Chapter 27
Chapter 27
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Translator: Ace
Chapter: 27
Chapter Title: The Ruthless Problem
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“Marcello, isn’t this going a bit too far?”
In the problem-setting room, Professor Roberto spoke up with a grave expression.
A mathematics professor at the University of Milan in Italy, he was a veteran who had served as an IMO problem setter for the past decade.
“More than half the students haven’t even touched the problems. This isn’t an exam—it’s outright abuse.”
Marcello gazed out the window.
Surely not, but it almost seemed like the students’ screams could reach all the way here.
“I’ll admit it was a touch excessive. But it was necessary.”
Roberto was a mathematician, but he was also an educator at heart. He firmly believed that igniting a passion for mathematics in students was just as crucial.
To him, Marcello’s approach felt excessively brutal.
“Our role isn’t just to inspire dreams in students and awaken them to the beauty of proofs? Not to crush their spirits.”
Marcello turned to face Roberto head-on.
“Roberto, you’re under a misconception.”
“What do you mean?”
Marcello took a step forward. His voice was low, but each syllable carried such weight that everyone in the committee room could hear it crystal clear.
“We’re essentially jewel appraisers.
No matter how much you polish a stone, it remains a stone. Dressing up stones as gems only harms the mathematical world.”
Roberto jerked his head up in shock.
Those were not words one expected from a lifelong academic.
“What kind of outrageous statement is that? Do you really think such talk is acceptable from an educator?”
“Then tell me this: what are the IMO gold medalists from the 2000s doing now?”
“Th-that’s...”
The question struck like a dagger to Roberto’s core.
It was a raw nerve for the IMO.
Systematic training was weeding out true geniuses. Could it even distinguish between students gifted at pattern recognition and those with genuine mathematical intuition?
These were doubts the mathematical community had raised about the IMO for years—and the IMO had yet to offer a convincing rebuttal.
“Past Olympiads weren’t like this. We unearthed shining talents. Gregory Margulis, Eliya Kronen, Grigori Perelman, Vladimir Drinfeld...”
Marcello’s eyes grew distant, lost in fond memories of bygone days.
“They’d wrestle with a single problem for years without tiring. Material wealth or fame meant nothing to them. They were pure souls thirsting for truth itself.”
A cold glint flashed in Marcello’s eyes.
“But what about now?
Most IMO gold medalists flock to finance or IT after graduation.
I won’t stand idly by. Cambridge didn’t summon me from there just to watch this unfold.”
“B-but this is excessive. We’ll face accusations of repeating the 1988 blunder.”
“Blunder?”
“Yes. Zero correct answers—only Eliya Kronen scored a single point. I heard the problem setters caught massive backlash afterward.”
“Why call it a blunder?
That mere 13-year-old, Eliya Kronen, grew into a brilliant mathematician, didn’t he?
He proved the 50-year Reid conjecture and claimed both the Fields Medal and Abel Prize. And it was those very setters who discovered him.”
“Are you saying it’s fine to sacrifice the many for a handful of geniuses?”
Marcello stared at Roberto with utter disbelief.
“Sacrifice?
Is that what you call it when students fail because the problems are too hard?
I’m doing what the Olympiad and mathematics world need most. A genius might be born anywhere right now. If we cling to safe, easy problems, we’ll never find them.”
“Then what about all those other kids?”
Marcello’s intentions made sense on some level.
But even charitably, most students wouldn’t even glance at problem 6.
“They’ll find their proper place. Not everyone needs to become a Perelman.
Even bombing the exam won’t stop them from becoming fine teachers or applied scholars. With effort, they could land on Wall Street, Silicon Valley, or anywhere they desire.
I just don’t want to hand an Olympiad gold medal plaque to students like that.”
Roberto fell silent.
A heavy hush blanketed the committee room.
But the accusatory glares toward Marcello had vanished.
Tap tap.
Yoo Seo-ha’s fingers drummed unconsciously on the desk.
His breathing came a touch quicker than usual, tickling the tip of his nose. A faint dryness tugged at his lips.
This was a side of Seo-ha unseen during the rest of the IMO.
Normally, the instant he read a problem, the path forward crystallized in his mind. Not this time.
The very first line made the corner of Seo-ha’s mouth twitch upward.
An intriguing blend.
Prime number theory, harmonic series, and quadratic residues.
Weaving disparate corners of number theory this intricately wasn’t easy.
The vicious cunning paired with delicate precision suggested a setter who was meticulous—and with a wicked streak.
In truth, Marcello hadn’t crafted this for the students’ benefit. He’d aimed to propose a research topic that would stump even seasoned mathematicians—like problem 6 from 1988.
‘n ≥ 3... distinct primes... sum of reciprocals equals (n-1)/n...’
Equations cascaded through Seo-ha’s mind like a waterfall.
Yet intuitively, he sensed every path led to a dead end.
Prime distributions, the divergence of infinite series, the rigid constraints of perfect squares, all tangled in intricate knots.
Thirty minutes ticked by.
Seo-ha’s scratch paper was a battlefield of erased calculations and fresh attempts.
Sweat beaded on his brow.
Suddenly, his pencil halted.
‘No solution?’
‘No, there has to be. I missed something.’
Seo-ha resolved to rethink everything from the ground up.
‘Sum of reciprocals, harmonic series, divergence—but here it converges, and the product forms a perfect square...’
‘Hold on.’
Something flickered past. Faint, but unmistakably real intuition.
‘What if there truly is no solution? Or just one?’
Seo-ha’s heart began to race.
Solutions usually didn’t exist, but what about an extraordinarily special case?
His brain fired on all cylinders, backtracking dead ends to probe every possible detour.
‘Got it!’
For n=4, if the four primes took a very specific form, it might work. But that was merely the foothold.
‘What a nasty personality.’
The deeper you chased a solution, the more it dragged you into quicksand. The problem was engineered to thwart arrival by that route.
The true answer wasn’t a proof of existence, but of non-existence.
Yet exceptions could lurk in the process.
In other words, the setter—almost certainly a personality case study—was demanding contestants prove the exception to that non-existence.
‘Pathetic.’
Marcello descended into the hall and surveyed the students tackling the problems.
Low whimpers echoed sporadically.
Most floundered, utterly lost on where to begin.
‘Like novice cooks who’ve memorized recipes by rote.’
They could whip up something halfway decent from their prep. But would the world call them chefs?
The recent spate of perfect IMO scores didn’t mean modern math had grown easier.
Quite the opposite.
‘The boundaries between mathematical domains are dissolving.’
Number theory, topology, geometry, analysis—deep dives into one field alone no longer yielded meaningful research.
‘Anyone serious about mathematics should feel that early on.’
Marcello’s gaze sharpened like a hawk hunting prey as he scanned the room.
He murmured low enough for only himself to hear.
“Mathematics is, of course, the art of creative thought.”
What set mathematics apart from physics most?
Unlike physics, shackled to interpreting natural phenomena, math embraced any proposition free of logical contradiction.
Imagination was thus the mathematician’s paramount virtue.
Problem 6 tested precisely that.
The goal, like 1988: 1 point out of 7.
‘Minimal progress on the problem.’
That was the ceiling of Marcello’s expectations.
He strolled slowly through the exam hall, observing. Most matched predictions.
Problems 4 and 5 were fusion math, barely within reach.
Even so, students were punch-drunk.
Frozen in place, clueless on starting points, or bravely grinding substitutions.
‘Tsk tsk. Is that what you call mathematics?’
A few showed promise—last year’s first- and third-place finishers.
Marcello’s eyes gleamed.
He was eager to see how these top prior talents would conquer his problem.
He checked his watch.
Little time remained. Glancing over, both were mired at the entrance.
He couldn’t hide his disappointment.
Then one student caught his eye.
The Korean, youngest participant this year.
He was filling his answer sheet with ferocious momentum.
Marcello’s steps halted near Seo-ha’s desk.
Standing at a distance to avoid disturbing, he watched the writing unfold.
His expression shifted from intent focus to surprise, then outright shock.
‘He plans to solve it all the way?’
Problem 6 wasn’t meant for full proofs. Even the core logic would sprawl excessively.
He’d intended points for bare-minimum approaches.
Yet this student had already scrawled over five pages. In a way that was astonishingly creative and elegant.
Marcello’s heart thundered.
The pivotal ideas he’d envisioned were materializing from the boy’s pen tip—one by one. No, surpassing them, with rigorous arguments even the setter hadn’t foreseen.
‘A phenomenal mathematician has arrived.’
God hadn’t forsaken mathematics after all.
For 20 years, the field had stagnated. Once, theory drove technological leaps; now technology raced ahead, leaving math in the dust.
‘Where on earth did this blessing come from?’
If Euler or Gauss returned to life, would they look like this? Marcello swallowed unwittingly.
Seo-ha penned the final line.
「Q.E.D.」
The Latin abbreviation for proof complete adorned the answer sheet’s end.
Marcello briefly lost touch with reality. His mind blanked white, then refocused.
Thirty years as a Cambridge professor, and he’d just witnessed talent surpassing anyone he’d ever seen.
Seo-ha scanned his answer once more.
‘Barely made it!’
Then realization dawned. Only 10 minutes left.
‘Ah...’
He’d dived too deep into 6, overelaborating.
Problems 4 and 5 remained untouched.
Seo-ha’s face drained pale.
‘I’m screwed.’