The first thought that came to Seoha’s mind when he checked the time was not Uhyun’s admonition that he absolutely had to rack up an overwhelming performance at the IMO.
‘Oppa, do you have to bring my gold medal too?’
His little sister, waiting at home for his medal.
Knowing Seoeun’s personality, she had surely been unable to hold back and had already drawn him wearing a gold medal in her sketchbook.
‘If I can’t keep my promise, she’ll be terribly disappointed.’
Cold sweat ran down his back.
Seoha quickly scanned Problems 4 and 5.
Solving a problem would take at least ten minutes, and writing out the answer would take another ten. With two problems left, the required time was doubled. Since the solution process was also part of the score, he couldn’t cut it down any further.
‘Ah! Is there no choice?’
Seoha drew in a deep breath.
‘Ducky.’
Perhaps because he had stopped it from solving Problem 6, no answer came back.
‘Ducky, you want to see Seoeun happy too, don’t you?’
At that moment, he felt something stir inside his head.
Seoha instinctively knew that Ducky cared for Seoeun as much as he did.
‘There isn’t much time. Please. Let’s do it together.’
Seoha allowed Ducky space.
In that instant, it felt as though something had come loose inside his brain. Like a tightly fastened screw slowly unwinding, Seoha’s ability, which he had always kept suppressed, was explosively released.
Seoha began reading Problem 4.
[From point P inside a cube...]
The moment he read the problem, comprehension followed.
A geometry problem, optimization, symmetry, topology.
Ducky’s obsessive precision instantly constructed a complex coordinate system. The moment Seoha’s intuition seized the core idea, Ducky transformed it into flawless equations.
Seoha’s hand began to move at an astonishing speed.
‘Set coordinates P(a,b,c), distances to the vertices of the cube...’
He understood as he read, and wrote at the same time.
The transmission time from his eyes to his brain, and then to his hand, had become almost zero.
Ducky systematically classified every possible case, while Seoha’s intuition selected the essence from among them. The two abilities began to work in perfect harmony, producing synergy.
Even so, however, the physical constraints of time remained.
Seoha glanced at the clock.
‘I can’t write out every part of the solution.’
A process that should have required ten steps was reduced to five.
Problem 4 completed.
Five minutes had passed.
He immediately moved on to the next problem.
[When choosing r marbles from n marbles...]
A fusion problem of combinatorics and probability.
As Seoha read down through the problem, Ducky rearranged every possible pattern inside his head.
The Inclusion-Exclusion Principle, recurrence relations, generating functions.
Every necessary tool flashed through his mind like lightning.
Seoha’s pencil moved smoothly, like that of a scribe.
‘The essence of combinations is selection and exclusion.’
Ducky arranged the n marbles in his mind into a perfect lattice. Each possibility appeared converted into a mathematical probability.
‘There’s a slightly deeper meaning here. Look at the chain reaction of conditional probabilities.’
Ducky responded immediately.
A complex probability distribution unfolded inside his head as a perfect tree structure.
[First selection: P₁ = r/n]
[Second selection: P₂ = (r-1)/(n-1)]
[Product of conditional probabilities...]
Even then, Seoha’s hand did not stop.
The answer was being completed at the same time as his thoughts.
‘There isn’t enough time. Only the essentials!’
A proof that would ordinarily have to be written over fifteen lines was compressed into five. But there were no logical leaps. By Seoha’s standards, every step was sufficiently persuasive.
Problem 5 completed.
“Time’s up!”
The exam ended at the exact same moment he wrote down his answer.
Marcello had been watching the entire process from two steps away.
The concentration and speed the boy had shown in the final moments.
It delighted him, yet also made him uneasy, as though he had witnessed something that surpassed human limits.
Before he realized it, he had approached Seoha and spoken to him.
“Are you all right?”
The boy’s expression was blank.
Whether he had not heard him or not, there was no answer.
After submitting his answer sheets, he rose from his seat and looked around.
His expression was somehow uncomfortable, as though something displeased him.
The boy muttered softly.
“Why are the desks arranged like this? The symmetry doesn’t match. Why are there twenty-one in the third row over there? If they needed space, they should have arranged them in a hexagonal pattern instead...”
In truth, Seoha was feeling discomfort. The imperfect arrangement of the desks grated on his eyes like a thorn lodged beneath a fingernail.
Marcello stepped closer and peered carefully into Seoha’s eyes.
His pupils were dilated, and his focus kept shifting.
‘This is...’
Marcello had spent decades immersed in mathematics and had experienced states of extreme concentration before. Because of that, he was able to grasp the boy’s condition quickly.
This boy was currently in a kind of “high” state.
When the brain becomes extremely activated in a specific area, the mind enters a mixed state of Flow and Hyperarousal.
‘No, is it somewhat different?’
The boy’s appearance as he solved the problem as if possessed looked different from what psychology commonly called a flow state.
At that moment, one figure came to Marcello’s mind.
‘Ramanujan?’
There were records in the Cambridge library saying that Ramanujan had looked similar to this when conducting mathematical research. (Ramanujan had studied at Cambridge.)
A mysterious ability to derive the answer immediately without a proof process.
Mathematical intuition rising from deep within the unconscious.
An unrealistic insight that surpassed logical thought.
That was how Seoha had looked when solving Problem 6.
As if he already knew the answer and was constructing the proof backward.
“Stop, Ducky.”
Seoha muttered softly to himself, then emerged from his state of concentration.
But the way he was gasping for breath still made his condition seem unstable.
Worried, Marcello asked once more.
“How are you feeling right now?”
Seoha raised his head and smiled brightly.
“Great. I got to solve the coolest problem ever.”
Only then did Marcello let out a small sigh.
‘It seems I was worried for nothing.’
For him, the problem setter, Seoha’s answer was a joy beyond words.
* * *
After the exam ended, they had three days of free time.
The results were scheduled to be announced at the awards ceremony four days later, so the students were able to enjoy sightseeing in London in the meantime.
“It’s finally over!”
Jihun shouted, throwing both arms high into the air.
It felt as though all the tension that had built up until now had released in a single moment.
“Now I can finally live like a human being.”
Dokyeong’s voice was full of liberation.
While preparing for the IMO, the Korean team had spent a more intensive period of time than ever before. Since this was his last IMO, Dokyeong was especially emotional.
“How do you feel?”
Sujeong asked Seoha.
“I want to go home soon.”
Being overseas and away from his family had taught Seoha what loneliness was.
Aside from that, there was something Seoha had to confirm.
The sense of exhilaration he had felt in that moment when he solved the problems together with Ducky. Seoha wanted to know what it was.
‘I wonder if Seoeun is doing well.’
Because of the time difference, Seoeun would force herself to stay awake until night to call Seoha.
“Right, you’re still at the age where you miss your family.”
Sujeong gave an old-fashioned ahem! and patted Seoha on the shoulder, pretending to be an adult.
“You all worked hard.”
Professor Park looked around at the students with a proud smile.
Regardless of the results, he sincerely believed that this year’s students had truly done well.
“For the next few days, don’t think about anything and let’s enjoy London. Is there anywhere you want to go?”
“Really?”
“We’re allowed to have fun?”
“Yes!”
At Professor Park’s words, everyone screamed.
“I want to go to the British Museum!”
“I want a Thames River cruise.”
“Let’s go to Buckingham Palace first!”
They might have been mature, but they were still high school students. In between studying, each of them had already picked out places they wanted to visit.
As if their model-student tendencies had not gone anywhere, the six of them soon gathered in one place, opened a travel booklet, and began planning their sightseeing.
“No, but we still have to go to a Korean restaurant.”
“We’re all STEM students, so what’s with Shakespeare’s birthplace?”
“Newton’s apple tree? Cambridge is too far!”
“The bookstore from Notting Hill? Didn’t that movie come out before we were even born?”
After a heated debate, the sightseeing course was decided.
The next morning, the Korean team went as a group to the British Museum on the Tube.
At the news that admission was free, even those who had not been interested in artifacts became intrigued.
“Wow! This is what’s great about Britain. As expected of a developed country!”
Everyone rejoiced at the free admission sign hanging at the entrance.
But once they entered the museum, the atmosphere slowly changed.
The enormous exhibition halls were packed full of artifacts from Egypt, Greece, and Mesopotamia.
“The scale is beyond imagination.”
Jiye murmured in a small voice.
The sculptures from the Parthenon, the coffin of an Egyptian pharaoh, Babylonian clay tablets—Seoha, who had read many books, could easily guess how these vast and magnificent artifacts had come to be in London.
“If I were Egyptian, I think I’d cry.”
Sujeong grimaced resentfully as she looked at a massive obelisk.
Seeing the students’ expressions, Professor Park spoke quietly.
“You’ve come to think in fairly grown-up ways.
It’s a complicated issue. The glory of the past, and perhaps karma as well. The British government must be having a headache over repatriation lawsuits. But it’s also true that because of it, we’re able to see things like this.”
After touring all the major artifacts, the Korean team stopped by the gift shop.
“Huh! What’s that?”
Seoha’s eyes widened.
On one side of the display case, various ducks were lined up.
A pharaoh, the Union Jack, Greek mythology, even a duck dressed as a Roman soldier.
Seoha hurried over and examined them one by one in detail.
“They’re rubber ducks. You really do like ducks, huh?”
Sujeong laughed as if she found it absurd.
Seoha admired them for a long while before finally choosing one Union Jack duck.
* * *
The next day,
The third-floor conference room of the mathematics building at Kingston University.
The six problem setters were utterly exhausted from three straight days of grading.
On the first day, they had all gone wild after seeing Seoha’s miraculous five-page proof.
A genius had appeared who had perfectly solved what could be called the hardest problem in IMO history.
But the answer sheets they saw after that were the problem.
Marcello, his shirt sleeves rolled up to his elbows, took off his glasses and rubbed the bridge of his nose.
In front of him, answer sheets that had already been reviewed were organized by score, and the cold coffee in his cup had dried up.
“Now, let us reach a conclusion today.”
At Marcello’s words, everyone nodded and took out their documents.
They were Seoha’s answers to Problems 4 and 5.
“I still think three points is the limit.”
Roberto unfolded the answer sheet.
“He jumps straight from here to here, skipping at least three steps in between.”
It was true that it appeared that way.
But that was not all that troubled the problem setters.
“The parts this student seems to have skipped may not actually be omissions.”
Marcello stood and drew a simple diagram on the whiteboard.
“This student has omitted unnecessary calculations and presented only the skeleton of the logic. There is no logical flaw. It is simply not kind.”
The Russian problem setter spoke for the first time.
“But this student’s logical development is extremely difficult to follow. Did it not take us more than a day to interpret the answer? This solution and its score will be made public. If we give it a high score, will everyone be able to accept it?”
But Marcello had no intention of backing down from his conviction.
“What matters is that this answer is not wrong.”
“Isn’t the IMO a competition for high school students? If we accept answers like this, how are we supposed to grade in the future?”
“Then let me ask the opposite.”
Marcello looked around at the committee members.
“Can any of you find a logical contradiction or mathematical error in this answer?”
Silence flowed through the room.
“There is none. Every step is correct, and the conclusion is correct as well.”
Roberto admitted it honestly.
“It is simply not in a form familiar to our eyes.”
Marcello drew his conclusion.
“Then this, too, is a complete mathematical argument. We have no right to deduct points merely because it is written in another language.”
However, due to fierce opposition from the majority of the committee members, Seoha’s answer did not receive full marks.
No matter how free it was of logical defects, it was far too much of a stretch to call it a perfect model answer.