I Got an Omnipotent Brain Chapter 86

Translator: Dreamscribe

"Excuse !"

Theodore slid down the corridor at a sprint.

Every ti he rounded a corner, his loose-fitting coat flapped like wings.

"Watch out!"

"Hey, no running!"

"What's with that guy?"

Students scrambled out of the way to avoid colliding with him.

[Looking for Chalkboard Cleaning Volunteers - Please note that all chalkboards will be wiped clean at 6 PM :)]

"Damn it."

The smiley face on the wall poster seed to be mocking him.

As he turned the last corner, he spotted students wearing green aprons. They were pushing out enormous industrial brushes while wearing masks that looked like oxygen respirators, apparently custom-made by the school. The sight was terrifying.

It was as if they were ready to erase everything without leaving a single trace.

Screeeech, screeeech.

"Wait!"

Theo spread both arms wide and blocked their path.

"You can't erase anything right now! There's a very important research sketch on the chalkboard down that hallway."

Apron A narrowed his eyes.

"I've never seen your face before. Who are you?"

"Theodore Langford, Stanford Mathematics Departnt."

"...That na sounds familiar."

"If you study math, of course you've heard of it. Look it up later and be impressed. For now, just give ten, no, twenty minutes!"

Apron B shrugged.

"That's a problem. If the schedule gets pushed back, the next team has to wait too."

In that instant, Theo's patience ran out.

"Then wait a little!

Is you guys waiting ten or twenty minutes really more important than a critical proof in mathematical history being erased?"

The students flinched at Theo's outburst.

"No, that's not what we were saying...."

"Fine. We'll take a break here for a bit."

Theo went to the departnt office and borrowed a high-resolution cara.

The equipnt manager stubbornly refused to lend gear to a student from another school, but Theo persuaded him by explaining that he needed to docunt Seo-ha's notes, and eventually the man handed over the expensive cara.

"All done now?"

When he returned, Seo-ha was standing in front of the chalkboard in the sa pose as before.

He frowned as if dissatisfied with the theorem he had just written, then resud the equation with a serious expression.

His carefree deanor made Theo feel like he was going to burst with frustration.

In the brief ti he had stepped away, an entire panel of the chalkboard had been covered with equations.

Theo scanned the board with his eyes.

Fortunately, it was content he had seen sowhere before.

"The theorem you're writing right now...."

"Yes."

Seo-ha answered without turning around.

"It resembles an approach Smale once attempted."

Smale was a mathematician who had received the Fields dal.

Theo felt complicated emotions toward this young mathematician whose logic bore resemblance to that giant of twentieth-century analysis.

"I don't think this path is wrong."

He was more stubborn than he looked.

Then again, with a brain like that, it was only natural.

"Really? Smale gave up in the end, you know. When the domain twists, the derivative vanishes."

Theo gave him a subtle hint.

The reason Smale had failed was that the space he had tried to handle was not entirely homogeneous.

In a space where the domain is curved, differentiation cannot express the rate of change.

When curvature arises, the tangent formulas at each point beco misaligned.

No matter how smoothly a function is connected, if the directions of those tangent lines are inconsistent, attempting to average the rates of change only introduces vectors from different directions that cancel each other out.

A sense of doubt struck him for a mont. Could Seo-ha really not know sothing he himself knew?

'He must already know this....'

Seo-ha nodded and continued the theorem. Then, as if it were nothing at all, he tossed out a single remark.

"I'm planning to make the domain not curve in the first place."

For a mont, Theo doubted his own ears, wondering if he had misheard.

"What?"

"Rather than unfolding the space, I'll adjust the density so it appears flat. By changing the coordinate system itself."

Theo felt as though the breath had been knocked out of him.

Adjusting the density of a space ant redefining the very asure of a topological space in which curvature exists.

To flatten the curvature of a space, one would need to assign different weights and deformation rates to each individual point.

In other words, one would have to rewrite the tric tensor (a mathematical tool that defines distance and angle in a space) for every coordinate that constitutes the space.

If even a single point's error occurred in that process, the continuity of the entire function would collapse. Geotrically, the space would beco not a surface but torn fabric.

'Riemannian geotry, calculus of variations, probability theory, asure theory, and topological invariants, all used simultaneously.'

The process was so dizzying it made his head spin. He had no confidence he could accomplish it even if he spent a lifeti.

From the boy who was doing all of this as though it were nothing, Theo felt sothing close to fear.

'Can this truly be an ability permitted to a human being?'

There was always a good reason why an unsolved problem remained unsolved.

Every great unsolved problem stood at the threshold of a domain beyond the reach of human thought.

That was why, by nature, these were places that rejected human approach, sanctuaries of the mind, so to speak.

But this boy was trying to go there now. Without any preparation, he was walking in with bare feet, trampling through the holy ground without hesitation.

"Is it really possible?"

Instead of answering, Seo-ha began writing new equations on an empty section of the chalkboard.

From this point on, even Theo could not easily follow along. But he thought he understood what Seo-ha was trying to do.

"I've only sketched it out for now, but I think it'll roughly work."

'Sketched it out? That? He thinks it'll roughly work?'

His brain felt like it was overloading from trying to process such absurd words.

But he had no ti to be confused.

Screeeech, screeeech.

The sound of wheels rolling toward them.

Apron A adjusted his mask and waved at Theo.

"Ti's up! We need to get to work too. We've got a lot of assignnts to do tonight!"

Several additional mbers had joined them from behind.

Two massive brushes entered the hallway side by side.

Seo-ha waved at them too.

“Okay! I’ll clean it up now!”

Seo-ha smiled innocently. Then he picked up the eraser and moved to wipe away the "sketch" he had just written.

In that instant, sothing snapped inside Theo's head.

"No!"

A roar like a lion's erupted and echoed through the corridor.

Grab.

Theo reflexively seized Seo-ha's wrist.

"What do you think you're doing?"

"Shouldn't I erase it? Those people must be busy too...."

Seo-ha pointed at the apron crew.

"Do you even know what you're about to erase?

This is a problem Smale devoted his entire life to and never solved. Dozens, hundreds of mathematicians threw themselves at it, and none of them could crack it.

And you're going to erase it just because it's cleaning ti?"

Seo-ha blinked.

"Uh.... No, that's not it. The content is all in my head anyway."

"Every last detail? Can you really be certain that nothing would be lost if you erased it?"

Overwheld by Theo's intensity, Seo-ha unconsciously took a step back.

When Theo turned around, the students holding the brushes gulped.

But contrary to what they expected, Theo smiled gently and pulled a credit card from his wallet.

"Hey! Friends. You've been working hard. Can I buy you all a coffee?"

The volunteers' faces lit up.

"Sure, we'd love that."

"Perfect timing. We were desperate for so caffeine."

"That'd be great, thanks!"

Theo smirked and gave them a pat on the shoulder.

"Go get coffees and sandwiches for everyone. anwhile, I'll sort all this out with that kid over there. By the ti you're done eating, we should be ready for you to start."

Seo-ha was impressed by how smoothly he handled it.

‘Oh! He’s a grown-up.’

There was a mature, composed ease to Theo's actions that spoke of soone well-versed in navigating the world.

"...."

Once they left, the hallway fell silent.

Theo's expression shifted in an instant as he pulled out the cara. His hands trembled slightly as he removed the lens cap.

Click.

Theo began photographing.

He divided the chalkboard vertically into sections, numbered them, and shot each one in sequence.

"The bottom right corner was the starting point."

"Good."

Click, click.

As he took photos, Theo ntally reconstructed the logical progression of Seo-ha's work.

After staring at it for hours, the flow ca to him naturally. The theorem was far more sophisticated than he had expected.

"So here, setting the density as w(x) and averaging the rate of change.... Ah! That's why you substituted it into a probability space to find a fixed point."

Seo-ha nodded.

"Yes, I believe a fixed point must exist. Though I haven't completed the full proof yet."

Click.

"Listen carefully. When you're researching sothing, you must always leave records.

mory fades with ti, and intuition that feels obvious today may never co back again."

Click.

Whether it was from personal experience, his words carried a peculiar weight of conviction.

"Gauss was reluctant when it ca to publishing papers. Even with non-Euclidean geotry, he already understood the principles but never published them.

How many years did the developnt of geotry end up being delayed because of that?"

Theo could never bring himself to like people such as Newton and Gauss.

Newton's eccentricities were well known, but Gauss was no ordinary person either. Of all his research, at most twenty percent had actually been published as papers. The rest vanished from the world entirely with his death.

“Such irresponsible people.”

'To waste a God-given mind like that.'

Whether or not Seo-ha could read Theo's thoughts, he looked at him with a resolute expression and spoke.

"Yes! If I ever make an important discovery, I'll make sure to present it to the academic community."

'What?'

Didn't that imply he would just throw away anything he deed unimportant?

Theo was certain Seo-ha had not understood what he ant. The way these people thought was sothing entirely beyond the comprehension of an ordinary person like himself.

Seo-ha gazed at the chalkboard.

He stood before the theorem he had written, his expression showing not a shred of doubt.

Click.

Theo captured one last photo, this ti of Seo-ha's face.

Laughter from the students drifted in from the end of the corridor.

“Coffee’s here.”

“Bagels are okay, right?”

It seed like he would be eating bagels quite often during his ti here.

* * *

"Co on in."

Seo-ha guided Theo to his research office.

Since Theo was an outsider, he had nowhere else to rest.

"Nice office."

Theo looked around as he entered.

"They told to use it only until the project is finished, but the deputy director said it would take several years."

Thud.

Theo sank into the sofa.

He was exhausted.

It had truly been a long day.

“Would you like so cold water?”

Theo's gaze, which had been scanning the room, stopped at one spot.

A few crumpled sheets of paper were sticking out from beside the trash can.

"What's this?"

He reached over.

[Dynamical Center of a Function]

Surprise flickered across Theo's eyes.

This was a formula defining the point that minimizes the second derivative, the position where a function changes most uniformly.

Seo-ha saw it and spoke as if making an excuse.

"Oh! That's sothing I thought of while researching an points. I was just doing it for fun."

"Damn it...."

Theo clutched his head.

"This is an idea that could later be extended to oscillation stability of nonlinear functions. It's the kind of problem that would be considered significant even in physics."

Why did God love these absentminded geniuses so much?

He truly resented the heavens.