Dennis returned to the lab.
The eyes of his team members were still hazy. He stood before the whiteboard and looked at them for a moment. Then, as if he had made up his mind, he called everyone together.
“Everyone, come here for a second.”
The team members dragged their chairs over and gathered around. Dennis clicked the cap off a marker and spoke.
“It’s embarrassing to admit, but I think I was trapped in a fixed idea. It was an attitude a mathematician should never have.”
He drew a large X over the formulas written in the center of the whiteboard. The team members’ eyes widened. It was an act of denying the logical structure they had been clinging to for over a month.
“It was probably because of the prejudice that formulas scribbled impulsively in a café couldn’t possibly be right. And on top of that, they were a concept above even the Turing machine. I doubt I was the only one who couldn’t believe it.”
The impatience that they might fall behind MIT, their rival, forever.
Perhaps that had been the cause. Even Quirin, the chair professor, had not been free from this. He had believed that if they could find a flaw in Seoha’s equations, he could recover his wounded pride.
The team members’ faces turned serious.
“We were arrogant.”
“Now that I think about it, I had a shallow motive too. Because it was that Seoha, of all people. I think I mistakenly believed that if I could find even one counterexample, it would mean I was a mathematician on the same level as him.”
“Then what do we do now, Dennis?”
Once he cast aside his preconceptions, everything came into sharp focus. In Dennis’s eyes there settled an exhilaration that went beyond rational conviction. He looked at everyone and said,
“Let’s believe that the thirteen stepping stones Yu Seoha left behind are already complete. And we’ll try filling the mud in between.”
Once he said it out loud, his heart felt lighter.
As a mathematician, he had no choice but to acknowledge Seoha. He had not realized it, but denying Seoha’s formulas had weighed on him the entire time.
But not everyone agreed.
“You’re telling us to just believe? Is that mathematics?”
Carter, a promising Harvard doctoral student, raised his hand and voiced his doubt.
It was a suspicion any mathematician ought to have. In particular, he had an exceedingly stubborn personality. Even when reading a single paper, it was his habit to trace backward from the references first. If he was not convinced, he would even ignore the words of his advisor. Though that was also the driving force that had made Carter an outstanding mathematician.
‘I’m glad you’re here.’
Because he would not have to worry about whether there was someone to point it out when the team went down the wrong path.
Dennis gave a gentle smile.
“We’re not believing. The evidence has already piled up, hasn’t it? Let’s gather every attempt that failed over the past five weeks.”
A few days later.
The atmosphere in the joint task force seminar room had changed slightly.
The partition that had divided Harvard and MIT had, at some point, been pushed off into a corner.
It had happened two days earlier.
Ellie had been thinking about meaningful mathematical grounds that could reinforce Seoha’s first-stage theorem. Then she happened to glance at the board across from her. Harvard’s Carter was handling the boundary conditions of the branch point density function.
‘Hm? You too?’
His equation bore a subtle resemblance to the direction of the logic she had been about to develop.
“…”
“…”
For a while, the two alternated their gazes between each other’s boards, then silently dragged their chairs over and met in the center.
That was the beginning.
“The measure diverges here. Couldn’t this be related to the boundary conditions?”
“Right. This is what we were researching, but look at the branch point density of this functor structure. The pattern is strange to dismiss as just a singularity. It’s a structure that repeats at specific intervals.”
Without anyone needing to take the lead, the two teams mingled together.
Things like contribution had already vanished from everyone’s mind. Hugo watched them with his arms crossed.
“What’s this? Since when did everyone get so close?”
Dennis came over before he knew it and stood beside him.
“You weren’t aiming for this? That’s why you said that to me, wasn’t it?”
Hugo shrugged shamelessly.
“It’s not exactly a secret at MIT. We spent time in the same space as Seoha, after all. Of course, it wasn’t easy for me to accept this either.”
“What do you mean?”
“Mathematicians are all used to accomplishing things alone. We thought it was romantic to grab onto an unsolved problem and wrestle with it alone for years.”
“Isn’t that obvious? What’s wrong with that?”
Hugo shook his head.
“There’s nothing wrong with it. But after being by Seoha’s side, at some point that romance started to feel a little narrow. If Columbus discovered the New World, isn’t it only natural that ambitious pioneers should leap into it?”
“Hahaha!”
“It’d be a problem if people discovered new land and thought it was India. It might be the largest continent on Earth.”
“That’s quite a grand-scale story. I get what you mean when you say working alone started to feel narrow. Then shall I become the Francis Drake of the New World?”
“By all means. It won’t be easy. There are quite a few at MIT who believe in Seoha like a religion.”
“Then we’ll just be the Knights of Columbus.”
Hugo clutched his stomach and snickered.
“A knightly order, huh… For Harvard, that’s a pretty romantic sense of taste.”
Everyone was in high spirits. The more they researched, the more the data fit the hypothesis as if by magic.
Carter still did not let go of his doubts, but without realizing it, he was being drawn into Seoha’s hypothesis. Before long, his suspicion was no longer focused on denying Seoha, but on how to perfectly implement the logic Seoha had omitted in the language of modern mathematics. It was the moment when the strictest verifier turned into the most fervent supporter.
“I found it! A way to convert computational complexity into Yu-Riemann geometry!”
“We’re done over here too. The topological equilibrium state of the uncountable space came out!”
Every time someone shouted in triumph, another piece of evidence supporting Seoha’s hypothesis was added to the whiteboard.
Amid that fervor, Hugo felt a strange thrill.
Newtonian studies, or Darwinism.
The influence certain individuals had on humanity was so enormous that the person’s very name could become a field of study.
Hugo thought that perhaps “Seohaism” might not begin at MIT, his alma mater.
* * *
“Seoha! Did you see this?”
Theo hurriedly opened the office door and came in.
Seoha was sitting at his desk, reading an email from Seoeun. His younger sister was in Japan to participate in the IMO. He looked at Theo with a puzzled expression.
“What is it?”
“Just watch.”
A BBC News live stream was playing on the tablet screen.
Harvard Science Center auditorium.
Two people stood side by side on the podium.
Whitman, the dean of the MIT Department of Mathematics, and Quirin Dusk, the chair professor of the Harvard Department of Mathematics.
Click!
Click!
There were one hundred seats. Half were occupied by figures from the mathematics and computer science worlds, and the other half by reporters from science-focused media outlets such as Science, Nature, and BBC Science Focus.
It was unusual for a large-scale press conference to be held at a university on Harvard’s level. Looking back, such events had only happened when major achievements were announced, such as cold fusion at room temperature, the discovery of the Higgs boson, and the detection of gravitational waves.
The sound of the reporters’ shutters did not cease.
Beep—
When Dennis pressed the remote, the topic appeared on the screen.
“Interim Report on the Verification of Stage One of Seoha’s Thirteen-Stage Hypothesis”
“A few minutes ago, we uploaded the report to arXiv. This event is to explain the results of that paper.”
After a brief silence, he continued.
“The Harvard and MIT joint task force conducted a thorough verification of Seoha’s first-stage hypothesis over two months. The result was this.”
“Stage One Verification Result: No Errors or Counterexamples Found”
Murmur, murmur.
The audience grew noisy. Reporters rushed to raise their hands. The reporter Quirin called on had a Nature badge on his chest.
“Then are you saying Seoha’s thirteen-stage hypothesis is true?”
Quirin handed the microphone to Whitman.
“Of course not. Not yet.”
He gave a meaningful smile.
“This result is not a declaration that Seoha’s hypothesis is correct. The verification of the remaining twelve stages has not even begun, and we are well aware that each stage is an independent difficult problem. Nevertheless, the reason we arranged this event is because we felt it necessary to correct the rumors spreading throughout academia.”
Another hand went up. It was BBC Science Focus.
“As you said, the fact that no counterexample was found does not immediately constitute proof that the hypothesis holds. How large do you believe that gap is?”
This time, Quirin stepped forward and took the question.
“In the process of attempting to disprove it, a considerable outline of the mathematical conditions necessary for the first stage of the hypothesis to hold has been revealed. This will become the foundation for formal proof work in the future.”
The press seats stirred.
“Formal proof?”
“What?”
“What did the professor just say?”
Click!
Click!
The two men chose their words carefully.
It was not yet the stage where they could speak with certainty. But the nuance had been conveyed clearly. The reporters hurriedly took out their mobile phones and sent messages to their editors-in-chief.
Beep.
“How do you feel? I think human history is going to change starting today.”
Theo asked as he turned off the tablet screen.
Seoha smiled faintly and shook his head.
“Turing’s theory has now fulfilled its role. It’s simply time for humanity to move on to the next stage.”
It would have been fine for him to feel a little proud, but Seoha was still looking toward the future.
Theo studied Seoha’s complexion, then spoke hesitantly.
“How is your body?”
Seoha had returned from a long vacation.
On the surface, it had been a reward for successfully developing Utopia, but the reality was different. After he returned from the café that day, his condition had visibly deteriorated.
Seoha quietly averted his gaze and said,
“I’ve gotten a lot better. The hospital said there’s nothing wrong too, so you don’t have to worry too much.”
“That’s what worries me more.”
Theo’s expression darkened.
Seoha could not bring himself to tell him that it was something he had brought upon himself.
That day, Seoha had stayed up all night at home, holding onto the formulas.
From stages one to seven, he could see the path. Establishing the theory and proving all the auxiliary lemmas would require considerable effort, but it did not seem impossible.
The problem, however, lay in the stages after that.
The bridge connecting stage seven and stage eight. When his thoughts reached that domain, structures began unfolding inside his mind.
‘Something is different?’
Seoha usually saw formulas with his eyes. Not as numbers, but as phenomena.
But this time was different.
He could not keep up with the speed at which they unfolded. One premise extended ten branches, and each of those branches split again into countless limbs, all appearing simultaneously.
‘The simultaneity of uncountable space?’
It was a concept he himself had defined.
There was no order. Cause and effect, too, existed in the same place.
Seoha stopped thinking.
The deeper he went, the more he felt as though his self as Yu Seoha was fading. It was uncanny. Like peering into the operating system of the universe created by God.
He tried to take a deep breath. But as if his lungs had shriveled, he could not breathe properly.
“Huff, huff!”
Ducky abruptly poked his head out and said,
‘Looks like it’s finally my time to step in.’
“You’re already helping me.”
Ducky smiled beneath the mask, showing white teeth.
Seoha thought he had seen that face of his somewhere before.
‘I’m saying help alone won’t let you see it. I will! Without you, I’ll do it on my own.’
“What?”
‘Over there!’
Ducky pointed with the tip of his finger to one side of the desk.
Seoha’s head turned with a creaking sound.
A beaver doll wearing a duck mask.
‘Take that off and put it on your face. Then you’ll be able to see the principles of the universe without restrictions.’
Seoha’s eyes widened.