Chapter 216

Translator: Dreamscribe

Dennis came back to the research room.

His team members' eyes were as dull as ever. He stood in front of the whiteboard and looked at them for a moment. Then, as if he had made up his mind, he called them all together.

"Everyone, come over here for a second."

The team dragged their chairs across the floor and gathered around. Dennis flicked the cap off a marker with a click and spoke.

"It's embarrassing to admit, but I think I'd fallen into a fixed way of thinking. That's the one attitude a mathematician should never have."

He drew a huge X across the equations written in the center of the whiteboard. His team's eyes went wide. It was an act that rejected the entire logical structure they'd been clinging to for over a month.

"It must have come from the assumption that an equation someone scribbled off the cuff in a café couldn't possibly be right. And on top of that, it was a concept that sits above the Turing Machine, of all things. I doubt I was the only one who couldn't bring himself to believe it."

The anxiety that they might fall behind their rivals at MIT for good.

Perhaps that was the real cause. Even Quirin, a Distinguished Professor, wasn't free of it. He'd believed that if he could expose a flaw in Seo-ha's equations, he could recover his wounded pride.

The team's faces turned serious.

"We were arrogant."

"Now that I think about it, I had a petty motive of my own. Because it's Seo-ha, of all people. I suppose I'd talked myself into thinking that if I found a counterexample, it would make me a mathematician on his level."

"So what do we do now, Dennis?"

Once the preconceptions were gone, everything came into focus. Something more than rational conviction rose in Dennis's eyes, a kind of exhilaration. He looked at all of them and said,

"Let's assume the thirteen stepping stones Yu Seo-ha left behind are already complete. And our job is to pack the mud in between them."

Saying it out loud put his mind at ease.

Any mathematician had no choice but to acknowledge Seo-ha. He hadn't been aware of it, but denying the man's equations had been weighing on him the entire time.

Not everyone was of one mind, however.

"Just believe it.... Is that mathematics?"

Carter, Harvard's promising doctoral student, raised his hand and voiced his objection.

It was the sort of doubt a mathematician ought to have. He was excessively stubborn by nature, especially. Even when reading a single paper, he had a habit of tracing the references backward. If something didn't convince him, he'd disregard it even coming from his own advisor. That was the very thing that had made Carter an outstanding mathematician, though.

'I'm glad you're here.'

With him around, there was no need to worry about whether anyone would speak up when the team wandered down the wrong path.

Dennis smiled gently.

"It's not about belief. The evidence has already piled up plenty, hasn't it? Let's gather together every attempt that failed over the past five weeks."

A few days later.

The joint TF seminar room looked a little different.

The partition that had divided Harvard from MIT had, at some point, been shoved off into a corner.

It had happened two days earlier.

Ellie had been puzzling over what meaningful mathematical grounds could reinforce Seo-ha's Step 1 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 equations bore a subtle resemblance to the direction of the logic she was trying to develop.

"...."

"...."

The two of them spent a while looking back and forth between each other's boards, then wordlessly pulled their chairs over and met in the middle.

That was how it started.

"The measure diverges here. Couldn't that have something to do with the boundary condition?"

"Right. This is something we worked on. Look at the branch-point density of this functor structure. The pattern's too strange to just write off as a singularity. It repeats at fixed intervals."

Without anyone leading the way, the two teams blended together.

Things like credit had already vanished from everyone's minds. Hugo watched them with his arms folded.

"What's this? When did everybody get so friendly?"

Dennis had come up beside him at some point.

"Don't tell me you weren't aiming for this. That's why you said what you said to me, isn't it?"

Hugo shrugged, playing innocent.

"It's not exactly a secret at MIT. We spent time in the same room as Seo-ha, after all. Of course, it wasn't easy for me to accept either."

"What do you mean?"

"Mathematicians are all used to getting things done alone. I used to think there was something romantic about grappling with an open problem by yourself for years."

"Isn't that just how it is? What's wrong with that?"

Hugo shook his head.

"Nothing's wrong with it. But once I'd spent time around Seo-ha, at some point that romance started to feel a little narrow. If Columbus discovered a new continent, isn't it only natural for ambitious pioneers to throw themselves into it?"

"Hahaha!"

"You've found a whole new land, and it's a problem if everyone goes on thinking it's India. When it might be the largest continent on Earth."

"That's a grand way to put it. I see what you mean about working alone feeling narrow. In that case, maybe I'll be the Francis Drake of the new continent (Sir Francis Drake, the famous 16th-century English pirate and explorer)?"

"Be my guest. It won't be easy. There are more than a few people at MIT who believe in Seo-ha like a religion."

"Then we'll just have to be the Knights of Columbus."

Hugo clutched his stomach, snickering.

"A knightly order.... That's pretty romantic taste, for Harvard."

Everyone was buzzing with excitement. The more research they did, the more the data fell into line with the hypothesis, almost absurdly so.

Carter still hadn't let go of his doubts, but without realizing it he was being drawn into Seo-ha's hypothesis. Before long, his doubt was no longer aimed at refuting Seo-ha; it was focused on how to render the logic he'd omitted perfectly in the language of modern mathematics. It was the moment the most exacting verifier turned into the most fervent supporter.

"I've got it! A way to substitute computational complexity with Yu-Riemann Geometry!"

"We're finished over here too. We've got the topological equilibrium state of uncountable space!"

Every time someone let out a cheer, one more piece of evidence supporting Seo-ha's hypothesis went up on the whiteboard.

In the middle of that heat, Hugo felt a strange thrill run through him.

Newtonian studies, or Darwinism.

The influence certain individuals had on humanity was so vast that their names themselves became fields of study.

Hugo found himself thinking that 'Seohaism' might not begin at his alma mater, MIT, after all.

* * *

"Seo-ha! Have you seen this?"

Theo threw open the office door and hurried in.

Seo-ha was sitting at his desk, reading an email Seo-eun had sent. His younger sister was over in Japan to compete in the IMO. He looked up at Theo with a puzzled expression.

"What is it?"

"Just look."

A BBC News live stream was playing on the tablet screen.

The grand auditorium of the Harvard Science Center.

Two men stood side by side on the podium.

Whitman, Dean of the MIT mathematics department, and Quirin Dusk, Distinguished Professor of mathematics at Harvard.

Click!

Click!

There were a hundred seats. Half were filled by people from the mathematics and computer science communities, and the other half by reporters from science publications like Science, Nature, and BBC Science Focus.

A large-scale press conference at a university of Harvard's standing was an unusual event. Looking back through the years, they'd been reserved for results of real weight, cold fusion announcements, the discovery of the Higgs boson, the detection of gravitational waves.

The reporters' shutters never stopped.

Beep-

Dennis pressed the remote and the topic appeared on the screen.

「Interim Report on the Verification of Step 1 of Seo-ha's 13-Step Hypothesis」

"A few minutes ago, we posted the report to the arXiv. This conference is to explain the findings of that paper."

After a brief silence, he continued.

"Over the course of two months, the joint Harvard-MIT TF carried out a rigorous verification of Seo-ha's Step 1 hypothesis. This was the result."

「Step 1 Verification Result: No Errors or Counterexamples Found」

Murmur, murmur.

The audience grew restless. Reporters raised their hands, each trying to get in ahead of the others. The one Quirin called on wore a Nature badge on his chest.

"So are you saying that Seo-ha's 13-Step Hypothesis is true?"

Quirin passed the microphone to Whitman.

"Of course not. Not yet."

He gave a meaningful smile.

"This result is not a declaration that Seo-ha's hypothesis is correct. Verification of the remaining twelve steps hasn't even begun, and we are well aware that each step is an independent open problem in its own right. Even so, we arranged this conference because we felt it was necessary to correct the rumors circulating through academia."

Another hand went up. BBC Science Focus.

"As you said, failing to find a counterexample isn't itself proof that the hypothesis holds. How wide would you say that gap is?"

This time Quirin stepped forward to take the question.

"In the course of attempting to disprove it, the outline of the mathematical conditions required for Step 1 to hold has largely come into view. That will serve as the foundation for formal proof work going forward."

The press section stirred.

"Formal proof?"

"What?"

"What did the professor just say?"

Click!

Click!

The two of them said no more.

It wasn't yet the stage where they could speak with certainty. But the nuance came across plainly enough. Reporters hurriedly pulled out their phones and fired off messages to their editors.

Beep.

"How does it feel? I get the sense human history is going to change from today onward."

Theo asked as he switched off the tablet screen.

Seo-ha smiled faintly and shook his head.

"Turing's theory has served its purpose. It's simply time for humanity to move on to the next stage."

He could have allowed himself a little pride, but Seo-ha was still looking ahead.

Theo studied Seo-ha's face, then spoke as if hesitant.

"How are you feeling these days?"

Seo-ha had come back from a long leave.

Officially it had been a reward for the successful development of Utopia, but the truth was otherwise. Ever since he'd come back from the café that day, his condition had noticeably declined.

Seo-ha glanced away as he answered.

"I'm much better. The hospital says there's nothing wrong, so there's no need to worry so much."

"That's exactly what worries me."

Theo's expression darkened.

Seo-ha couldn't bring himself to tell him that he'd brought it on himself.

That day, Seo-ha had stayed up all night at home, wrestling with the equations.

From Steps 1 through 7, he could see the road. Establishing the theory and proving every lemma would take considerable effort, but it didn't look impossible.

The trouble lay in the steps after that.

The bridge connecting Step 7 to Step 8. The instant his thoughts reached that territory, a structure began unfolding inside his head.

'Something's different?'

Seo-ha normally saw equations with his eyes. Not as numbers, but as phenomena.

This time was different.

He couldn't keep pace with the speed at which it unfolded. A single premise sent out ten branches, and each of those branches split again into countless more, all of it visible at the same instant.

'Simultaneity of Uncountable Space?'

It was a concept he had defined himself.

There was no order to it. Cause and effect occupied the same place as well.

Seo-ha stopped thinking.

The deeper he went, the more he felt his sense of self as Yu Seo-ha thinning away. It was bizarre. Like peering at the operating system of a universe God had created.

He tried to draw a deep breath. But his lungs felt shriveled up and the air wouldn't come.

"Huff, huff!"

Ducky suddenly poked his head out and said,

'Looks like it's finally my turn, doesn't it?'

"You're already helping me."

Ducky grinned, baring his white teeth beneath the mask.

Seo-ha had the feeling he'd seen this face of his somewhere before.

'What I'm saying is that help alone won't let you see it. Me! Without you, I'll do it on my own.'

"What?"

'Over there!'

Ducky pointed at one corner of the desk with a fingertip.

Seo-ha'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 with nothing holding you back.'

Seo-ha's eyes went wide.

*****

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