1936.
In an age when even the word “computer” did not yet exist, a twenty-four-year-old young man published a paper.
[On Computable Numbers, with an Application to the Decision Problem]
The paper’s core was simple, but its contents were revolutionary.
Turing devised an imaginary machine, the Turing machine, that moved along a paper tape, reading and writing symbols. He proved that this simple device, so long as it had the proper instructions, could perform any complex mathematical calculation in the world.
There were various electronic devices even then, but this was a concept that changed the paradigm of civilization. A universal machine that could perform any function if only its software were changed. It was the moment the theoretical mother of the computer was born.
‘Alan Turing.’
Whenever Seoha thought of him, he felt a complicated emotion.
He had not known it as a child, but only after time had passed did he realize that this had been a kind of fear.
Because Turing and he had so many similarities, as though stamped from the same mold.
As a child, Turing wondered how honeybees found their way home. He personally followed the bees around and drew maps on which he observed their routes in meticulous detail.
Seoha had done the same thing. He had spent all day in the yard following ants around, doggedly tracing the paths they took. Where they turned, at what point they hesitated, and by what standard they found their way again.
It was the same when going to school.
Turing discovered that his bicycle chain came off after a certain number of rotations. Then how was he to solve it?
Turing carried out exactly what Seoha had thought of.
Wherever he went, he counted the number of times he pedaled with precision. Then, just before the chain came off, he got down and adjusted its length.
Seoha was certain that if Turing had been born in the modern era, he would have done the same thing as him with traffic lights. He would surely have studied signal cycles and found the most efficient travel route and stride length.
He did not adapt well to school education.
Teachers disapproved of Turing, who immersed himself excessively in mathematics, saying he was indulging in intellectual vanity. But Turing, already in his teens, was teaching himself Einstein’s theory of relativity, which had only recently been published at the time.
‘Wouldn’t I have been the same if I hadn’t met my teacher?’
Turing grew up in foster care.
His father, a civil servant, had been posted to India, and his mother had also left her son behind to follow him.
What remained for him was terrible solitude and a sense of loss.
Turing sent many letters to his parents in India. In them, there was no heartfelt longing such as “I miss you.” Instead, they were filled with explanations of mathematical theorems he had newly discovered and devices he had designed himself.
Some, seeing this, judged Turing to have been a child lacking human emotion. But to Seoha, young Turing’s heart came through as clearly as if he could grasp it in his hand.
It was the only language the boy knew.
Turing must have wanted to say this to his parents.
‘Mother, Father! Look at this complex and beautiful rule! Isn’t it wonderful? Let’s talk about this together!’
But his parents could not understand those words.
Then, as if by fate, he met a friend.
Christopher Morcom.
The first person he met who fully understood his language and his inner self.
For the first time in his life, Turing must have found inner peace. But Morcom died of tuberculosis at the age of seventeen.
‘How painful must it have been?’
A salvation once tasted is far too sweet to ever return to the past.
In the letters he sent to Morcom’s mother, he often mentioned the possibility that the soul existed. And as if trying to keep the dead Morcom tethered to the world, he began to study it.
‘What would it have been like if it were me?’
He would not have been able to accept his death. Turing was the same.
What he devoted his entire life to proving.
He must have thought that what made a human being human was not the body, but the ability to think.
But if a machine could think like a human, then what, exactly, was different between a person and that machine?
Emotion, too, was nothing special to him.
Pain and pleasure, attachment and loss. If all of these were merely signal patterns responding to external stimuli, then a machine could possess them in the same way.
There was no way to know whether Turing truly thought so.
But Seoha saw in his actions a consistency others did not. He could never have given up on a being who understood and comforted him.
The result of that effort was the Turing machine.
A vessel that could contain the soul of the friend who had left him, and an expression of longing for someone who would never let him be isolated.
‘Alan Turing. I pity you.’
A universal machine was, in the end, a device that could become anything depending on what software was input into it.
If it had learned Morcom’s logic, Turing could have been with the friend who returned in a machine’s body forever.
But he was alone until his death, unbearably lonely, and in the end, at home, he bit into an apple injected with cyanide and entered eternal sleep.
This might perhaps have been the future he himself would have faced. Tears welled up in Seoha’s eyes.
Fortunately, he had been lucky.
His beloved family.
They had not left Seoha alone to sink into himself.
The affectionate gazes of his parents, and Seoeun, who would run to him with a bright smile whenever she saw him, called him back to the world of reality when he had nearly been buried in mathematics. And Seoha learned how to negotiate with his inner self in order to be with the people precious to him.
‘Hmph!’
Ducky, whose freedom had been restricted, wore a dissatisfied expression. But Seoha was more than satisfied with his own choice.
He secretly wiped away his tears with his sleeve and offered his gratitude. To everyone who had made it so that he was not alone.
At the same time, there was something he desperately wanted to prove to Turing.
The fact that machines could never replace humans.
And he wanted to tell him.
That the friend you lost was a precious being who could not be replaced by anything.
* * *
The number of viewers was soaring frighteningly.
It was an unfamiliar sight even for Massholic’s Lee Junil, who had one million subscribers.
‘Is it because the thumbnail came out so well?’
The producer who had come to the site had used a colloquium photo of Yu Seoha in a suit, instead of Junil’s scruffy face, and a shot of Sujeong today, making it look like a pictorial.
A handsome man and a beautiful woman. The composition on the screen looked like a drama poster.
As expected of a capable producer!
He clenched his fist beneath the table.
‘But she’s seriously quiet.’
After greeting them for the first time, Sujeong had been quietly looking only at the wall. The viewers were delighted, saying that even that looked like a painting, but as a broadcaster, it was not something he could simply leave alone.
He decided to try breaking the ice first.
“Ms. Sujeong?”
“Yes?”
She answered without taking her eyes off the wall.
“Ms. Sujeong, you have a very deep connection with Director Yu, don’t you?”
“Yes, that’s right.”
Perhaps because it was a topic that interested her, Sujeong finally turned her gaze and looked at him.
“I’d be grateful if you could tell us a little more about that.”
As if recalling the past, Sujeong’s eyes grew distant.
“The first time we met was at a math competition venue. Back then, Seoha—no, Director Yu—was barely a little over ten years old.”
“He was very young, then?”
“Yes, it’s an old connection.”
“You still remember something that happened ten years ago?”
“There’s no way I could forget it. It was the first day I failed to win the grand prize at a math competition.”
“Ah!”
The memory was still vivid.
“I was in middle school then, so I was young too. Everyone around me was a high school student. But then this tiny kid came trudging over and sat down in the seat next to me.”
“I can picture it.”
“When I later found out that child had won the grand prize, I was so shocked… From then on, through the IMO, science gifted high school, MIT, and Team Apex. I suppose I’ve been following Seoha all along.”
└It’s like some kind of movie. Girl meets a boy?
└No, wait, were those places you could get into just because you wanted to follow someone?
The viewers’ reactions were good.
Junil decided to draw out this topic a bit more.
“At that point, aren’t you childhood friends? Aside from family, you must have spent the longest time together.”
“That’s how I think of it.”
“As a fellow mathematician, don’t you ever feel jealous?”
Sujeong paused for a moment before answering.
“At first, it’s not as though I didn’t feel that way. I had never met anyone smarter than me before. But now, all I feel is gratitude.”
“Haha! Thank you for teaching me what defeat is. Is it something like that?”
At his playful words, Sujeong shot him a sidelong look.
“You probably won’t understand even if I explain it in words right now. But someday, I’m sure there will come a day when you do.”
Ssssk.
Seoha, having used up the whole sheet of paper, moved to the side.
Junil thought it seemed all right to move on to the main subject now.
“But what exactly happened today? Why was this event suddenly put together?”
Things that could not be understood unless one was a mathematician.
Sujeong wore a troubled expression. But soon she relaxed her face and began speaking calmly.
“Archimedes’ eureka…”
“Yes, I know! A moment of realization.”
“It’s a moment that comes to anyone, even if they’re not a mathematician. It might be a new recipe you were pondering in the morning, or a flash of musical inspiration. But in Seoha’s case, it’s a little different. Should I say the scale is larger?”
Junil looked puzzled.
“I understand what you mean, but it isn’t very specific.”
“I’ve seen Seoha fall into that state exactly twice.”
“When was that?”
Sujeong wore a meaningful expression.
“When he proved the four color theorem and the Riemann hypothesis.”
“Gasp!”
Junil covered his mouth with his hand in alarm.
└What the hell, suddenly ㄷㄷㄷ
└Are you saying today is an event on the level of the Riemann hypothesis?
└A huge event like that on this humble broadcast? Massholic hyung, did you hit the jackpot today?
Gulp.
Junil pulled his chair close and asked,
“Could you explain it to the viewers? What exactly is that formula?”
Sujeong wondered how she should explain this.
Since it was a broadcast many people were watching, it would be better to explain it in a way that caused as little ripple as possible. Saying that he was digging into a Millennium Problem would be too provocative.
“Mm?”
Seoha’s eyes had grown moist. He stood with his eyes closed for a moment, then subtly wiped away his tears with his sleeve. Then he began writing formulas with ferocious momentum.
Sujeong, who had been staring blankly at it, unwittingly let her true thoughts slip.
“In mathematics, there is a difficult problem called the P versus NP problem. It’s one of the Millennium Problems.”
Junil’s eyes widened.
“Yes! I know that one too. It’s an extremely famous problem, after all. Don’t tell me Director Yu is solving that right now?”
Sujeong shook her head.
“P versus NP is like the final boss of computational complexity theory, whose foundations were laid by Alan Turing. Seoha originally wanted to solve that problem. Probably because he wanted to guarantee Utopia’s safety. But…”
Her words trailed off. Junil felt as though he would burst with frustration.
Complex formulas were being written on the blackboard. Sujeong’s eyes moved rapidly, following them. But from a certain point, the logic leapt as though warping, and at last flew beyond the realm she could understand.
“But?”
Sujeong glared at the wall. But all she could understand was the conclusion.
“Seoha is questioning something even more fundamental than that.
Turing’s theory of computation says that machines can solve every problem humans can solve. Since there had been no counterexample until now, it was accepted as a true proposition in computer science.
But just now, Seoha said that isn’t the case.”
At the scale that had grown far too large, Junil’s mouth fell open.
Theo was just as astonished.
An intuitive conclusion that skipped over the process.
Perhaps this was how Hardy had felt when he first saw Ramanujan’s letter. And it was being broadcast to the world in 4K.
The grimoire that would later drive numerous mathematicians mad was revealed to the world in this way.