Clap, clap, clap!
The applause would not stop. The heat in the room was like that of a concert hall. Before the semester had even begun, the lecture hall he had expected to be quiet was packed without a single empty seat.
Excited voices of students could be heard from all around.
“Seoha! Welcome to Texas!”
“Could you teach at our school?”
“You’re handsome!”
A kindly looking professor stood at the lectern with a pleased smile. It was Professor Abraham Fisher, a Wolf Prize laureate and the pride of the University of Texas mathematics department. Looking at Seoha, he spoke in a playful voice.
“Welcome, young genius. Forgive the discourtesy. Because of the single email you sent, our undergraduates haven’t been able to sleep for a week.”
‘Ah!’
Only then did Seoha grasp the situation.
Professor Abraham had shown tremendous interest in the email he had sent. Then he had asked for permission to share it with his undergraduates.
Seoha had said it was fine without thinking much of it, but he had never imagined it would turn into something this big.
With a bewildered expression, Seoha walked toward the front of the lecture hall.
“Your question was truly fascinating. Thanks to you, we had an enjoyable week as well.”
Seoha glanced at the blackboard.
[Is evolution strong evidence against P=NP?]
It was the question he had asked.
The fact that living organisms had evolved through four billion years of trial and error—did that not in itself deny the existence of a P algorithm that could find the correct answer all at once?
In his paper, Professor Abraham had said this:
“The DNA division and replication system of living organisms is the most powerful example of how P=NP operates in the real world.”
Cell division, which occurs when life is born, involves a number of cases greater than the number of atoms in the universe. And yet nature finds the optimal structure in mere seconds and creates 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 can imitate. Life systems have already freely surpassed the wall we call NP.”
As Seoha read that part, a question had arisen in his mind.
The major evolution of life is generally achieved through mutations. Slowly, through billions of years of trial and error. If P was NP, shouldn’t life have achieved perfect evolution from the very beginning?
As he walked down the aisle, Seoha glanced sideways at the desks where the students were seated.
Papers underlined with highlighters and covered in sticky notes. Computational complexity textbooks, and even printouts of Wikipedia screenshots clearly searched up in a hurry.
Just as Professor Abraham had said, the signs of intense study were unmistakable.
“Come on up here.”
Before he knew it, Seoha had gone all the way up to the platform.
The students’ admiring gazes felt burdensome. It had not been planned, but Seoha steadied himself.
What academic field had drawn the most attention in the world over the past few years? Mathematics. The phenomenon of students favoring mathematics was not something happening only in Korea.
Various media outlets such as newspapers, television, and YouTube had highlighted Seoha from many angles.
The significance of his mathematical achievements, the expectations of what might change because of them, and gossip about just how much money he had made.
Naturally, people were deeply interested in money, and there were no small number of programs that focused only on that and churned out sensational content.
[The Teenager Who Earned the Most Money in History]
[A Billionaire Just from Doing Math?]
[How Much Will Yu Seoha Earn in Royalties Over His Lifetime?]
Seoha was indifferent to the media’s behavior, and MIT did not impose any particular restrictions as long as Seoha’s image was not harmed. Since MIT was also receiving attention because of him, there was even a tendency to secretly enjoy it.
But that alone could not explain the phenomenon taking place throughout the developed world.
The fundamental reason students had come to favor mathematics was that the value of mathematicians had skyrocketed.
The competition rate for Ivy League mathematics departments had already surpassed that of medical and engineering schools. Prestigious engineering universities in Europe were also showing moves to elevate pure mathematics into an independent college.
Every student’s eyes were fixed on Seoha.
Seoha took a deep breath, then slowly opened his mouth.
“Nice to meet you, everyone. My name is Yu Seoha.”
Clap, clap, clap!
Thunderous applause.
The students looked at him with expectant eyes.
“We held a discussion with the undergraduates on the topic you raised. Life, evolution, and mathematics. As people walking the path of mathematics, is it not a question we ought to ponder? In the process, there were a few questions we could not resolve. That is why everyone was waiting for you here.”
They were students with tremendous passion. Even though it was vacation, not a single one of them showed any sign of complaint.
Seoha looked down at his own clothes.
Jeans and a white T-shirt. If he had known something like this would happen, he would at least have put on a shirt.
“Thank you for welcoming me.
I can fully feel from the heat in this lecture hall just how fiercely Professor Abraham and all of you spent the past week. As the one who first raised the topic, I would also like to take part in the discussion.”
In contrast to the overwhelming volume of media coverage, Seoha had barely been exposed to the public.
Was that why? Countless rumors about him circulated.
Among them, the rumor that Seoha almost never met people was accepted as established fact. The reason given was that there were almost no people in the world with whom he could hold a conversation. Therefore, the image they had of Seoha was that of a socially inept genius.
“Shall we speak openly with one another? I’m also curious what answers the talented students of the University of Texas will present.”
Smiles spread across the students’ faces.
The Seoha they saw in person was far from the rumors. He was around their age, dressed similarly to them. He looked almost like any student one could see anywhere on campus.
And yet anyone could feel it.
The confidence that could only be shown by someone of overwhelming intellect, and at the same time, the composure to be considerate of others, could be glimpsed in his bearing. Someone bravely raised a hand first.
“First, thank you for visiting our university. Doctor… Ah! You’ve received the Fields Medal, but you’re not a doctor yet, are you?”
Hahaha!
Laughter burst out here and there at the student’s joke.
“Seoha! I understand that you reject P=NP. If so, how should we explain the process of cell division in living organisms, which finds answers at an abnormally rapid speed?”
Low murmurs of agreement broke out throughout the lecture hall.
Professor Abraham was also watching Seoha with interest. Seoha smiled faintly and began writing formulas in one corner of the blackboard.
“In other words, your argument is that ‘life knows the answer.’ …Am I right?”
The students nodded.
“But if a magical algorithm called P=NP truly existed in the universe, then immediately after the birth of the first single-celled organism, life would have leapt at once into a highly intelligent organism optimized for its environment.”
A blond female student seated in the very front row shot her hand up.
“Then isn’t that a contradiction? It is a fact that cells perform an enormous amount of computation in a fleeting instant.”
The student’s expression seemed genuinely curious.
It was interesting.
Seoha’s voice rose slightly in pitch.
“That is why I thought about an answer that is not a contradiction. I had planned to discuss that with Professor Abraham today.”
When Seoha glanced to the side, the professor gave a playful shrug.
“Professor Abraham focused on the efficiency shown by the replication system of life. But I would like to point out its errors. If it were truly a flawless law, then no errors whatsoever should exist.”
The lecture hall fell silent.
“But what is reality like? Life is constantly wrong. Mutations, deformities, cancer. Even normal replication is not perfect.”
Then what on earth was the conclusion?
The students tilted their heads. Looking at them, Seoha slowly opened his mouth.
“I hypothesize that cell division is not the result of computation.”
Seoha drew a picture on the blackboard.
“Let us assume there is a sieve shaped like this. It is similar to the tool used to sift flour when making desserts.
Using this, we can obtain fine flour without calculating the size of the particles. This is not mathematics. But what about the result?
I wondered whether perhaps cells go through a process similar to this. Not computation, but physical filtering—the structure itself filters out impossible cases from the start.”
Murmurs spread among the students.
“Whoa!”
“If that’s the case, doesn’t it actually explain everything?”
“I disagree. It’s only a hypothesis. It could be that the theory and calculations of nature are perfect, but errors occur in actual application.”
“I think it’s right, though? There isn’t a single contradiction in the explanation!”
“It’s in a completely different direction from our professor’s, isn’t it?”
From their reactions, Seoha felt a strange sense of incongruity.
It felt as though Abraham had invited him here hoping he would refute his own argument. When Seoha looked at the professor, Abraham nodded as if asking him to do just that.
A student sitting in the back carefully raised a hand.
“Mister…”
“Please call me Seoha.”
It seemed there was no suitable title for him, since he was neither a professor nor a doctor—not even a master’s degree holder.
“Seoha, then how should we explain the many similar structures found in nature? After countless trials and errors, will they all arrive at the same optimal solution?”
It was evidence that had lent weight to the claim that P=NP.
Fractal structures, the Fibonacci sequence, the golden ratio. They were patterns that nature repeatedly created. Nature had been using the same answers again and again since before humans existed.
Seoha hesitated for a moment.
Should he make a serious argument to undergraduates? But he, too, wanted to repay their pure passion.
“First, let me make clear that this is my personal view.”
At the change in his expression, the atmosphere grew heavy.
“Nature does not seek the optimal solution. It has never even tried to. The universe is simply trying to survive. This is how I see the discipline of mathematics. Amid those billions of years of traces, the result called order was left behind, and mathematics is the discipline that discovers it.”
The impromptu seminar ended.
Seoha answered questions until the students no longer raised their hands. Once their doubts had been resolved, the students poured out casual questions like, “So do you have a girlfriend?”
There were also many students who brought newly published introductory texts on Yu-Riemannian geometry and received his autograph.
The pure intellectual passion of undergraduates.
Having been away from school for a while because of his military issue, Seoha felt as though he could breathe freely here for the first time in a long while. His own name printed on the book cover felt unfamiliar. At some point, Professor Abraham had quietly approached his side.
“What do you think? The University of Texas.”
“It was far more impressive than I expected.”
“Have you any thoughts of giving lectures here?”
“The dean won’t allow it.”
Professor Abraham laughed loudly.
“Hahaha! I said the same thing to Dean Whitman, and he cursed at me for more than ten minutes.”
The two of them slowly walked to the office.
A teaching assistant brought in coffee he had carefully brewed. He kept stealing glances at Seoha’s face. It was obvious from his expression that he was trying hard to suppress his excitement.
“First, let me apologize.”
As soon as they sat down, Professor Abraham bowed his head deeply to Seoha. At the unexpected action, Seoha was at a loss and waved his hands.
“No, not at all. I was the one who suddenly sent you an email when we had never even interacted before.”
“No, please accept my apology. It was improper.”
“…Was there a special reason?”
He let out a groaning sigh.
“Students are profoundly influenced by their teachers. In any field, that is unavoidable. That is why I am truly afraid.”
“…”
“They are barely around twenty years old. They are easily swayed by the opinions of others. All the more so when the words come from me, a Wolf Prize laureate and chair professor; they have a tendency to accept them without any criticism. That is why I wanted someone authoritative to come and tell them that mathematics is not actually like that. It is something I cannot do myself.”
“Do my words have that much authority?”
Abraham looked dumbfounded.
“You’ll have a hard time of it soon enough, too. Once you stand at the lectern, you’ll be faced with hordes of students writing down your lectures as if they were the words of Socrates.”
“I’ll be careful.”
“I’m sure you’ll do well. You’re a cautious man. You held your tongue earlier, didn’t you?”
“Pardon?”
“Over billions of years, the result called order remained. The meaning implied by those words.”
Seoha’s eyes widened.
But soon he looked at him and nodded.
“I believe there exists a single principle that runs through that order.”
“Hohoho. You’re even worse than I am.”
Superstring theory, once a leading candidate, had failed to produce even a single scientific prediction. After that, mathematics and physics had essentially given up on it. It was thought either not to exist, or at the very least, to be beyond the reach of present-day mathematics.
“It definitely exists.”
Seoha’s face was full of conviction. A strange light entered Abraham’s eyes.
He was sincerely grateful to Seoha.
Had mathematics ever drawn this much attention in the past century? Mathematics, treated only as a tool of physics and the language of engineering, had returned to the center of scholarship because of him. It was because humanity had witnessed pure mathematics changing reality.
‘Perhaps it may be able to go even farther.’
“Then first, you’ll have to solve this.”
Smoothly.
He took out a USB flash drive and handed it to Seoha.
“These are整理整理 the research my teacher and I have done all this time. I’ve gathered all the unpublished papers as well.”
“What? Why give this to me?”
Abraham’s eyes opened wide.
His teacher was Leonid Levin, the first to propose the P=NP theory. Abraham had wanted desperately to carry on his teacher’s will and solve the problem, but the materials he left behind were both a treasure and riddled with traps.
“Because they’re things I cannot give to anyone else. They’re unfinished, so I can’t publish them, and if I gave them to my students, they might ruin them.”
“Then why…”
“Because you won’t be misled. You’ll be able to pick out only what you need and use it.”
“…”
The sunlight outside stretched along the window.
Before they knew it, the light had reached deep into the office.
“I likely won’t be able to solve this problem before I die. It is truly regrettable, but watching you has made me realize something. Truth will not open its door to the likes of me. Don’t feel burdened. If need be, you may throw it away.”
“N-no. Thank you!”
The meaning of a scholar handing over both his teacher’s research and his own. How could Seoha fail to understand it?
Seoha’s hand trembled as he received the flash drive.
But for the first time in decades, Abraham felt lighthearted.
He sank into regret.
‘Master. I was far too inadequate a disciple to fulfill your will. But perhaps, in at least one respect, I was better.’
He had found someone capable of handling Levin’s eccentricities.
Once Seoha looked inside, he surely would not feel as grateful as he did now.