'll develop the habit of taking the initiative in their studies and improve their problem-solving abilities.”
Normally, research projects began after enrollment, with students choosing a topic and working on it over a semester. Sometimes, the research continued for an entire year.
Students used that time to prepare for external academic competitions or present their research, accumulating achievements they could include in their school records.
“The teachers don't need to feel burdened by this. It's only practice, after all. If the students ask for help or guidance, you can provide it. Everything else will be left up to them. What do you think?”
“But they've only just graduated from middle school.”
“If they work together in groups, they'll manage. It'll also help them develop teamwork.”
“Then shouldn't there be some kind of reward?”
Kim Yun-taek frowned at Kim Seon-ho's suggestion.
The new students were still finding their feet. He could probably have pushed the idea through without anyone complaining. But now that the matter had been raised, his conscience would trouble him if he simply refused.
“Hmm. In that case, why don't we present an award at the entrance ceremony? We already give certificates and scholarships to the students who placed first through third in the entrance examination, don't we? Let's award a scholarship to the student who takes first place in the research project as well.”
Since science high schools did not charge separate tuition fees, the scholarship would be paid as actual cash directly into the recipient's bank account.
“Do you think the principal will approve?”
“We just have to get the approval.”
“I think it's a good idea. It will help students develop a research-oriented mindset from an early stage.”
After the teachers discussed their various opinions, the proposal was approved.
As Kim Yun-taek looked around at his colleagues, each lost in thought, he reviewed his strategy.
Lee Min-chan's group was practically guaranteed to win first place. None of the students would be able to carry out proper research in such a short period. If he gave Lee Min-chan just a little assistance, the boy would produce a respectable result.
The research project would also provide an opportunity to gauge Kang Woo's abilities. Kim Yun-taek did not particularly believe that Kang Woo was an outstanding student, but if the boy handled the project well and showed promise, he could bring him under his own supervision.
Kim Yun-taek smiled with satisfaction.