“Kids, come eat!”
Miyeong, who had risen early to make breakfast, called the children in a loud voice.
A moment later, Seoha and Seoeun came down from the second floor.
“Mom! There are so many side dishes!”
“Why did you make so much?”
The dining table was splendid.
Besides the side dishes they often ate, there was grilled hairtail, seasoned cockles, pan-fried tofu... Dishes that were not easy to find in America had been laid out.
“If there’s anything you want to eat, just tell me anytime!”
Miyeong took off her apron and sat down.
As she picked the flesh from the hairtail with her chopsticks, Seoeun opened her mouth wide.
Ahh—
“Mmm, it’s delicious!”
Seoha watched them with a contented expression.
His heart had not been at ease all this time.
No matter how much he told them to spend money, his parents had not touched his account. If things seemed too hard, he had even thought of forcing money into their hands...
“Hahaha! Honey, I’m off to work.”
“Get there safely.”
Both their faces were filled with smiles.
The things they had tried not to show in front of their children all this time.
Frugality, giving up, endurance.
With the burden lifted, the couple’s shoulders looked much lighter.
“I’m off to school.”
“Mom, bye-bye!”
When they opened the front door, the scent of spring came rushing in.
Before they knew it, the season had changed again, and green leaves were sprouting on the bare branches.
A faint floral fragrance drifted from the garden.
“The weather’s nice today.”
Seoeun spread both arms wide and breathed in.
Seoha lifted his little sister and set her on the back seat of the bicycle.
As Seoha stepped on the pedals, Seoeun 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—”
Seoha sang along with the song in his heart.
“Get there safely!”
Even after Seoeun boarded the school bus, she looked at Seoha and waved for a long time.
“Shall I get going now?”
The closer he got to campus, the more people there were with a similar air about them.
Professors on their way to work, students coming out after all-night experiments, researchers out for morning exercise.
Seoha mingled with them and entered the campus.
“Good morning, Seoha.”
“Hi.”
He exchanged greetings with passing students.
Instead of the familiar math department, Seoha headed for Building 33, where the engineering departments were clustered.
Past the corner was a long corridor, and like other buildings at MIT, it had a fine blackboard.
‘So they came by.’
A smile spread across Seoha’s face.
For the past month, Seoha had been exchanging conversations with someone here. In numbers and symbols, of course.
It had begun the day he visited Building 33 to meet Root.
“Huh?”
An intricate drawing had been drawn on the blackboard.
A circular frame with a thin metal plate attached, and a force applied at its center.
The equations written below were an attempt to find the surface with the minimum elastic energy when a load was applied.
In other words, it was a problem asking, “Where should one press to dent the metal plate with the least force?”
In engineering, elastic plate theory usually ended with finding an approximation and verifying it in the lab.
‘We put in the approximation and it works? Problem solved!’
Engineers would be happy enough with that conclusion.
But mathematicians were not.
‘Why is it possible?’
‘Is the most optimal model unique?’
‘Does the same solution exist under all conditions?’
‘Can we prove that this formula holds in every case?’
They were a breed that could only be satisfied after finding answers to all of those questions.
He laughed.
The engineering student who had written this formula seemed unable to tolerate the rule-of-thumb mathematics commonly used in engineering.
‘Shall I help just a little?’
Scratch, scratch.
In the situation shown in the drawing, pressing the circular plate at the center would yield a symmetrical solution.
Seoha did not give the answer. He merely indicated the correct direction. In a way engineers would never use.
He left a small symbol beside the circular frame.
「κ(t)」
(kappa * a function showing the degree of bending over time)
This should be enough.
Because anyone who understood this problem would realize that a single symbol completely changed the direction of the calculation.
It was Seoha’s own form of consideration. He hated it when someone told him the answer to a problem.
The next morning,
a routine was added to Seoha’s day.
Stopping by Building 33 to check the blackboard.
“Ah.”
As Seoha turned the corner, he let out a small sound.
The blackboard was filled densely.
With the single symbol he had left behind, this person had spent the whole night developing a completely different form of partial differential equation.
‘They got stuck here.’
An elastic plate model in which curvature and torsion changed simultaneously.
A note had been left underneath.
[Assuming continuous curvature flow, torsion occurs structurally. How should this part be handled?]
“So they were someone who understood mathematics.”
They were not just an engineer.
They had seen the mathematical structure that emerged in the process of solving the problem and stopped the formulation. If they had been an ordinary engineering student, they would have been satisfied with obtaining an approximation and ignored an “inconvenient variable” like torsion.
After all, it was a variable that dug so deeply into the fundamental structure of the problem that one had to reconsider the existence of a solution from the beginning.
The equations he had written were not the language of engineering.
Scratch, scratch.
Seoha picked up the chalk and left another note.
‘Redefine the boundary r(t).’
Seoha smiled brightly.
If torsion were included as part of the energy, his concern could be resolved.
“This will probably be the end of the conversation.”
Seoha set down the chalk.
The hint he had left was extremely burdensome.
The world of pure mathematics, where it was uncertain whether a solution existed at all. Though the person had mathematical understanding, could he, as an engineer, really follow this far?
If so, he would be a born mathematician.
The next day, Seoha headed to Building 33 out of habit.
He turned the corner and stopped walking.
“What an impressive person.”
The blackboard had been filled again.
Beneath the hint he had left, someone’s equations had been neatly developed.
[If torsion is included as an energy term, the change in the boundary expands into a third-order variational problem.
‘Δκ – g(x, y, t) = 0’
Assuming that a solution to this PDE (partial differential equation) exists, how should we proceed to the next stage?]
And one final line written at the end.
[Let’s continue.]
Seoha felt the hair on his head stand on end.
Someone was walking into the dark forest of mathematics.
Relying on the dim flashlight Seoha shone, he was stepping 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.
Seoha began writing down the proof.
Equations, arrows, curves, questions, rebuttals, implications, blanks...
The conversation continued for a month.
The problem that had asked, “Where should one press to make the metal plate dent easily?” gradually expanded.
A month later, there was no longer any trace of engineering left on the blackboard.
A path leading to the “existence of solutions,” an area that could never be known through engineering simulations,
a difficult problem belonging to the deepest reaches of modern geometry.
Before long, the blackboard was filled with the equations they had written.
Step, step.
Theo came to Building 33.
He spent a long time examining the problem written on the blackboard.
“So this is what you’ve been doing lately...”
Summarized, the problem Seoha was solving was this.
‘In an elastic plate that includes simultaneous changes in torsion (τ) and curvature (κ), when a specific boundary r(t) is given, does a minimum-energy surface exist?’
“What on earth is this?”
An undergraduate passing by asked Theo.
They were no slouches when it came to mathematics either, but this was a problem on another level.
“You see that metal plate over there?”
Theo pointed to the place where their discussion had begun.
“Yes.”
“If you push it, it bends, and if you pull it, it stretches.”
“That’s obvious.”
Theo chuckled.
“A metal plate can bend, twist, or stretch. The boundary of the metal plate isn’t fixed either. Force can’t only be applied in one place. It could be one point, or ten, or a hundred.
Under such complicated conditions, does there even exist a shape that can be deformed with the absolute minimum energy?”
“Uh...”
The eyes of the student listening to the explanation grew distant.
“And there are people who try to solve problems like this.”
Once curvature, torsion, and even boundaries were included, the proof could only expand into a sixth-order partial differential equation, or beyond.
A free boundary problem.
The problem Seoha was handling was one of the most difficult areas in modern mathematics.
‘If he solves even this, the world will be in an uproar.’
This was a difficult problem in differential geometry, but in the engineering world, it was a long-cherished task.
Because the moment it was revealed that a “minimum-energy surface” existed, fields that had depended on approximations for decades, from airplane wings to drone structures, would all have to be redesigned.
‘By the way, who is this?’
The person exchanging questions and answers with Seoha.
It was close to one-sided guidance from Seoha, but he was following this complex proof.
‘I’ll have to take pictures of this too.’
Click.
Theo was diligently collecting every record Seoha left behind.
* * *
Only after several days did Seoha return to Building 33.
It was because he had recently had to attend consecutive meetings at the Department of Transportation. The signal optimization project, which had now finished its pilot, was soon to be expanded across all of Boston.
‘As expected, they came by.’
Traces of efforts to approach the existence of a solution.
While conversing with him, Seoha had made up his mind to try solving this problem.
‘Should I get permission?’
It was a problem that had begun from a joint discussion.
It might be rude to say he would do it alone, so Seoha decided to leave a note asking for understanding.
“Huh?”
As he picked up the chalk, he saw words written in the corner.
[Who are you? A professor?]
Come to think of it, the two had never asked about each other.
Crash—
There was the sound of someone falling over near the vending machine.
Seoha turned his head.
An Indian student who looked to be in his mid-twenties,
thin, with hunched shoulders.
He was carrying an old backpack on his back, and one strap was completely frayed, threads sticking out.
“Ah...”
He looked startled to see Seoha.
Rattle.
A can of coffee that had fallen from the vending machine rolled toward Seoha.
Seoha picked it up.
“Are you all right?”
When he handed him the coffee, the man nodded.
“Yes, I am all right.”
A South Indian accent.
He seemed like a student who had not been in America long.
With an intimidated expression, he bowed deeply to Seoha, who was much younger than him.
Clothes far removed from fashion, an old calculator stuck in the side pocket of his backpack.
His appearance suggested financial hardship.
He raised his head and quickly scanned the blackboard.
Seoha intuitively knew that he had been his conversation partner. Seoha smiled brightly and held out his hand.
“My name is Yu Seoha. Are you an engineering student?”
At the sound of Seoha’s name, his shoulders flinched.
“...Yes. First-year master’s student in mechanical engineering. My name is Srinivasa. You may call me Sri.”
“That’s a good name.”
At Seoha’s words, he looked puzzled.
“Do you know what it means?”
“The one in whom blessings dwell. It was Ramanujan’s given name.”
He was startled.
“You know Sanskrit? Everyone would only know 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 little.”
“To tell the truth, I was waiting today in case you came.”
“Did you need something?”
As if the sentences had been memorized in advance, he spoke quickly.
“I intend to make today the last day of our questions and answers. I wanted to thank you for answering my questions for an entire month. I was certain you were a professor...”
He wiped the can on his clothes and held it out to Seoha.
Seoha was pleased, thinking that he had had the same thought as him.
“Ah! You were planning to try solving it on your own! I was just thinking the same thing...”
“No.”
Sri shook his head.
“I mean that from now on, I will take my hands off this problem... no, off mathematics.”
“What?”
To the puzzled Seoha, he pressed his palms together and bowed his head.
“Thank you for everything, namaste.”
In Seoha’s hand was the can of coffee, still not yet cold.
Click.
“Ugh... Bitter.”
Black coffee without milk or sugar.
It was a taste still too early for Seoha.
“What a shame. When he likes mathematics that much.”
He could guess the reason.
Though he could not agree with his thinking.
“You can make a lot of money with mathematics too...”
Unfortunately, Sri could not hear him.