Chapter 202
Translator: Dreamscribe
Clap clap clap!
The applause wouldn't stop. The heat in the room was like something out of a concert hall. The lecture hall, which everyone had expected to be sparse before the semester began, was packed without a single empty space.
Here and there, the voices of excited students rang out.
"Seo-ha! Welcome to Texas!"
"Won't you lecture at our school?"
"You're so handsome!"
A professor with a benevolent expression stood at the podium, wearing a satisfied smile. It was Professor Abraham Fischer, a Wolf Prize laureate and the pride of the University of Texas mathematics department. Looking at Seo-ha, he spoke in a playful voice.
"Welcome, young genius. Forgive our rudeness. Because of one email you sent, our undergraduates haven't slept in a week."
'Ah!'
Only then did Seo-ha grasp the situation.
Professor Abraham had expressed enormous interest in the email he'd sent. And he had asked for permission, saying he wanted to share it with his undergraduates.
Seo-ha had said it was fine without much thought, but he'd had no idea it would become such a big deal.
With a dazed expression, Seo-ha walked toward the front of the podium.
"Your question was truly fascinating. Thanks to it, we had a delightful week ourselves."
Seo-ha glanced up at the blackboard.
[Is evolution powerful evidence against P=NP?]
It was the question he had posed.
The very fact that living organisms had evolved through four billion years of trial and error, didn't that negate the existence of a P algorithm, one that could find the correct answer in a single stroke?
In his paper, Professor Abraham had written this.
"The DNA division and replication systems of living organisms are the most powerful example of how P=NP operates in the real world."
The cell division that occurs at the birth of life involves more possible cases than there are atoms in the universe. And yet nature, in mere seconds, finds the optimal structure and produces perfect life.
"The speed at which a cell replicates three billion base pairs while correcting errors is the pinnacle of parallel computation, something no modern supercomputer could ever imitate. The system of life is already freely crossing the wall we call NP."
Reading this section, a question had arisen in Seo-ha's mind.
The major evolution of life is generally brought about by mutation. Gradually, over billions of years of trial and error. If P equals NP, then shouldn't life have already achieved perfect evolution from the very start?
As he passed down the aisle, Seo-ha stole sidelong glances at the desks where the students sat.
Papers underlined in highlighter and plastered with sticky notes. Computational complexity textbooks, and even Wikipedia screenshots that plainly bore the traces of a frantic search.
Just as Professor Abraham had said, the signs of fierce study were unmistakable.
"Come, come up here."
Before he knew it, Seo-ha had climbed onto the platform.
The students' admiring gazes were a burden. It hadn't been planned, but Seo-ha steadied his heart.
What had been the most talked-about field of study in the world these past few years? Mathematics. The phenomenon of students favoring mathematics was not something happening in Korea alone.
Newspapers, broadcasts, YouTube, and various other media had spotlighted Seo-ha from every angle.
The significance of the mathematical achievements he had accomplished, the expectation of what might change going forward because of them, and gossip-like matters such as just how much money he had earned.
Naturally, people were very interested in the money, and there were no small number of broadcasts that focused solely on this and churned out sensational content.
[The Teenager Who Earned the Most Money in History]
[He Only Did Math, So How Is He a Billionaire?]
[How Much Will Yu Seo-ha Earn in Royalties Over His Lifetime?]
Seo-ha was indifferent to the behavior of the media, and MIT, too, imposed no particular restrictions as long as it didn't harm Seo-ha's image. Since MIT was also drawing attention because of him, there was even a subtle tendency to enjoy it.
But this alone could not explain the phenomenon that was occurring across the developed world.
The fundamental reason students had come to favor mathematics. It was because the market value of mathematicians was skyrocketing.
The admission competition for Ivy League mathematics departments had already overtaken that of medical and engineering schools. Even Europe's prestigious engineering universities were showing signs of moving to elevate pure mathematics into an independent college of its own.
Every student's eyes turned to Seo-ha.
Seo-ha drew in a deep breath, then slowly opened his mouth.
"It's a pleasure to meet you all. My name is Yu Seo-ha."
Clap clap clap!
A thunderous round of applause.
The students were looking at him with expectant eyes.
"We held a discussion with the undergraduates on the topic you raised. Life and evolution, and mathematics. Isn't that a problem those who walk the path of mathematics ought to ponder? In the process, there were a few questions we couldn't resolve. So we've all been waiting here for you."
They were students with tremendous passion. Even though it was the middle of vacation, not one of them showed a hint of complaint.
Seo-ha looked down at his own clothes.
Jeans and a white T-shirt. If he'd known something like this would happen, he should have at least worn a proper shirt.
"Thank you for the warm welcome.
Just how fierce the week you and Professor Abraham spent must have been, I can feel it well enough from the heat in this lecture hall. As the one who first raised the topic, I'd like to take part in the discussion too."
Contrary to the overwhelming volume of media coverage, Seo-ha was hardly exposed to the public.
Perhaps that was why rumors about him ran rampant.
Among them, the rumor that Seo-ha rarely met with people was accepted as established fact. And the reason given was that there was almost no one in the world capable of holding a conversation with him. Thus the image these students held of Seo-ha was that of a genius utterly lacking in social skills.
"Shall we speak with each other frankly, holding nothing back? I'm curious what answers the brilliant minds of the University of Texas will come up with."
Smiles spread across the students' faces.
The Seo-ha they saw in person was far from the rumors. Around the same age, dressed in similar clothes. He looked like the kind of student one might see anywhere on campus.
But anyone could sense it.
A confidence that only someone of overwhelming intellect could display, and at the same time, an ease that showed consideration for others, glimpsed in his manner. Someone bravely raised a hand first.
"First, thank you for visiting our university. Doctor.... Ah! You've received the Fields Prize, but you're not a doctor yet, are you."
Hahaha!
At the student's joke, laughter burst out here and there.
"Seo-ha! I understand that you reject P=NP. In that case, how should we explain the process of cell division in living organisms, which finds answers at a speed that defies common sense?"
Across the lecture hall, a low murmur broke out, as if in agreement.
Professor Abraham, too, was watching Seo-ha as if intrigued. With a slight smile, he began writing an equation in one corner of the blackboard.
"Your argument, then, is 'Life knows the answer'. ...Is that correct?"
The students nodded.
"But if a magical algorithm called P=NP existed in the universe, then immediately after the birth of the first single-celled organism, life would have leapt in a single bound into a highly intelligent being optimized for its environment."
A blonde female student sitting in the very front row shot her hand up.
"Then wouldn't that be a contradiction? Because it's a fact that cells perform enormous computations in a fleeting instant."
The student's expression showed genuine curiosity.
It was interesting.
Seo-ha's tone rose slightly.
"That's why I considered an answer that isn't a contradiction. I'd intended to discuss it with Professor Abraham today."
When Seo-ha glanced to the side, the professor gave a playful shrug.
"The professor focused on the efficiency demonstrated by life's replication system. But I'd like to point out the errors. If it were truly a flawless law, then no error whatsoever should exist."
The lecture hall fell silent.
"But what about reality? Life gets it wrong endlessly. Mutations, deformities, cancer. Even ordinary replication isn't perfect."
So then, what on earth was the conclusion?
The students tilted their heads. Looking at them, Seo-ha slowly opened his mouth.
"My conjecture is that cell division is not the result of computation."
Seo-ha drew a picture on the blackboard.
"Let's suppose there's a sieve shaped like this. It's similar to the tool used to sift flour when making desserts.
Using it, we can obtain fine flour without calculating the size of the particles. This isn't mathematics. But what about the result?
I wondered whether cells might go through a process similar to this. Not computation, but physical filtering, the structure itself filtering out impossible cases from the very beginning."
A murmur spread among the students.
"Whoa!"
"Doesn't that actually explain everything?"
"I disagree. It's just a hypothesis. It could be that nature's theory and computation are perfect, and the error occurs only in actual application."
"I think he's right? There isn't a single contradiction in the explanation!"
"That's a completely different direction from our professor's, isn't it?"
From their reactions, Seo-ha felt a curious sense of dissonance.
It was as if Abraham had summoned him here hoping he would refute his own argument. When he looked at the professor, he nodded as if to say, please.
A student sitting in the back cautiously raised a hand.
"Mister...."
"Please call me Seo-ha."
It seemed there was no suitable title for a man who was neither a professor nor a doctor, nor even a master's holder.
"Seo-ha, in that case, how should we explain the countless similar structures found in the natural world? Would they all arrive at the same optimal solution after countless trials and errors?"
Evidence that had lent weight to the P=NP argument.
Fractal structures, the Fibonacci sequence, the golden ratio. Patterns that nature produces over and over. Nature has been repeatedly writing out the same answer since before humans existed.
Seo-ha hesitated for a moment.
Whether he ought to present a serious argument to undergraduates. But he wanted to repay their pure passion.
"Let me first say that this is my personal opinion."
At his changed expression, the mood grew heavy.
"Nature does not seek the optimal solution. It has never even tried to. The universe merely seeks to survive. I view the discipline of mathematics this way. Within those traces spanning billions of years, a result called order remained, and mathematics is the discipline that finds it out."
The impromptu seminar came to an end.
Seo-ha took questions until the students stopped raising their hands. Once their doubts were resolved, the students poured out casual questions like, "So do you have a girlfriend?"
There were also many students who brought the just-published introductory book on Yu-Riemann Geometry to get his signature.
The pure intellectual passion of undergraduates.
Seo-ha, who had been away from school for a while due to military matters, felt as if he could finally breathe again here after so long. His own name printed on the book cover felt unfamiliar. Before he knew it, Professor Abraham had quietly drawn near to his side.
"How is it? The University of Texas."
"It was far more impressive than I expected."
"Have you any thought of lecturing here?"
"The dean wouldn't allow it."
Professor Abraham laughed loudly.
"Hahaha! As it happens, I said the same thing to Dean Whitman and got cursed at for over ten minutes."
The two of them walked slowly and made their way to the office.
A teaching assistant brought out coffee he had carefully brewed. He kept stealing glances at Seo-ha's face. The signs of him struggling to suppress his excitement were unmistakable.
"Let me apologize first."
As they took their seats, Professor Abraham bowed his head deeply to Seo-ha. Startled by the unexpected gesture, Seo-ha waved his hands, not knowing what to do.
"No, please. I'm the one who suddenly sent an email when we'd had no dealings with each other."
"No, please accept my apology. It wasn't proper of me."
"...Was there a particular reason?"
He let out a heavy sigh.
"Students are profoundly influenced by their teachers. In any field, this is unavoidable. And that is what truly frightens me."
"...."
"They're barely twenty or so. Easily swayed by others' opinions. All the more when the words come from me, a Wolf Prize laureate and a distinguished professor, they tend to accept them without any criticism. So I wanted someone with authority to come and tell them that, in truth, mathematics isn't like that. It's something I couldn't accomplish myself."
"Would my words carry that much authority?"
Abraham made an incredulous expression.
"You'll soon have a hard time of it yourself. Once you stand at a podium, you'll meet plenty of students who write down your lectures as if they were the words of Socrates."
"I'll be careful."
"You'll do just fine, no doubt. You're a prudent man. Didn't you hold your tongue earlier as well?"
"Sorry?"
"That over billions of years, a result called order remained. The meaning that phrase implies."
Seo-ha's eyes widened.
But before long, he nodded, looking at him.
"I believe there exists a single principle that runs through that order."
"Ha ha ha. You're an even greater one than I am."
Superstring theory, once a strong candidate, had failed to make even a single scientific prediction. Since then, mathematics and physics had, in effect, given it up. They regarded it as either nonexistent or, at the very least, something the mathematics of the present day could not reveal.
"It most certainly exists."
Seo-ha's face looked utterly certain. A gleam kindled in Abraham's eyes.
He was sincerely grateful to Seo-ha.
Had mathematics ever received this much attention over the past century? Treated only as a tool of physics and the language of engineering, mathematics had, thanks to him, stood at the center of scholarship again after so long. It was because humanity had witnessed the fact that pure mathematics could change reality.
'Perhaps he can go even farther.'
"Then first, you'll have to solve this."
Slip.
He took out a USB memory stick and handed it to Seo-ha.
"These are things that organize the research my teacher and I have done over the years. I've gathered all the unpublished papers as well."
"What? Why give this to me?"
Abraham's eyes went wide.
His teacher was Leonid Levin, the man who first proposed the P=NP theory. Abraham had earnestly wished to carry on his teacher's legacy and solve the great problem, but the materials he had left behind were treasure and trap in equal measure.
"Because they're things I can't give to anyone else. They're unfinished, so I can't publish them, and if I gave them to my students, it could ruin them."
"Then why...."
"Because you won't be deceived by them. You'll be able to pick out and use only what you need."
"...."
The sunlight beyond the window stretched down along the glass.
Before anyone noticed, the light had reached long into the office.
"I'll probably never solve this problem until the day I die. It's truly regrettable, but watching you, I came to realize it. That the truth won't open its door to someone as ordinary as me. Don't feel burdened. You can throw it away if it comes to that."
"Ah... No. Thank you!"
The meaning of a scholar handing over the entirety of his own research and his teacher's. How could he fail to understand what it signified?
Seo-ha's hands trembled as he received the memory stick.
But Abraham, for the first time in decades, felt unburdened.
He sank into rueful reflection.
'Teacher. I was far too lacking a disciple to fulfill your will. But wasn't I at least better in one respect?'
That he had found someone capable of handling Levin's eccentricity.
If Seo-ha looked inside them, he surely wouldn't hold the same grateful heart he did now.
*****
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