I Got an Omnipotent Brain

”Kids, come eat!”

Mi-young, who had woken up early to prepare breakfast, called out loudly to the children.

A moment later, Seo-ha and Seo-eun came downstairs from the second floor.

”Mom! There’s so many side dishes!”

”Why did you make so much?”

The table was stunning.

Beyond the usual side dishes, there was grilled hairtail, seasoned cockles, pan-fried tofu... dishes they hadn’t easily come across in America were laid out before them.

”If there’s anything you want to eat, just say the word!”

Mi-young took off her apron and sat down.

When she used her chopsticks to pick apart the hairtail flesh, Seo-eun opened her mouth wide.

Ahm-

”Mm, it’s so good!”

Seo-ha watched them with a contented expression.

He hadn’t been at ease for a while.

No matter how much he told them to spend money, his parents never touched his account. He had been thinking of forcing it into their hands if things seemed too hard for them, but...

”Hahaha! Honey, I’m heading to work.”

”Be safe out there.”

Both their faces were full of smiles.

All the things they had tried so hard not to show in front of their children.

The frugality, the sacrifices, the endurance.

With that weight lifted, the couple’s shoulders were visibly lighter.

”I’m off to school.”

”Mommy, bye-bye!”

The moment the front door opened, the scent of spring rushed in.

The seasons had shifted again before anyone noticed, and green leaves were sprouting on branches that had been bare.

A faint floral fragrance drifted from the garden.

”The weather’s so nice today.”

Seo-eun spread both arms wide and took a deep breath.

Seo-ha lifted his little sister up and set her on the back seat of his bicycle.

As Seo-ha pedaled, Seo-eun swung her legs behind him and sang a song she had learned at school.

”Spring is coming, flowers are warming-

Butterfly fly, across the sky-”

Seo-ha sang along silently in his head.

”Get there safe!”

Even after Seo-eun boarded the school bus, she kept waving at Seo-ha for a long time.

”Time to go.”

The closer he got to campus, the more he saw people who gave off a similar air.

Professors heading to work, students emerging from overnight experiments, researchers out for their morning exercise.

Seo-ha blended in with them and entered the campus.

”Good morning, Seo-ha.”

”Hi.”

Greetings were exchanged with passing students.

Instead of heading to the familiar math department, Seo-ha made his way toward Building 33, where the engineering departments were clustered.

Around the corner was a long corridor, and just like the other buildings at MIT, it had a magnificent chalkboard.

’Someone’s been here.’

A smile spread across Seo-ha’s face.

For the past month, Seo-ha had been carrying on a conversation with someone here. In numbers and symbols, of course.

It had started the day he visited Building 33 to meet Root.

”Oh?”

An elaborate drawing had been sketched on the chalkboard.

A thin metal plate was attached to a circular frame, with force being applied at the center.

The equations written below were an attempt to find the surface with minimum elastic energy when a load was applied.

In other words, it was asking: ’Where do you press to crumple a steel plate with the least amount of force?’

In engineering, elastic plate theory typically ends once you obtain an approximation and verify it in the lab.

’I plugged in the approximation and it works? Problem solved!’

Engineers would be perfectly happy with that level of conclusion.

But mathematicians were not.

’Why is it possible?’

’Is the most optimal model unique?’

’Does the same solution exist under all conditions?’

’Can you prove this equation holds in every case?’

They were the kind of people who could only be satisfied after finding answers to all of these questions.

He couldn’t help but smile.

Whoever this engineering student was, they apparently couldn’t stand the rule-of-thumb math that passed for standard in the engineering department.

’Maybe I’ll give them a little nudge.’

Scratch scratch.

In the situation depicted, pressing the circular plate at the center would yield a symmetric solution.

Seo-ha didn’t give the answer. He only pointed in the right direction. In a way no engineer would ever think to approach it.

He left a single small notation next to the circular frame.

「k(t)」

(kappa * a function showing the degree of curvature over time)

That should be enough.

Anyone who understood this problem would realize that a single symbol could completely change the direction of the calculation.

It was Seo-ha’s own form of consideration. He deeply disliked having someone just hand him the answer to a problem.

The next morning,

a new routine was added to Seo-ha’s day.

Stopping by Building 33 to check the chalkboard.

”Ah-.”

Seo-ha rounded the corner and let out a small sound.

The chalkboard was packed full.

From the single symbol he had left behind, this person had spent the night developing an entirely different form of Partial Differential Equation.

’This is where they got stuck.’

An elastic plate model where curvature and torsion change simultaneously.

A note had been left below.

[If we assume continuous curvature flow, torsion arises structurally. How should this part be handled?]

”So they’re someone who understands math.”

This was no ordinary engineer.

They had looked at the mathematical structure that emerged during the problem-solving process and stopped to think it through. An engineer would have been satisfied with the approximation and simply ignored inconvenient variables like torsion.

It was the kind of variable that forced you to reconsider the very existence of a solution from scratch, digging into the fundamental structure of the problem.

The equations this person had written were not in the language of engineering.

Scratch scratch.

Seo-ha picked up the chalk and left another note.

’Redefine the boundary r(t).’

Seo-ha grinned.

If torsion were included as part of the energy, the person’s dilemma could be resolved.

”The conversation probably ends here.”

Seo-ha set down the chalk.

The hint he had left was an enormously daunting one.

The world of pure mathematics, where it wasn’t even certain whether a solution existed. This person had mathematical understanding, sure, but could an engineer really follow this far?

If so, they would be a born mathematician.

The next day, Seo-ha headed to Building 33 out of habit.

He rounded the corner and stopped in his tracks.

”What an impressive person.”

The chalkboard had been filled again.

Below the hint he had left, someone’s equations were neatly laid out.

[If torsion is included as an energy term, the boundary variation expands into a third-order variational problem.

’Δκ – g(x, y, t) = 0’

Under the assumption that a solution to this PDE (Partial Differential Equation) exists, how should we proceed to the next step?]

And then, one final line at the very end.

[Let’s continue.]

Seo-ha felt the hairs on the back of his neck stand up.

Someone was walking into the dark forest of mathematics.

Relying on the faint flashlight that Seo-ha held out, he was stepping forward into a fog where nothing ahead could be seen.

”If you’ve come this far, I don’t think it matters who you are.”

Scratch scratch.

Seo-ha began writing out a proof.

Equations, arrows, curves, questions, rebuttals, hints, blanks...

The conversation continued for an entire month.

The problem that had started by asking ’Where do you press to easily crumple a steel plate?’ kept expanding.

A month later, there was no longer any trace of engineering on the chalkboard.

A path leading to the ’existence of a solution,’ a realm that engineering simulations could never reach.

It was one of the deepest unsolved problems in modern geometry.

Before anyone realized it, the chalkboard had been filled with the equations the two of them had written.

Step step.

Theo came to Building 33.

He spent a long time examining the problem written on the chalkboard.

”So this is what he’s been up to lately...”

To summarize the problem Seo-ha was working on:

’On an elastic plate that simultaneously incorporates changes in torsion (τ) and curvature (κ), given a specific boundary r(t), does a Minimal Energy Surface exist?’

”What on earth is this?”

A passing undergraduate asked, looking at Theo.

They were no slouches at math themselves, but this was on a completely different level.

”See that metal plate over there?”

Theo pointed to where their discussion had begun.

”Yeah.”

”If you push it, it bends. If you pull it, it stretches.”

”Well, obviously.”

Theo smirked.

”A steel plate can bend, twist, or stretch. Its boundary isn’t fixed either. And force doesn’t have to be applied at just one point. It could be one, or ten, or a hundred.

Under all these complex conditions, does a shape that can be deformed with the absolute minimum energy even exist?”

”Uh...”

The eyes of the student listening to the explanation went distant.

”There are people who try to solve problems like this.”

Once curvature, torsion, and boundaries were all involved, the proof would inevitably expand into a sixth-order Partial Differential Equation, or beyond.

A Free Boundary Problem.

The problem Seo-ha was dealing with was one of the most difficult areas in modern mathematics.

’If he manages to crack this one too, the world is going to lose its mind.’

It was an unsolved problem in differential geometry, but for the engineering world, it was a long-cherished goal.

The moment it was shown that a ’Minimal Energy Surface’ existed, everything from airplane wings to drone structures, fields that had relied on approximations for decades, would all have to be redesigned.

’By the way, who is this person?’

The one exchanging questions and answers with Seo-ha.

It was closer to Seo-ha’s one-sided guidance, but this person was keeping up with the complex proofs.

’I should photograph this too.’

Click.

Theo had been diligently collecting every record Seo-ha left behind.

* * *

It was several days before Seo-ha returned to Building 33.

He had been attending consecutive meetings with the transportation bureau. The signal optimization project, having completed its pilot phase, was set to expand across all of Boston before long.

’They’ve been here, as expected.’

Traces of someone’s effort to approach the existence of a solution.

Through the exchange with this person, Seo-ha had made up his mind to try solving this problem.

’Should I ask for permission?’

It was a problem that had started from a joint discussion.

It might be rude to just go ahead and work on it alone, so Seo-ha decided to leave a note asking for their understanding.

”Hm?”

As he picked up the chalk, he noticed writing in the corner.

[Who are you? A professor?]

Come to think of it, the two of them had never once asked about each other.

Crash-

The sound of someone falling over came from near the vending machine.

Seo-ha turned his head.

A student of Indian descent who looked to be in his mid-twenties.

Thin build, with slightly hunched shoulders.

He wore a worn-out backpack on his back; one strap was completely frayed, with loose threads sticking out.

”Ah...”

He looked startled when he saw Seo-ha.

Clatter.

A coffee can that had fallen from the vending machine rolled toward Seo-ha.

Seo-ha picked it up.

”Are you okay?”

When Seo-ha handed the coffee over, the young man nodded.

”Yes, I’m fine.”

A South Indian accent.

He seemed like a student who hadn’t been in America for long.

With a timid expression, he bowed deeply to Seo-ha, who was considerably younger than him.

Clothes that looked far removed from any fashion trend. A worn-out calculator sticking out of the side pocket of his backpack.

His appearance suggested someone struggling to get by.

He raised his head and quickly scanned the chalkboard.

Seo-ha instinctively knew this was the person he had been exchanging with. Seo-ha smiled brightly and extended his hand.

”I’m Yu Seo-ha. Are you an engineering student?”

Upon hearing Seo-ha’s name, the young man flinched.

”...Yes. First-year mechanical engineering master’s student. My name is Srinivasa. You can call me Sri.”

”That’s a wonderful name.”

He gave Seo-ha a puzzled look at that.

”You know what it means?”

”One in whom blessings dwell. It’s Ramanujan’s first name.”

He jolted in surprise.

”You know Sanskrit? Everyone only knows him as Ramanujan...”

Ramanujan’s full name was Srinivasa Ramanujan Aiyangar.

Srinivasa was his first name, and Ramanujan was a middle name taken from his father’s name.

”Just a tiny bit.”

”Actually, I was waiting here today hoping you might come.”

”Is there something you need?”

As if he had rehearsed the lines beforehand, he spoke in a rapid stream.

”I’d like to end our exchange after today. I wanted to thank you for answering my questions for an entire month. I was absolutely sure you were a professor...”

He wiped the can on his clothes and held it out to Seo-ha.

Seo-ha was glad to realize the young man had been thinking the same thing he had.

”Ah! So you were planning to work on it alone! I was just about to suggest the same...”

”No.”

Sri shook his head.

”What I mean is that from now on, I’m going to step away from this problem... no, from mathematics entirely.”

”What?”

As Seo-ha looked at him in bewilderment, Sri pressed his palms together and bowed his head.

”Thank you for everything. Namaste.”

In Seo-ha’s hand was the coffee can, its warmth not yet faded.

Click.

”Ugh... bitter.”

Black coffee with no milk or sugar.

It was still too early a taste for Seo-ha.

”What a shame. He loves math that much, and yet.”

He could guess the reason.

He couldn’t agree with the decision, though.

”You can make good money with math too, you know...”

Unfortunately, Sri was no longer there to hear it.