The day of the exam dawned.
Seoha had been up since early morning, looking out by the window. Duck figurines were lined neatly along the windowsill.
Seoha’s gaze lingered for a long while on one of them.
‘Ducky, what do you want? Do you want to destroy me?’
The duck seemed to shake its head.
Instinctively, Seoha felt that the cohabitant in his mind bore him no malice. Ducky simply loved mathematics with pure sincerity.
‘I think we can get along well together. Don’t you think so too?’
“Seoha, let’s have breakfast!”
Jihoon, fresh from his shower, snapped Seoha out of his thoughts.
When he looked at the clock, it was already 7:30.
Seoha hurriedly changed his clothes and left the room.
When he went down to the dining hall, the entire Korean team had gathered.
‘It doesn’t look like anyone failed to sleep.’
Professor Park studied the students’ complexions, then nodded.
Three years ago, there had been a student expected to win a gold medal with ease, yet he had failed to display even half his usual ability. The cause had been lack of sleep due to nerves.
The English breakfast was well-liked enough that almost no one could complain about it.
Bacon, sausages, hash browns, grilled tomatoes, mushrooms, baked beans, black pudding, fried bread, and even crisp toast with various jams.
Everyone was brightly taking whatever food they wanted onto their plates. Seoha, not knowing much, ordered “Everything,” only to be startled when his plate was piled so full it nearly overflowed.
After finishing breakfast, on the way to the exam hall,
Representatives from each country walked in silence. Some were reciting formulas one last time, while others took deep breaths to calm their nerves.
When they entered the auditorium, the vast space came into view all at once.
The sight of hundreds of desks arranged in neat rows was magnificent. Students moved to find their seats, admission slips in hand.
Seoha found his seat as well.
[KOR-1]
It was the seat assigned to Seoha, number one of the Korean national team.
On the desk lay a white answer sheet, a pencil, and an eraser. Seoha sat down and looked around. Liu Chen was seated diagonally behind him to the right. He glanced at Seoha, then looked away. A faint hostility could be felt.
But Seoha looked at him without any particular emotion.
In the world of mathematics, everyone was simply a companion walking the same path. There was no reason to dislike him.
‘Ah, is that not necessarily true?’
Newton and Leibniz.
In the late seventeenth century, the two were known to have invented the theory of calculus at nearly the same time. Scholars today believe Newton conceived of it about ten years earlier, but they also judge that Leibniz independently completed his own system of calculus through his own efforts.
But what had it been like at the time?
Until the day he died, Leibniz was accused of having stolen Newton’s achievements.
‘He must have felt incredibly wronged.’
The problem sheets were distributed inside envelopes.
The proctor was watching the clock.
“You may begin!”
The proctor’s declaration rang out.
All the students opened the problems at once.
At last, it had begun.
* * *
To Liu Chen, mathematics was both a blessing and a curse.
“You have talent in mathematics. From now on, you are not to go to school.”
The command of his father, a professor at Tsinghua University, was absolute.
China legally prohibited homeschooling, but in private schools for the children of the elite, anything was possible.
His father was a man who was rarely satisfied.
No matter how outstanding Liu Chen’s results were, he never praised him.
Not when he won the Beijing elementary school mathematics competition, nor when he took the grand prize in the national middle school competition at the age of ten.
“Talent alone can achieve nothing. A genius who does not work hard is worth less than an ordinary person.”
To him, first place was merely the result Liu Chen was expected to bring back as a matter of course.
The year he turned fourteen,
All contact with his acquaintances was cut off.
Games, comics, TV—the leisure activities that teenagers were supposed to enjoy as a matter of course—he had given up long ago. All that remained to him was mathematics alone.
Every morning, he woke early and sat at his desk until midnight.
He held a pencil until his fingertips hardened, and solved problems until his eyes grew dim.
Even after he turned fifteen, Liu Chen’s life became even more extreme.
He had been selected as a national team candidate and entered a special training camp.
The camp was located in a quiet area on the outskirts of Beijing.
There, Liu Chen lived for a year with one hundred prodigies gathered from across the country.
Sixteen hours of study a day,
Seven days a week.
There was no rest.
And that was how he seized first place individually at the IMO.
All of China shouted his name.
Liu Chen would never forget the thrill of the moment when the gold medal was placed around his neck at the awards ceremony.
Before he knew it, the situation had reversed.
He had once hated his own talent, but now Liu Chen no longer had the confidence to live without mathematics.
Liu Chen glanced at Seoha, who was sitting in front of him.
‘That kid?’
Since yesterday, a strange rumor had been circulating within the Chinese team.
A rumor that a twelve-year-old boy had taken first place in Korea’s national team selection.
When he checked, it turned out to be true.
‘What was I doing when I was twelve?’
It was the period when he had been receiving hellish home training from his father.
He certainly would not have been at a level where he could participate in the IMO.
‘A monster? Maybe in Korea. That kid would never pass the Chinese preliminaries.’
Even in the history of Chinese mathematics, the youngest participant in the IMO had been fifteen.
And yet Dokyeong, who had been so timid that he could barely meet his eyes, had shown confidence. For some reason, Liu Chen found that incident strangely irritating.
The sound of envelopes being torn open could be heard throughout the exam hall.
Liu Chen also carefully opened his envelope and took out the problem sheet.
[Problem 1]
It was a number theory problem. A field he had solved to sickening exhaustion.
But even as he read the problem, he kept getting distracted.
Liu Chen subtly turned his head and looked at Seoha.
‘That fast?’
Not even two minutes had passed since they began reading the problem, yet he was already writing down his answer.
‘Focus. Solving quickly doesn’t mean getting a higher score. He must have gotten lucky and found a problem he knew.’
What mattered in number theory was an appropriate change of variables. If a solution satisfying the conditions existed, there had to be a systematic way to find it.
Liu Chen wrote down several cases on blank paper, trying to find a pattern. Substituting small numbers first and searching for patterns was the basic approach to number theory.
But no matter how he examined it, no clue appeared.
‘The problems got harder?’
It was a type of problem he had never seen before.
But it did not matter. He had already experienced this countless times. If it could not be solved through a combination of basic theorems, then he had no choice but to search directly.
Various numbers to substitute appeared in Liu Chen’s mind. It would take some time, but he would solve it in the end.
Flutter.
‘Hm?’
The sound of paper turning.
‘Impossible!’
Yu Seoha had already moved on to problem 2.
‘Did he skip it because it was too hard?’
But there was not the slightest sign of frustration on the boy’s face. On the contrary, was he smiling?
Perhaps because he had lived for too long in the world of competition, Liu Chen was overly conscious of his opponent.
* * *
Seoha was in a good mood.
‘The quality of the problems is excellent!’
The moment he read problem 1, his heart began to pound. The elegant regularity hidden within the array of integers was visible at a glance.
It looked complex, like a code, but if one pierced through to its core, an astonishingly simple and perfect arrangement emerged.
The problem, which appeared on the surface to be number theory, was dissected piece by piece by Seoha’s mathematical intuition.
Seoha lifted his pencil and began calculating. It was the process of reconstructing a complex algebraic structure and finding the pattern hidden within it.
He raised ordinary integers into an extended number field and reinterpreted the given conditions there. Then the relational expressions that had seemed devoid of order revealed an astonishingly clear structure.
‘Amazing.’
Perfect order existing within chaos.
Seoha loved the moment he discovered something like this.
Problem 2 was a combinatorial geometry problem.
It dealt with the relationships between points and lines on a plane.
Whenever he saw a problem like this, Seoha felt as though he could understand the problem setter’s heart. Surely this person truly loved mathematics.
The arrangement of points satisfying the given conditions, and the perfect symmetry created by those points.
There were few hints, but for Seoha, that only made the process more enjoyable.
In his mind, countless figures changed shape and size, intertwining with the points and lines of the problem. And then he found a candidate that fit the conditions.
‘Projective geometry?’
Points and lines began to transform into conic sections.
One of the astonishing properties of geometry discovered by nineteenth-century mathematicians.
Seoha, who had been solving the problem, soon wore a gloomy expression.
‘Even mathematicians from two hundred years ago discovered things like this...’
As Seoha studied mathematics and the history of mathematics, he could not help but marvel at the achievements mathematicians of the past had built up over thousands of years. At the same time, a powerful desire arose within him to become part of that history as well.
‘I’ll discover plenty of things no one else knows from now on.’
Seoha steeled himself.
“Haa...”
“Damn it.”
“Ugh.”
Sighs like groans could be heard throughout the exam hall.
Marcello, one of the problem setters, watched this and nodded with a satisfied expression.
‘Now this is a real exam.’
Marcello was a professor in the Department of Pure Mathematics at the University of Cambridge. Having devoted himself to mathematical research for thirty years, he had become the chair of the IMO problem committee starting this year.
He had deep concerns about the changes that had occurred in the IMO over the past decade or so.
‘It’s become too easy.’
Starting in the 2010s, the number of perfect scorers at the IMO had begun to increase sharply. In the past, a perfect scorer had been someone who might appear once in ten years, but now they were appearing almost every year.
Two years ago, when they had failed badly at adjusting the difficulty, there had been more than ten perfect scorers. At this rate, the prestige of the Olympiad itself would be called into question.
Of course, the global improvement in the level of mathematics education had played a role. But Marcello judged that this was not the only cause.
Decades of accumulated past problems had appeared, along with educators who systematically analyzed and categorized them. And students learned problem patterns as though memorizing formulas.
Practiced technique rather than creative thought.
Trained memory rather than mathematical intuition.
Past IMO winners had gone on to leave distinct mathematical achievements behind. Like Grigori Perelman, who proved the Poincaré conjecture, one of the Millennium Prize Problems.
But now?
Was this truly the right kind of exam?
Marcello had his doubts.
At the same time, he felt sorry for the majority of the participants.
Because his values would not be favorable to them.
‘The Mathematical Olympiad should be an exam that identifies talent.’
Finding those with the makings of true mathematicians had been the original purpose of the IMO at the time of its founding.
Now, it was time to return to the beginning.