Translator: Dreamscribe
Su-jeong was sitting in the audience.
Thump, thump.
'Huh? What's wrong with ?'
Just thinking about seeing him again after so long made her heart race for no reason.
Su-jeong gripped the program pamphlet in her hands tightly.
'This is so stupid. I'm just here to watch a presentation.'
She tried to scold herself, but her heart refused to settle.
The lights dimd, and Seo-ha walked out.
Without realizing it, Su-jeong drew in a sharp breath.
'He's changed so much.'
In just one year, he had grown almost beyond recognition. He was much taller, and his shoulders had broadened.
He used to hunch his shoulders whenever he got nervous, but now, even in front of this many people, he didn't seem the least bit intimidated.
His once soft features had sharpened considerably. There was still a trace of boyish youth in his smile, but the air around him had changed entirely.
'Still, he's not exactly an idol, is he?'
Having known Seo-ha since they were children, Su-jeong couldn't understand why the dia made such a fuss.
She looked around.
'This is insane.'
The author of the Complex Analysis textbook she used in class was sitting in the front row.
Seo-ha had beco important enough to draw people like that to a lecture.
The moderator took the microphone.
"Today, we will hear a new answer to a problem that has remained unsolved for decades: Smale's an Value Conjecture.
Please welco the author of the paper. Seo-ha Yu!"
Clap clap clap!
A wave of gentle applause filled the hall.
Su-jeong clapped enthusiastically along with them.
Seo-ha bowed deeply to the audience, just like he used to when he was little, then stepped up onto the podium.
At his signal, the lights dimd and the projector cast its glow.
"The an Value Theorem is a concept that has been used since ancient tis. But Stephen Smale questioned whether a an value could still exist when that theorem was transported into the realm of complex numbers.
I intend to answer his question with: 'It does exist.'"
Seo-ha had thought he only needed to deliver a clean proof, but Theo had told him:
"A good number of the people there won't be able to follow your formulas. You have an obligation to explain it in a way even they can understand."
The two of them had spent the entire holiday deliberating over how to structure the lecture.
A shape appeared on the screen.
A single curve drawn in white lines against a black background, with two points marked on it.
The left one was blue, and the right one was red.
"There are two points. A starting point and an ending point.
The function moves between them, changes, and sotis loses its direction."
At Seo-ha's gesture, the curve shifted smoothly.
Whoooosh...
Sound effects played.
The curves swayed as if swept by waves, then shuffled chaotically, trading places as they moved.
The audience let out quiet gasps.
"Smale's question was this:
Even within this complex motion, does a an exist sowhere?"
When Seo-ha paused, the curve on the screen froze.
The two points stopped moving along with it.
"This was the problem.
The curve we're looking at isn't actually flat. To the eye, it looks like an ordinary line, but in the world of complex numbers, this line is twisted countless tis. As if there were an invisible dinsion hidden within it."
At his gesture, the curve slowly began to shift, transforming into sothing three-dinsional.
Not a line but a surface, not a surface but a curved manifold; the curves warped and writhed. Then they surged violently before finally bursting out beyond the edges of the screen.
"Oh my!"
"Whoa!"
"Jesus!"
Startled audience mbers let out short cries from all around.
One professor pushed his glasses up with an amused grin.
"This is the true face of the world we call a plane. It may look smooth on the surface, but within it lie countless folded and twisted layers.
This is also why Smale's an value remained an open problem."
The professors in the front row folded their arms and nodded.
This was sothing no one had managed to accomplish in decades.
"I tried converting this into a plane."
At Seo-ha's words, the air in the lecture hall shifted in a subtle way.
As if to say this was where the real substance began, the mathematicians' eyes lit up.
"This process required twenty-one auxiliary lemmas. Each curved surface distorts under different conditions, so they had to be resolved one by one."
The screen moved again at Seo-ha's gesture.
A massive structure of countless overlapping curved surfaces appeared.
Between the surfaces were thin gaps, and within each gap flowed irregular streams of color.
"The first lemma:
Maintaining a uniform contact condition between the curved surfaces."
As he finished speaking, the rough, uneven contact surfaces aligned themselves cleanly.
"That kid..."
Cronen, having grasped Seo-ha's intent, laughed heartily.
"The second lemma:
Removing the nonlinear distortion that arises near the extrema of the curves."
The folded surfaces unfurled. And the warped lines within them straightened out evenly, reconnecting.
The audience stared at the screen in a daze, as if they had forgotten to breathe.
"The third:
Resolving the topological tangles that occur on the complex plane."
The scale grew larger and larger.
This ti, the entire screen rotated. Like a complicated knot being untied, the surfaces returned to their places and began to align on their own.
The fourth, the fifth...
With each completed lemma, the results materialized on the screen in real ti, matching Seo-ha's explanations.
As if by magic, each ti Seo-ha's hand moved, the world within the screen was transford.
"The seventh:
An intrinsic displacent to minimize discontinuity."
Thousands of curves appeared on the screen simultaneously.
When Seo-ha raised his hand, they began to move. Like water flowing, they naturally found their way to their proper places.
The chaotic curves flowed organically, as though they had co alive.
Seo-ha's lemmas continued.
Everyone was drawn into the screen as if spellbound.
At his gestures, lines and surfaces that had writhed in disorder gradually settled into order.
And the gaps at the boundaries began to close.
After repeating this twenty tis, the structure looked nothing like it had at the start.
"The final lemma.
Connecting all local variations of the curved surfaces into a single plane."
Flash!
"Wow..."
"Oh my God!"
Soone leapt to their feet.
They were witnessing a miracle unfold before them.
The completion of a theorem once thought impossible within the complex plane.
An endlessly tangled space converging into a single surface.
The world within the screen was now a perfect plane.
Just as it had looked at the very beginning, a single white line connected the blue point and the red point.
Between them, a single green point blood into existence.
"Now we can find the an point. At this green point, the positional relationship between the red point and the blue point becos perfectly equal.
This is the an value I found, the equilibrium that erged at the end of countless discontinuities and distortions."
The mathematicians were too moved to speak for a long while.
Clap clap clap!
Applause spread outward.
The soft sound grew louder and louder until it washed over the entire lecture hall like a wave.
"Ah!"
"No way. He actually solved it?"
Exclamations of disbelief burst forth.
Scholars turned to one another, whispering in excited voices.
Elijah Cronen wore a peculiar smile as he stroked his chin.
"So? How does it feel, seeing the one that got away?"
Whitman shrugged with a wry smile.
"It wasn't a fish, it was a whale. He was too big for my net from the start. I believe Seo-ha's lecture today will have a profound impact on our fellow mathematicians going forward."
"In what way?"
"A revolution of sorts. A revolution in perspective. The math world has been too rigid for too long.
I think a more creative and open-minded atmosphere will erge from here."
Whitman nodded.
"To be honest, I've been learning a great deal from Seo-ha myself."
"At your age?"
"Age doesn't matter in scholarship. I'm still growing.
For a long ti, the math world has been too focused on simplifying problems. But Seo-ha did the opposite. He acknowledged the complexity and resolved it piece by piece."
Cronen shook his head.
"Not just anyone could have done that.
What Seo-ha accomplished is, frankly, close to a miracle. Imagine hundreds upon hundreds of threads hopelessly tangled together, and he picked out the single strand that led to the answer.
It's the kind of proof that demands a terrifyingly sharp intuition."
Seo-ha was taking questions from the audience.
Professors probed for gaps in the theory, pressing him on conditions not explicitly stated in the paper.
But Seo-ha wore a broad smile, looking not the least bit burdened. Cronen thought he understood why.
'He's not trying to fight.'
He had always thought the very term "thesis defense" was flawed.
If you win the defense, does the theory beco true?
Cronen shook his head.
It wasn't sothing divided into victory and defeat. Truth was either already revealed, or it wasn't.
Seo-ha yearned purely for truth.
That was why he could enjoy even the Q&A.
One professor raised a hand.
"Do you consider your flattening process to be complete? Isn't it possible that discontinuities still remain?"
Seo-ha thought for a mont, then nodded.
"I can't say the probability of that is zero. If that turns out to be the case, new auxiliary lemmas may be needed."
Another professor asked:
"Then wouldn't it be premature to regard this theory as a completed law?"
Seo-ha shook his head.
"The systems and perspectives that humans work with can always be expanded.
But even within that expansion, the laws I have established will not change. If anything, through that process, my theory will continue to be proven and serve as the foundation for other theories."
Seo-ha held not the slightest doubt in the theory he had built.
The professor who had asked the question let out a deep sound of admiration.
From the back, another professor began to clap.
Soon the applause spread to those around him. Before the colloquium, there had been no shortage of those who underestimated Seo-ha. Not out of arrogance, but because of his age.
But in this mont, no one was thinking about age.
Seo-ha bowed deeply.
Applause erupted once more.
This ti, it was not cheering, but applause carrying respect for a young mathematician.
* * *
Su-jeong slipped quietly out of the venue.
Her steps felt heavy.
At first, she had planned to go find Seo-ha after the presentation and say hello.
She had wanted to ask him.
How he could have left without a word to her, whether things had been hard for him all this ti.
But when she actually stood at the door, she couldn't bring herself to step through.
Mathematicians whose nas even she recognized were showering him with praise. Seo-ha now belonged to an entirely different world.
She had wanted to brag.
About finishing top of her class this sester. About receiving a collaboration offer from a company despite being only a freshman.
And about how she had stunned everyone by rocketing up the LOGIA rankings.
She had wanted to look him in the eye with the sa confidence she once had and say, "I'll be the one supporting you."
"This isn't enough."
To be soone who could stand beside him, she first needed to earn the right to be there.
Su-jeong clenched her fists tightly.
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