So I Solved the Riemann Hypothesis

A weekly magazine reporter asked for an interview, and when I readily agreed, this was the kind of article they put out.

[The young rising star of the mathematics world, 28-year-old genius professor Shin I-jun. He takes on humanity’s greatest unsolved problem, the Riemann Hypothesis!]

Seeing the article spouting all kinds of hype—'century's genius,' 'the hope of Korean mathematics'—I frowned.

It was true that, from other people's perspective, my career history might look flashy.

Early graduation from science high school, three years completed as an undergraduate at Seoul National University. While studying in the U.S. for my doctorate, I published three top-tier papers in a row, and the moment I returned, my alma mater handed me a professorship. That was when I was 26.

At a glance, I was definitely an easy target for reporters.

That still didn't make this kind of substance-free article acceptable...

"Professor, I saw the magazine. You came out looking great."

I turned toward the voice behind me.

"Ah, Seol-ae."

Han Seol-ae.

The only graduate student in my lab right now, and the student I cared for most.

She came over carrying two cups of coffee.

"Not very well. They asked me to explain the research I'm working on, and I kindly did, but that reporter cut all of that part out."

"It's a magazine, not an academic journal. Readers aren't interested in anything too difficult; they're more interested in the professor's face and credentials. You’re probably secretly pleased, too, Professor."

"Well, I've never really cared about public opinion or other people's approval, so I wouldn't know."

"Really? If I ended up in a piece like that, I'd probably cut it out and keep it as a family heirloom."

I've never really yearned for other people's approval in my life. Maybe I was just born that way.

Unless I'm reborn, changing this personality would be impossible.

I chatted with Han Seol-ae for a bit, then took a sip of the coffee she handed me.

The bitter caffeine woke my brain up.

"By the way... about the master's thesis you wrote, Seol-ae."

"Yes, Professor."

Han Seol-ae had just finished her master's program and passed her thesis defense without a hitch.

Her research paper explored an original topic that combined topology and algebraic geometry. I was impressed by the ideas in it.

"An approach that leverages homology under these conditions... that's refreshing. It'd be a shame to just let this result go. Let's polish it and submit it to an overseas journal."

As expected, Han Seol-ae's talent was real. She had the ability to see directions others couldn't.

If she kept studying here, she'd be able to write top-tier papers.

"Let's prepare the next paper right away. Next month is the doctoral application period, right? Have you prepared the documents?"

At my question, Han Seol-ae's expression stiffened a little. Unlike usual, today she seemed somewhat hesitant.

"Professor, actually, I have something I need to tell you."

"Go ahead. If it's about scholarship money, I'll do whatever I can."

She parted her heavy lips and said,

"I... I'm going to put off going on to a doctorate for now. After finishing my master's, I've decided to take a break from studying for a while."

It was an unexpected answer. When she joined the lab, she'd said in her own words that she wanted to go all the way to a doctorate.

"May I ask why? It can't be because the research is too hard."

"I've decided to have a child. I talked it over with my husband, and if not now, the timing just won't work."

"Ah... I see."

Han Seol-ae is married, and her husband is someone I know very well.

A friend of ten years, from the same high school as me.

In other words, before she was my student, she was my friend's wife.

"So it was a decision you made together with Jin-hu. I'll support you both."

I sent my congratulations, but Seol-ae's voice trembled ever so slightly.

"I'm sorry. If it were up to me, I'd want to go straight into a doctorate and keep studying... but honestly, I don't have the confidence to juggle a PhD while giving birth and raising a child. I don't want to neglect my child because of my own selfishness, either. So I've decided to put off enrolling."

Her voice carried the apology of someone who felt she'd disappointed me.

I wondered what I should say, looked out the window for a moment, and then finally spoke.

"Seol-ae, have you ever heard of Sofia Kovalevskaya?"

"Huh? No, I haven't. I don't know her well."

"She was a 19th-century Russian female mathematician. She, too, gave birth to a daughter and put mathematics aside for five years. She had a research gap at an important time, and even drew disapproving looks from the people around her. But five years later she returned to academia, became a professor at Stockholm University, and left a historic mark in differential equations."

Han Seol-ae looked at me in surprise.

"Mathematics doesn't run away. It will be there, waiting for you until you come back. So don't apologize. Becoming a mother is just as valuable as doing mathematics—no, maybe even more so."

"Professor..."

"If you ever want to study again later, come back anytime. I'll make sure your spot is waiting for you. The lab door is always open. Even if it's not my lab, as long as it's within my reach, I'll help you."

"Thank you, Professor. Thank you so much."

Han Seol-ae's eyes reddened.

She bowed her head and expressed her thanks.

✒️✒️✒️

"Seol-ae, congratulations on graduating."

When I handed over the bouquet, Seol-ae smiled brightly.

The graduation gown and mortarboard suited her quite well.

It felt like just yesterday she was looking exhausted in the lab, revising her master's thesis all night, and now she was already graduating. It was deeply moving.

"Thank you for everything, Professor Shin I-jun. I was able to make it through safely thanks to you."

"Think nothing of it. It was because you did well, Seol-ae."

Han Seol-ae scratched her head awkwardly. Just then, someone from behind seized my shoulder.

"Hey, Professor Shin! Long time no see?"

"What, you came?"

Yoo Jin-hu.

My best friend of ten years, whom I'd known since high school, and Han Seol-ae's husband.

And he was also the one who had recommended my lab to Han Seol-ae.

Suddenly, I remembered when she'd first come to apply to my lab.

I had been flustered when my friend's girlfriend showed up for the interview, but after seeing her passion and talent, I accepted her as a graduate student, and that's how things led to the present.

Jin-hu handed Seol-ae the bouquet and chatted with her in a relaxed, friendly way.

"Looks good. I'll take a photo of the two of you as a couple. Strike a pose."

"Oh, thanks. Make sure you take a good one."

When I picked up the camera, Yoo Jin-hu and Han Seol-ae pressed close together and struck a pose.

Click!

Seen like this, they were a perfect match.

A child born between two such good-looking people would surely be blessed with beauty as well.

The thought crossed my mind.

After the graduation ceremony ended, Jin-hu came over and asked quietly,

"I-jun, want to grab a drink later? Just the two of us?"

"What are you talking about? It's Seol-ae's graduation today, so you should take better care of Seol-ae. Otherwise you'll get in trouble."

"It's fine. I already got permission from my wife."

At Jin-hu's words, Seol-ae nodded with a gentle smile.

"It's okay, Professor. Please go with my husband. I have to stop by my parents' place today, too."

That punk Jin-hu. So he was excited about drinking because his wife was going to her parents' house.

"Really? Then... sure, let's drink."

When I agreed, Seol-ae gave us a light wave and left first.

"Then I'll head home first. Don't stay out drinking too late, okay?"

✒️✒️✒️

"Cheers—"

The draft beer glasses clinked together with a crisp sound.

The cold liquid cooled my throat pleasantly.

As Jin-hu picked at the macaroni side dish and ate, he asked,

"How's it been lately? Busy?"

"Yeah, it's the end of the semester, so I'm swamped. Between handling Seol-ae's graduation paperwork and the first-years' final exams... just thinking about grading already makes my head hurt."

"Even a genius professor hates grading, huh?"

"Genius or not, do you know how much grunt work it is to catch every little wrong number? I just want to focus on my own research."

Jin-hu chuckled and gulped down his beer.

"So now it's vacation. What are you going to do? Head to an overseas conference or something?"

"No. I'm not going anywhere this break. Looks like I'll be doing nothing but research."

"Don't tell me you're going after that Riemann... thing again?"

"The Riemann Hypothesis."

I answered seriously. Jin-hu made a face and shook his head.

"Hey, didn't some mathematician go schizophrenic trying to solve that? Take it easy. You're really going to fry your brain if you keep this up."

"But this time it really feels different. All last semester, there was something in my head I could almost grasp. I'm going to hole up in the lab for these next three months and focus on that alone."

"Really? Well, if it's something a smart guy says, it must be different."

Jin-hu thought for a moment, then suddenly spoke with a serious expression.

"I just remembered, if the Riemann Hypothesis gets solved, won't Bitcoin crash?"

"Huh?"

"The Riemann Hypothesis is that unsolved problem about the secret of primes, right? Since modern cryptography is based on primes, if the secrets of primes get cracked, supposedly not just Bitcoin but the whole encryption system would collapse? I saw that in a documentary."

"What are you talking about... that's all conspiracy theory. Modern cryptography isn't so weak that it would collapse from one paper."

"Really? Either way, it would be a source of fear for investors trying to manage risk. That's enough. Crypto isn't a field that runs on reason, after all. Anyway, if you solve it, make sure to tell me first. I'll short Bitcoin. What are friends for?"

"Haa... fine. Enough about me—what about you lately?"

Jin-hu paused for a moment, then scratched his head bashfully.

"Actually, I got promoted at the company this time."

"Oh, really? Congratulations. As expected of Yoo Jin-hu."

"Thanks to that, I think I can raise one or two kids without trouble. So my wife decided to focus on childcare with peace of mind, too."

"That's good. You were worried about money so much before; now you can finally breathe easy."

I felt happy too when something good happened to my friend.

We started drinking beer one after another in high spirits.

"Have you thought of a name for the baby?"

At my question, Jin-hu sighed deeply as if he'd been waiting for it.

"Hmm... that's actually the biggest headache. If it's a boy, my wife gets to choose, and if it's a girl, I do... but I just couldn't decide. I narrowed it down to a few candidates, though..."

"Naming is always the hardest part."

"Hey, I-jun. Since we're at it, why don't you pick one for me? You're the smartest one among our classmates, after all. If a smart guy names the baby, maybe our kid will be born smart too."

"What right would I have...? It only means something if the parents choose it."

I waved him off, but Jin-hu kept insisting.

"Come on, just pick one! I'll show you the candidate list. Here, look."

Jin-hu opened the memo app on his smartphone and handed it over. There were a dozen or so girls' names listed there, showing the care he'd put into it.

I reluctantly scanned the screen.

After thinking for a moment, I pointed at one of the names on the list.

"Personally, A-yeon looks good. Yoo A-yeon. It has a clear, intelligent feel to it, which I like. Second place goes to Yoo A-rin."

"A-yeon? Yoo A-yeon... Yoo A-yeon... Nice! I like it too. That's decided!"

"I'm just giving my opinion, and you're the one who has to keep agonizing over it in the end. Are you even listening? Hey!"

In the end, Jin-hu ignored me completely and sent Han Seol-ae a KakaoTalk message saying he'd decided on the baby's name.

"Haa..."

I started feeling a little guilty about having named my friend's child on a whim.

I couldn't help imagining the day when a daughter named A-yeon would be born and realize that her name had been chosen not by her parents, but by me—and at a drinking party, of all places. Just imagining it was terrifying.

And so our drinking went on until late at night, and we left the place pleasantly tipsy.

✒️✒️✒️

Vacation started, and the campus grew quiet.

After my only student graduated and left, the lab felt much wider and quieter than usual.

Labs that research statistics or applied mathematics are popular, so they're always packed with graduate students, but pure-math labs aren't popular, so few people apply.

Because of that, having a place like this with nobody in it isn't rare.

I didn't feel lonely.

On the contrary, I was glad to have three months to immerse myself completely in my research.

[All nontrivial zeros of the Riemann zeta function have real part one-half.]

To prove this proposition written on the whiteboard, I kept trying all kinds of approaches.

Delivery food piled up at my door, and I lived on the sofa in a cycle of short naps.

A quick look in the mirror showed I was a complete mess.

A scruffy beard and sunken eyes.

But my mind felt clearer than ever before.

I tried rewriting the equations with the Mellin transform, then the Fourier transform, then twisting them with Cantor integrals.

Undeterred by hundreds of thousands of failures, I kept going.

Then, one dawn in the third month, at 4 a.m.

In the pitch-dark lab, with only the desk lamp shining on the paper.

I suddenly let out a dry laugh.

"...No way."

I had derived a self-adjoint operator that matched the explicit formula and trace formula of the Riemann zeta function exactly.

In other words, I'd found evidence that the Riemann Hypothesis was true.

No way, it had to be a coincidence.

I shook my head back and forth.

Then I furiously wrote out the equations and checked them again.

But no matter how many times I verified it, I couldn't get a result showing that I was wrong.

In other words, the only result left was that I was right.

"For real?"

I solved the Riemann Hypothesis? By finding this one operator?

I actually succeeded in finding what no one had found in 160 years?

To put it another way, it was like finding a single needle in a vast desert.

Of course, it required a deep understanding of modern mathematics, relentless determination to find it no matter what, and all the luck heaven could bestow.

I had succeeded at the needle hunt that everyone had failed at for those 160 years.

At the very pinnacle of modern mathematics.

One of the seven great mathematical problems, each with a $1 million prize.

One of them.

I.

solved it.

I wiped my sweat-soaked face with my hand.

"Heh, huh-hahahahahaha!"

A laugh laced with ecstatic joy slipped out between my fingers.

I quickly organized the insights flooding my mind before I forgot them and uploaded them to my personal cloud.

And before that ecstasy had even faded,

I felt a pain in the center of my chest, as if it were being tightly squeezed shut, and toppled to the floor.

"Kuh!"

The cold tile floor touched my cheek.

My arm went numb, and my vision blurred.

My chronic heart condition had, of all times, flared up at this worst possible moment.

No. Not yet. I have to tell the world about this. How did I find it... I can't let this equation disappear.

"I... can't... die... like this..."

But regardless of my will, strength drained from my body and my vision began to go black.

✒️✒️✒️

When I came to, everything around me was pitch-dark.

I couldn't move my body properly, and it felt suffocating and frightening.

So, without realizing it, I instinctively burst into tears.

"Waaah!"

The sound that came from my mouth was different from the voice I knew as my own.

Panicking, I tried to clamp my mouth shut, but I couldn't stop crying on instinct.

Then suddenly a bright light stabbed at my eyes, and someone lifted me up with warm hands.

"Congratulations! It's a healthy daughter."

I tried to open my eyes, but my eyelids were too heavy.

After a long while, when I finally managed to open them, I was in someone's arms.

"A-yeon... thank you for being born healthy."

I saw a face looking down at me, smiling brightly with tears in her eyes.

And that face, and that voice, belonged to someone I knew very well.

'Oh, Seol-ae?'

"Hng, hng-eh?"