The students exclaimed in admiration as they listened to the stories.
If what they had just heard was true, those geniuses were not human. They were monsters.
“...After graduating from this school, all three went abroad to study and majored in mathematics. Today, those alumni are considered the Koreans most likely to win the Fields Medal, often called the Nobel Prize of mathematics. You can become just as remarkable as your seniors. Geniuses! Let's challenge ourselves to become geniuses!”
Anyone who had attended a science high school or Hanguk University had probably heard a legend or two about the greatest geniuses in the school's history. Back when Kang Woo was studying physics at Hanguk University, he had also heard tales about the three great geniuses of the Physics Department.
But legends changed and grew with time. After he was appointed a professor at a provincial university, he had heard the younger students telling a new version of the story and could only smile wryly.
He did not know why there were always three geniuses in these stories, but, astonishingly, one of the names in the latest version of Hanguk University's three great physics geniuses was Son Kang-woo. He was supposedly the tragic genius who, despite his brilliance, had failed to secure a professorship at a university in the Seoul metropolitan area.
At any rate, he remembered dismissing the whole business when he heard he was counted among the three great geniuses. ‘Have all the real geniuses frozen to death or something?’
Perhaps that was why he felt nothing in particular when he heard about Goryeo Science High School's three great geniuses. It was all just gossip for people who liked to talk.
Kang Woo was the least interested person in the class when it came to tales of geniuses. Son Cha-hee, on the other hand, was listening with the brightest eyes of anyone there.
She clenched her fists, her competitive spirit burning. From what she had heard, every one of those seniors had been extraordinary, but she felt that, with enough effort, she might be able to accomplish the same things.
‘I'll win a gold medal and prove that I'm a genius.’
She sincerely envied the three students who had gone down in Goryeo Science High School's history as its greatest geniuses. She wanted to be like them.
“So you mustn't be satisfied with learning only what is taught in class. High school mathematics mainly deals with calculus, but historically speaking, calculus had already reached its conclusion through the work of countless geniuses in the eighteenth and nineteenth centuries. Modern mathematics hardly deals with calculus at all.”
“Then what does it deal with?”
“Equations involving calculus, such as the Bessel equation and Laplace's equation, are studied in engineering. Mathematics deals with strange creatures like Fermat's Last Theorem and topology.”
Kang Woo sighed. He had felt rather proud when the Bessel equation was mentioned in Earth science class that morning, only for the mathematics teacher to treat it as an outdated relic that afternoon. He felt strangely betrayed. All those differential equations he had struggled with at university had been dismissed as useless in one fell swoop.
“Of course, we must remain faithful to our textbooks during regular lessons. But in your research projects, you'll be dealing with much deeper mathematical problems. If you love mathematics, I hope you'll go beyond the textbook and try studying real mathematics in depth. The time you spend persevering through those challenges will nurture your genius.”
The students applauded again.
Having finished his lengthy speech, Jeong Myeong-uk flashed a grin and finally revealed his wicked side.
“Now, in that spirit, we're going to have a test today.”
“Gasp!”
Cries of dismay erupted all around the room.
At that moment, Kang Woo seriously reconsidered enrolling at this school. What kind of school held exams every single day?
They had promised enjoyable discussion-based classes, but instead of discussions, all they seemed to do was take tests. Of all the people he could have ended up possessing, why did it have to be a new student at a science high school? If he had gone to an ordinary high school, he could have spent his days relaxing.
‘Should I just transfer to a regular high school?’
As he sighed repeatedly, the question paper and answer sheet Jeong Myeong-uk had passed around reached his desk.
Of all the things in the world, exams were what he hated most, whatever the reason for them. Looking around, he saw that everyone wore expressions as though they had bitten into something foul. They were all suffering together.
The students' sighs grew heavier when they saw the questions.
Kang Woo opened the question paper on his desk and could scarcely believe his eyes.
‘What is this?’
The questions were simple, yet completely unexpected.
- Derive the formula for the roots of a cubic equation.
- Based on this, discuss the formula for the roots of a quartic equation.
The quadratic formula had been drilled into their heads countless times in middle school. According to one education critic, diligent students who gained admission to Hanguk University had worked through quadratic-equation problems at least ten thousand times by the time they took the college entrance examination. It was a criticism of mathematics education focused on memorizing formulas and solving repetitive problems.
The quadratic formula was used so often that everyone knew it by heart. There were very few high school students who did not know it. Even students who had given up on mathematics knew the quadratic formula.
But a formula for the roots of a cubic equation?
No matter how far back he searched through his memories of middle school and high school, he could not remember ever learning one.
Kang Woo was not the only person troubled by the question. Son Cha-hee felt much the same way.
She remembered something her mathematics teacher at the academy had said while preparing them for the gifted-school entrance examinations.
After filling the blackboard with a mass of complicated expressions, the teacher had explained...
- The graph of a cubic function must cross the x-axis. In other words, a cubic equation must have anywhere from one to three real roots. There is also a formula for finding those roots. Long ago, in the era of university-specific entrance examinations... Before the generation that took the College Scholastic Ability Test, there was the Academic Aptitude Test generation, and before that, the Preliminary Examination generation. Back then, university entrance examinations included memorization questions of this kind.
- But such questions are never asked nowadays. A problem you solve merely by memorizing a formula can hardly be called mathematics. Naturally, it won't appear on the entrance examination for schools for the gifted either. That's why our academy doesn't teach the formula for solving cubic equations. You don't need to know it.
‘Haaah... I was told it was a useless problem.’
She could not understand why a question like this had suddenly appeared to trip her up.
Go Hyeon-seong was flustered too. Hadn't he challenged Kang Woo to a mathematics contest at lunchtime? And Son Cha-hee was at stake, no less.
Although Kang Woo had distinguished himself during physics class, Go Hyeon-seong had assumed mathematics would be another matter. Someone who had not studied ahead would surely struggle with mathematics, so he had naturally expected to win. But now he was faced with a problem he did not know how to solve either.
Flustered, Go Hyeon-seong glanced back in search of Kang Woo. Fortunately, the boy sitting at the very back wore an indifferent expression. There was no sign that he recognized the problem and was about to solve it in a flash.
‘Phew, that's a relief. That bastard definitely doesn't know it either.’
Having finally calmed himself, Go Hyeon-seong stared intently at the question. Perhaps heaven would be moved if he wished for an answer hard enough.
Sensing the atmosphere in the classroom, the mathematics teacher, Jeong Myeong-uk, spoke again.
“The formula for the roots of a cubic equation is known as Cardano's formula.”
Cardano was an Italian mathematician of the sixteenth-century Renaissance. When he heard that Tartaglia of Venice had discovered a method for solving cubic equations, Cardano tried to learn it. Worn down by Cardano's persistent demands, Tartaglia finally revealed the method after making him swear never to disclose it.
A few years later, however, Cardano published Tartaglia's method in a mathematics book he had written. Cardano gained fame as a result, and the cubic formula became known as Cardano's formula.
Tartaglia was furious at having his fame stolen, but the damage had already been done.
Cardano was also a gambler who applied probability theory to gambling. He was an astrologer as well, and it was said that he had predicted the day of his own death and then committed suicide on that very day to prove his prediction correct.
The students listened with bated breath to Jeong Myeong-uk's fascinating account of the mathematician.
“It's a formula discovered by a mathematician in the sixteenth century. If you, living in the modern age, can't derive it, you should be ashamed of yourselves.”
“Oh, come on, sir. Those people were geniuses!”
“You're geniuses too. Of course, anyone who can solve it immediately probably learned it before. But... I doubt there's anyone like that here, is there?”
The students felt their blood stir. Their flushed faces betrayed their growing determination.
Jeong Myeong-uk looked around the classroom and clenched his fist.
“I'll give you a simple hint. If you can derive the formula from this hint, then you're geniuses too. If you're having trouble, try thinking about how the quadratic formula is derived.”
Kang Woo frowned at the hint Jeong Myeong-uk had written on the board.
‘What is that supposed to mean?’
Naturally, this was outside his area of knowledge. When it came to mathematics unrelated to physics, he was no different from the other students.
Written on the board was...
- Take a close look at the factorization identities for cubic expressions.
“Ah! Sir! What's that supposed to mean?”
“The hint's harder than the question!”
Complaints poured out from the students, but Jeong Myeong-uk remained unmoved, apparently convinced that he had given them more than enough help.
“A genius would have a sudden flash of insight just from seeing that hint. Now, where are the geniuses?”
Jeong Myeong-uk was confident because this was a type of problem no longer taught in recent years. In other words, since the students would not have learned it at their academies, those who had not studied ahead would be at no disadvantage. Everyone was starting on equal footing.
That was why he had chosen the question. He considered it fair to everyone.
“Ugh.”
The students racked their brains for a long time.
Kang Woo also examined the question paper and the hint on the blackboard, but eventually gave up trying to figure it out. It was a problem he had never thought about before.
‘We're living in an age when computers can find the roots of cubic equations in no time using numerical methods...’
No matter how he looked at it, the problem was hopelessly old-fashioned. Besides, he believed that being good at physics was enough for him, so he had no particular desire to earn points in mathematics class.
He was about to close his answer sheet and go to sleep when his eyes met Jeong Myeong-uk's. He immediately straightened up as though he had been electrocuted. The mathematics teacher's bald head was positively intimidating.
‘Haaah, it's hard even to get some sleep here.’
By then, he had completely forgotten his wager with Go Hyeon-seong. Frankly, he did not care whether he won or lost, so it had slipped his mind.
Just then, a boy raised his hand. It was Jeon Sang-cheol, who belonged to the same group as Go Hyeon-seong. He ranked immediately below Son Cha-hee in their class.
“Do we have to write out the entire proof?”
“If you know it, write it down.”
“If we make a substitution...”
Huh? Had that guy solved the problem?
Kang Woo was startled by what Jeon Sang-cheol said.
Once Jeon Sang-cheol indicated that he had solved it, several students began writing furiously on their answer sheets, as though his success had been contagious. Go Hyeon-seong was among them.
‘Damn it. That guy can solve it too?’
Suddenly, Kang Woo remembered the wager. Anger flared within him. What was at stake did not matter. The thought that he did not want to lose the bet abruptly took possession of his mind.
Kang Woo changed his mind too. There was no way he could lose to Go Hyeon-seong. Naturally, this had nothing to do with Son Cha-hee.
He clenched his fist and stared hard at the hint on the board.
‘There's no reason I shouldn't be able to solve a problem that people in the sixteenth century solved.’
In the sixteenth century, even the notation used for equations had been rudimentary. Compared with the notation of that era, modern mathematical notation was far more convenient and efficient.
Cardano and Tartaglia might have been geniuses of their century in Italy, but Kang Woo had no reason to consider himself inferior.
It might have been a joke, but wasn't he one of the three great geniuses of Hanguk University's Physics Department?
‘Huh? My brain is actually starting to work!’
He could begin to see how the hint might be applied. For a moment, he felt as though he had suddenly become a genius.
Ever since entering graduate school, Kang Woo had always pursued something new. He had ventured into unknown territory where no one else had gone, devising new methods as he worked to solve the problems of room-temperature nuclear fusion. Those experiences now filled his thoughts.
If you kept working at a problem you did not understand, you would eventually find a solution. Often, the answer was not far away at all, but hidden in knowledge you already possessed.
He was a genius! Not merely as a joke, but a genuine genius!
For some reason, he even felt as though his mind had become sharper than it had been when he was Son Kang-woo. And he had no intention of losing to people from the sixteenth century, much less to someone like Go Hyeon-seong sitting up ahead.
When the time was up, Jeong Myeong-uk collected the answer sheets himself. He finished grading them in no time.
Looking over the results, Jeong Myeong-uk spoke.
“Four students correctly derived the formula for solving cubic equations. Those students are...”