Monday,
Seoha woke earlier than usual.
The dawn air seeping in through the window was cold. Mid-November—the winter was already right on their doorstep.
Today was the first preliminary round of the Korean Mathematical Olympiad.
Seoha rose from his blankets and opened the window. The cool air sank deep into his lungs, chasing the last of his sleep away.
He changed into light workout clothes and quietly stepped out the door.
At six in the morning, the village was quiet, but he could sense people here and there preparing for the day. Seoha began to run with an easy stride.
There was a reason Seoha had started running.
The mathematician Ramanujan,
dead at thirty-two from malnutrition and tuberculosis.
The cause was an extremely irregular lifestyle and a lack of exercise. Every day, he sat for long hours, devoting himself solely to mathematical research.
The history of mathematics was an extraordinarily fascinating storybook to Seoha.
There was nothing more enjoyable than following the development of mathematics in East and West and glimpsing the lives of great mathematicians.
How Gauss had instantly calculated the sum from 1 to 100 at the age of seven, the story of how Euler continued his research even after losing his sight, and even the absurd anecdote of Galois, who, on the eve of a duel, devoted himself to organizing his mathematical theories.
It was wondrous to him that they, too, had once had childhoods like his, moments when they had fallen under mathematics’ spell, and times when they had despaired or felt ecstasy.
At times, Seoha even felt as if he were leaping across time and space to speak and breathe with them.
‘If only Ramanujan had lived a little longer…’
The loss his death dealt to the world of mathematics was incalculable.
Of the roughly 3,900 formulas and theorems Ramanujan left behind during his brief thirty-two years of life, many were only proven true sixty years after his death, at the end of the twentieth century.
Only after computers had advanced did it become clear just how accurate his intuition had been.
‘What would have happened if he’d lived to seventy?’
Even within his short life, the infinite series and continued fraction theories he studied became foundations for modern cryptography and computer science. And the theta functions he left in his final letter were now being used to determine crucial dimensions in superstring theory and M-theory, the greatest topics in modern physics.
What was most unbearable was that there were still many parts of his theta functions that had yet to be understood.
‘What a nasty personality.’
Why did mathematicians toss out such important problems without proof and then just leave?
Seoha could not understand them.
How could they so confidently release unfinished ideas into the world?
Ramanujan in particular had often said that the goddess Namagiri gave him formulas in his dreams, omitting the proof process and writing down only the results.
And yet almost none of them were wrong, which was enough to drive Seoha mad.
The history of the mathematicians he had read about was, in truth, a battle against health.
And so he ran.
Huff, huff.
His breath rose all the way to his throat.
Once he actually began, he found that running had many benefits besides health.
His mind, which had automatically counted his steps at first, eventually stopped calculating. And then came the ideas that naturally surfaced as he ran.
Answers that had not appeared when he sat and struggled over them would sometimes occur to him in the middle of a run.
Half a year had passed since he began running.
At first, he had been panting before he could even run ten minutes, but now thirty minutes was easy.
‘Is this what endorphins are?’
He saw someone in the distance.
“Seoha! Take some cucumbers and tomatoes with you!”
Mr. Choi, who ran a greenhouse, waved at Seoha.
“Thank you, sir! My mom will love them!”
Seoha was already a celebrity in Okcheon.
After making a loop around the village, Seoha returned home. A pleasant warmth circulated through his whole body, and his mind felt neatly organized.
“You’re back! What did they give you this time? Hurry up and wash, then come eat breakfast!”
Miyeong took the bag from Seoha’s hand.
After showering and sitting at the table, he found a breakfast spread more lavish than usual.
‘My parents seem more nervous than I am.’
“Mom, you could’ve just made it like usual…”
“But today’s an important day. You need to eat properly before you go.”
In truth, Miyeong had not slept properly the night before.
She knew very well that her son was outstanding, but a parent’s heart was simply like that. She kept dozing off and waking up, preparing the meal, and before she knew it, the number of side dishes had grown.
“Wow! There’s so much delicious stuff!”
Seoeun, who had woken up early and seemed exhausted with her eyes half-closed, screamed and sat down in front of the table.
Seeing her, Cheolho said,
“Mom made all this so your brother would do well on his exam.”
“Then there’s nothing to worry about. Oppa doesn’t have anything he doesn’t know, does he? Whenever I ask him something, he answers everything. Mom and my teacher say they don’t know all the time!”
At Seoeun’s words, the whole family burst into laughter.
* * *
A high school in downtown Daejeon,
By the time Seoha arrived at the exam site, many students were already there.
‘Wow! There are this many people.’
This year, there were about eight thousand KMO participants nationwide.
Exam sites had been prepared in sixteen cities and provinces across the country, and even in the Daejeon region to which Seoha had been assigned, more than five hundred students had gathered.
One building was not enough, so they had been divided among three high school buildings. It seemed as though every student in the country who was good at math had come.
The number selected in the first round would be two hundred, and making it into that group would become a credential for applying to college through special talent or science gifted student admissions.
In the hallways and classrooms, many students were already absorbed in their final preparations.
The student seated in front had his hands clasped and his eyes closed.
Another student was muttering something as he repeatedly recited formulas written in a notebook.
It was a kind of tension Seoha had never seen before.
The proctor entered.
“We will now begin the first preliminary round of the Korean Mathematical Olympiad. The exam time is three hours, with a total of twenty-five questions, all multiple-choice with five options.
This is an important test to select the talent that will represent Korea, so I hope all of you take it without regrets.”
Beep—
The question sheets and answer sheets were distributed, and the exam began.
‘Will there be any new problems?’
He had heard that every year, the first round of the Olympiad included ingenious problems designed to identify truly exceptional students.
Seoha’s heart thumped.
Question 1.
[When four coins are tossed at the same time, what is the probability that exactly two land heads up?]
A probability problem.
It could be solved easily using combinations or binomial coefficients.
Seoha did not even write down the solution and immediately chose the answer.
Question 2.
[When coloring the four vertices of a square red, blue, and green, how many distinct coloring methods are there?]
‘Haha!’
A coloring problem. It made him laugh.
It reminded him of the four-color theorem, which he still had not solved. Seoha had not forgotten the problems he had failed to prove so far.
Whenever a clue came to mind, he was testing new approaches that could be applied.
‘Compared to the four-color theorem, this is nothing.’
It could be solved easily by applying Burnside’s lemma. The size of the rotation group was 4, and if he calculated the colorings fixed by each rotation…
Seoha’s hand moved without hesitation, selecting the correct answers.
As he solved the problems, the difficulty rose.
Question 7 had cleverly set a trap to make it easy to miss a condition, but it was useless against Seoha. He saw numbers not as fragments but as a group of patterns. Even if the conditions changed, the structure of the entire group did not.
Question 10 was the same. It had a structure that forced one to fall into a trap after calculating the solutions on both sides of the function. But Seoha perceived the roots not as numbers, but as trajectories on a graph.
From Question 11 on, the truly difficult problems began.
A geometry problem using complex numbers, an analysis problem dealing with the limit of a sequence, graph theory, and so on.
‘Huh?’
The tip of Seoha’s pen stopped as he solved the problems.
‘This is strange.’
1, 4, 2, 5, 3, 2, 5, 3, 1, 4, 3, 1…
Seoha stared at the answer sheet he had half marked.
The numbers from 1 to 5 were distributed evenly.
In Seoha’s mind, a 5 x 5 square grid took shape. Then the marked numbers were assigned coordinates and began to be rearranged within it.
At that moment, Seoha realized that the numbers arranged horizontally and vertically were balanced to an uncanny degree.
‘An orthogonal array?’
It was not a coincidence.
The probability of numbers like this appearing by chance was one in five hundred thousand. If the orthogonal pattern was taken into account, it was less than one in one hundred billion.
Someone had clearly embedded the answers to every question into a single combinatorial structure on purpose.
Seoha set the problems aside and began solving the puzzle.
Numbers filled the chessboard-like grid in his mind. Going down the vertical columns, the numbers did not overlap. Moving across the rows, the five numbers were mysteriously distributed without omission.
‘A Latin square.’
Seoha immediately formed a hypothesis.
If he viewed the problems as coordinates (i, j) on the grid and found the values of coefficients a and b, he would be able to restore every answer.
‘The correct answer is (a·i + b·j) mod 5 + 1.’
Seoha put down his pen.
All twenty-five cells were filled with numbers.
It was a beautiful structure showing order in every row and every column.
Seoha felt as if he knew the answer to the next problem. The position corresponding to coordinate (3, 3).
‘Number 4.’
He verified the hypothesis.
His hand moved faster as he solved the problem.
The correct answer was, without fail, number 4.
A smile spread across Seoha’s face.
It was as if the unseen designer of the exam were speaking to him.
‘Can you see this rule?’
Fewer than ten students achieved a perfect score on the first round of the KMO each year.
This was a message of praise from the problem setter to the students who got every answer right. Of course, he had not expected the students to notice it at all.
But Seoha had filled it all in midway through the exam.
Questions 14, 15, 16…
There was no need to solve the problems; the answers were already before his eyes.
Without going through the calculations, he immediately plugged in the answers. Whenever he checked, they were always correct.
In that way, up to Question 24, everything fit together without a single error.
And then the final Question 25.
‘Number 5?’
The answer that should clearly have been number 1 was pointing to a different number.
Seoha’s right eyelid twitched.
There was no way the grid formula was wrong. It had been perfect for twenty-four questions, and only failed at Question 25?
‘Did I miss something?’
In his mind, he retraced the entire process up to that point. But there was no error anywhere.
Just in case, he gripped his pen tightly and solved Question 25 again from the beginning.
Polycubes.
A combinatorics problem using rotations, reflections, and symmetry.
But the answer was still number 5.
Thump, thump.
Seoha’s breathing slowly grew rough.
‘This isn’t a sequence or a puzzle problem. It’s an exam where I have to write the answer.’
His head knew that, but the hand marking the answer trembled.
‘Just mark number 5 quickly and end it.’
He squeezed his eyes shut and brought the marker to the answer sheet.
But he could not fill it in.
An imperfect pattern, an unexplained exception.
He could not acknowledge it and ruin the array.
Cold sweat ran down Seoha’s forehead.