dhibooks Chapter 47, this question, damn it, is unsolvable?
Chapter 47, this question, damn it, is unsolvable?
Robert's momentum waned, but he still couldn't help but retort:
"But...but what you're doing is too extreme!"
We will face criticism from the outside world; they will accuse us of repeating the mistakes of 1988!
"A mistake?" Marcelo asked, as if he had heard something utterly ridiculous.
"That's right! In 1988! The accuracy rate for that question that year was an unprecedented zero! A complete wipeout!"
Of all the geniuses in the world, only Ilya managed to get a mere 1 point!
Have you forgotten how severely the academic community criticized the committee member who set that question back then?
"What kind of mistake is that?" Marcelo retorted. "What did Ilya, who was only thirteen at the time, do afterward?"
Robert remained silent.
Because that thirteen-year-old child later grew up to become one of the greatest and most outstanding mathematicians on the planet.
He proved the Reid conjecture, which had puzzled the mathematics community for fifty years!
He unsurprisingly won both the Fields Medal and the Abel Prize!
And the very same exam-setting committee that you all vehemently criticized back then was the one that unearthed such a genius from the sea of people!
"You mean..." Robert's lips trembled.
"Is it justifiable to sacrifice the majority in order to discover a very few geniuses?!"
Marcelo stared at Robert with the look one might give someone an "incomprehensible idiot."
"Sacrifice? Students who can't solve problems because they're too difficult deserve to be called sacrifices?"
"I am doing the most indispensable rescue work for the Olympiad and for the entire mathematics community!"
Right today, right at some table outside, a genius who will dominate the next century might just be born!
If we continue to cling to those mediocre, boring, and low-quality problems that can be solved simply by rote memorization, we will never, ever be able to distinguish their existence!
"What will happen to all those hopeful children who are left?!"
Robert understands Marcelo's original intention.
But no matter how optimistic you think about this test paper, most students probably won't even be able to get close to question 6, and will be completely crushed by the despair of that question!
"They have hands and feet, they won't starve."
The world doesn't need, nor should it require, everyone to become Perelman.
Even if they fail the exam here, with their intelligence, they can still become excellent university teachers or work in applied mathematics in the future.
"As long as you're willing to work hard, you can make a lot of money anywhere you want, from Wall Street to Silicon Valley."
Marcelo looked out the window again.
"However, I absolutely will not allow the sacred title of 'Olympic gold medalist,' which represents the supreme potential of the mathematics community, to be awarded to this group of problem solvers who only know how to apply formulas."
Robert fell completely silent.
The atmosphere in the spacious office was so oppressive that it was hard to breathe.
But the resentment in his eyes as he looked at Marcelo had unknowingly dissipated.
Instead, there was a helpless sigh that only he could hear.
......
Inside the examination room.
Su Hao's eyes were fixed intently on the exam paper.
His breathing was slightly more rapid than usual, and he felt an itchy sensation on the tip of his nose due to extreme tension. Even his lips felt dry.
This is an extremely rare physiological response.
Throughout his journey at the IMO, Su Hao had never shown such a state of heightened vigilance.
In the past, no matter how bizarre or strange the questions were, as long as his eyes scanned the question and he finished reading it...
It's like having a cheat code activated; a perfect approach leading straight to Rome will automatically form in your mind.
But this time, it's completely different.
The moment his gaze fell upon the core of the question, Su Hao's lips curled up little by little.
This question is so interesting.
This is a combination of mathematical structures that is extremely bizarre and interesting.
Prime number theory forms the skeleton, harmonic series forms the skin, and quadratic residues form the flesh and blood.
These three branches of number theory, which are almost completely unrelated in their underlying logic, are forcibly interwoven in an extremely counterintuitive yet exquisitely subtle way.
These are definitely not garbage exam questions that can be cobbled together by simply flipping through past exam question banks.
Every character in this question radiates a nauseating malice and meticulousness.
Su Hao would stake his life on it to guarantee that the person who set this question was absolutely a cunning and extremely twisted and vicious old bastard!
In fact, Su Hao's guess was completely correct.
When Marcelo created the question, he never intended it to be a test for high school students.
He was arrogant and condescending, and he insanely proposed a research topic that would drive even seasoned mathematicians crazy.
Just like the 6th question in the 1988 college entrance exam that destroyed the confidence of a generation.
"n ≥ 3... distinct prime numbers... the sum of their reciprocals is frac{n-1}{n}..."
Su Hao closed his eyes slightly, his brain working at high speed.
Countless complex algebraic expressions, topological structures, and theorem corollaries poured down, collided, and fissuring in the darkness deep within his consciousness like a burst dam!
But his exceptional intuition was frantically sending out piercing warning signals:
Something is wrong!
There's a huge pit!
No matter which derivation route you take, you will eventually crash into a dead end!
Prime numbers are distributed on the number line in a disordered, ghostly manner;
The divergence of infinite series is destined to lead to the abyss;
Perfect squares are structurally constrained like shackles within a modular system...
No matter which side you start from, these three mountains will instantly surround you, completely annihilating all logical deductions.
Thirty minutes passed in the blink of an eye.
The draft paper in front of Su Hao was already densely covered with formulas that were half-written and then roughly crossed out.
All that remained were the numerical corpses of his repeated charges, only to be ruthlessly repelled.
A drop of cold sweat slid down his forehead and landed heavily on the paper, spreading out a blot of ink.
Suddenly, Su Hao's pencil, which was spinning rapidly like a sewing machine, came to an abrupt halt in mid-air.
An extremely radical, even treasonous, judgment cleaved through the fog in his mind like lightning:
Is this problem... damn it, unsolvable?
No. Absolutely not.
This is the world's highest-level IMO stage; there is absolutely no way such a low-level blunder would occur.
There must be something extremely hidden that was missed in some extremely minor algebraic structural transformation process that was obscured by common sense.
Su Hao took a deep breath and suddenly opened his eyes.
Without hesitation, he swung a heavy hammer in his mind, completely overturning and crushing all the deductions he had made in the previous thirty minutes into dust!
Starting from scratch!
Let's re-examine the most fundamental mathematical principles!
The sum of reciprocals essentially points to a harmonic series, which inevitably diverges.
However, the summation result here is confined to an extremely strange convergence value...
Furthermore, their product must also be a perfect square...
and many more!
In the darkness, it was as if a match had been suddenly struck and lit.
Extremely faint, yet dazzlingly bright in this deathly silent mind.
What if... this bizarre Diophantine equation, in the conventional sense, has no solution at all?
Or perhaps, it only has a unique solution under some extremely abnormal circumstances?