It had been an enjoyable time.
For Seoha, the sight of mathematicians gathered in one place was a novel experience as well.
After the dean’s speech ended, the first session began.
Under the title “Unsolved Problems and Young Researchers,” the panelists each spoke candidly about their failures.
An elderly professor said,
“I wasted four years clinging to Fermat’s Last Theorem. When Andrew Wiles proved it, one part of me felt relieved, and another part was left hollow.
It took me another three years before I could pursue other research. No matter what I did, I couldn’t find the will for it.
So, everyone, choose an unsolved problem if you must, but do not allow it to swallow your life.”
Clap, clap, clap!
Applause burst out.
As the sound died down, a middle-aged professor slowly took the microphone.
Adrian Keller.
It was a name Seoha knew well.
“When I was young, I once challenged the Riemann Hypothesis. At the time, I believed it was my destiny. But years passed with no results.
At home, I was a nonexistent person. My wife grew exhausted raising our child alone, and I grew thinner and thinner, staying up all night in the laboratory. I thought if I pushed just a little further, something would emerge.”
He opened a bottle and took a sip of water.
“For most researchers who pursue unsolved problems, a particular moment comes. The moment when they must decide when to stop.
In the end, I chose my family, and even now I believe that choice was right.
But it is painful. Because I still think about the Riemann zeta function every day. Even when I enter the lecture hall and teach calculus to students, even when I eat dinner with my family.”
He looked around at the participants with deep-set eyes.
“This is what I consider the most wretched form of failure. I sincerely hope that all of you will become better researchers than I was. With that, I will conclude.”
A brief silence fell. Then quiet but heavy applause spread through the hall for a long time.
“Do you regret having challenged the Riemann Hypothesis?”
Someone asked.
The professor, who had been returning to his seat, turned back.
“What pains me is not the Riemann Hypothesis itself. It is the fact that I faced it and came to know my own limits.
Sometimes, even knowing you will be broken, you still want to throw yourself at a problem. Many mathematicians of the past went through such a process and left us clues like dying messages.
What torments me is my cowardice in not even having had the courage to do that.”
The intent of this session was clear.
Do not chase unsolved problems simply for honor or reward.
And yet, someone would surely choose that path regardless.
For that was the essence of mathematics as a discipline, and it had advanced by using humanity’s tenacious curiosity as its driving force.
That was why the professors were asking the young researchers gathered here a question.
“How much are you prepared to bear?”
It was a session that gave Seoha much to think about as well.
Break time.
The participants scattered in small groups into the lobby and hallways.
A long line formed in front of the coffee machine, and every small table was filled with the murmuring of researchers holding cookies and cups.
Seoha filled a paper cup with water, took a sip, and then walked toward the end of the hallway. He wanted to get away from the crowded people.
After walking for a while, he saw the professor who had just come down from the stage sitting on a bench in a corner at the end of the corridor.
As if troubled over something, he was bent forward with his head in both hands.
‘Is he ill?’
Just as Seoha was about to pass by without thinking, he heard the man’s voice.
“Yu Seoha?”
Seoha turned around.
“Elijah Cronen called me. He said you were challenging the Riemann Hypothesis and asked me to give you advice that might help.”
“You know Professor Elijah?”
“We were once in the same laboratory.
I’m sorry I couldn’t be of much help. Still, thanks to Cronen, for the first time I was able to confess my true feelings in front of people.”
Seoha felt sorry to see him suffering.
Though he was a researcher who had left behind considerable achievements, he himself could not acknowledge them and regarded himself as a failure.
“Professor Adrian.”
He was ashamed.
“I have read all of your papers, Professor. Your attempt to approach the distribution of the zeros of the Riemann zeta function from statistical and analytic perspectives was remarkably fresh.
In the process, there were results, but at the same time, I realized that it led to a dead end. And because of that, I became convinced that probability theory and the language of physics must be brought in together.”
Perhaps he had never imagined that Seoha would have read his papers. Adrian lifted his head and stared blankly at him.
“Your research was a great help in setting the direction I should take. You have already left behind valuable research for those who come after you. At the very least, I have clearly received it.”
Adrian’s eyes reddened.
“I see. I see... So my research wasn’t completely meaningless after all.”
Seoha stepped away to give him some time alone.
No mathematician can stand alone.
Had not even the great Newton confessed that his achievements were thanks to the mathematicians of the past?
Even if they fail to reach the summit, mathematicians desperately leave behind traces of their existence. And those traces become footholds for the next generation.
Within the papers Seoha had read all this time were the pain and frustration of countless authors.
Once that thought came to him, Seoha was able to steady his heart again.
‘No matter when it happens, I will solve it.’
The longing in his chest was growing ever stronger.
* * *
An old residential district on the outskirts of Boston.
Thud.
“Thank you.”
Seoha got out of the taxi and looked around.
The cold winter wind brushed between the bricks with a low whine. Holding a small map in his hand, Seoha walked down a narrow alley.
In a neighborhood where even the faded signs had been painted over several times, Seoha found his destination in a corner.
Beeeep.
When he pressed the doorbell, a creaking sound came from inside. A moment later, heavy footsteps approached.
Click.
As the old door opened, a chilly smell drifted out. The smell of paper, dust, and old books. It felt as though he had come to a used bookstore.
“Come in. You’re far younger than I expected.”
Deep wrinkles and graying hair.
Mikhail Orsen looked at Seoha with a surprised expression.
“Hello, Professor.”
When Seoha bowed his head, Orsen let out a subtle smile and opened the door wide.
“Come in. To come all the way to a shabby place like this—youth truly is reckless.”
The inside of the house was like a small library. Piles of books and notebooks that seemed to reach the ceiling, along with bundles of faded papers, occupied the tables and the floor.
“Sit.”
When Seoha sat down carefully, the old sofa creaked.
Drip, drip.
Orsen brought an inexpensive coffee pot from the kitchen and served instant coffee.
“Now tell me. How on earth did you know of me and come looking?”
Orsen’s voice was low and rough. He sounded like someone who had not conversed with others in a long time.
Seoha opened his bag and began taking out papers one by one.
[A Study on the Zeros of the Riemann Zeta Function and Spectral Statistics]
[A Study on the Correlation Between Quantum Chaos and the Distribution of Primes]
[Chaotic Eigenvalues and the Critical Line Hypothesis]
[On the Mathematical Interpretation of the Hilbert-Pólya Operator]
Each time Seoha placed a paper on the table, Orsen’s complexion grew paler. In the end, he closed his eyes and let out a deep sigh.
“These are studies I found interesting. I noticed that all of these authors cited your papers, Professor Orsen.”
With stiff hands, he picked up the papers and turned over the covers.
“They are old colleagues and students of mine. Besides them, there were researchers who left out citations out of fear their papers would be rejected in peer review. I don’t resent them. Everyone has to make a living.”
Orsen had studied the relationship between quantum chaos and the Riemann Hypothesis for a very long time.
But this was now a theory on the verge of being discarded.
Research funding would no longer come.
Orsen trailed off, then brought out a small cardboard box from inside the room. On the side of the box, written in marker, were the words:
「R - Flow / Discarded」
A theory interpreting the Riemann zeta function as a flow, and likely a box gathering the discarded ideas among them.
When he opened the lid, Seoha saw it filled with yellowed calculation sheets, printed graphs, and notebooks with worn covers. Scribbled notes were attached in every margin.
“What do you think of Riemann’s hypothesis?”
He stared at Seoha with piercing eyes. Seoha felt he understood what the man wanted to confirm.
“Professor, I do not see the zeros of the Riemann zeta function as a static structure. They are moving waves.”
Seoha thought.
The reason great mathematicians had failed to prove it for nearly two hundred years.
Perhaps it was because the zeros of the Riemann zeta function were not “fixed points,” but fleeting instants when oscillation ceased on the complex plane.
At Seoha’s words, Orsen’s body trembled.
The theory he had wanted to argue for his entire life.
There had been several preliminary presentations and private responses of approval, but every time it had been submitted for formal review to major journals, it had been rejected on the grounds of “irreproducible” and “insufficient evidence.” He had carefully gathered all of those into the cardboard box.
Bang!
Orsen slammed his palm down hard on the table.
“Yes! That’s exactly what I meant! How can you explain a flowing river by looking at a picture?”
Orsen spent a long time explaining to Seoha why he had come to think this way.
From how he first drew inspiration from the saying that the distribution of primes was like music, to an anecdote about helping with a resonator experiment in graduate school.
He was talkative.
Once his mouth opened, words poured out without end, as if he were venting years of resentment. Seoha quietly listened to all of his pent-up anger and regret.
He took an old printout from the box and spread it on the floor.
Each sheet had small circles and arrows drawn on it. Above them, handwritten notes such as “spacing,” “repulsion,” and “GUE (Gaussian Unitary Ensemble * a statistical model that appears in random matrix theory)?” were densely written.
“But there is no proof.”
He let out a deep sigh.
“That was not a domain I could handle. With my ability, I could neither predict its movement nor quantify it.
My life’s research proves that much. That this is as far as I go.”
Seoha was glad that a researcher who had thought the same way as him existed. The purpose of coming all the way here had already been fulfilled.
“I enjoyed today. It was truly a great help.”
He had to return to the hotel before the steakhouse closed. Seoha rose from his seat.
“Hmm?”
Orsen blinked at him as he was about to leave.
“Yes?”
“Did you not come because you needed my research materials?”
There was confusion and disappointment mixed in his voice.
“Your papers have already helped me greatly. I was simply curious what kind of person you were, Professor.”
A smile spread across Orsen’s lips.
He took out a notebook from the bookshelf. Time could be felt in its old leather cover.
“This is the last notebook I wrote. I never managed to publish it as a paper. I got cancer.”
“Ah...”
As Seoha grew flustered and tried to find words of comfort, Orsen shook his head.
“All my life, I envied geniuses. I kept thinking, ‘If only I had a mind like theirs, I could have solved this.’
But now, I am grateful that a genius like you has taken an interest in my theory. I do not know whether it will be of any help, but please do not refuse it.”
He placed the notebook into the cardboard box and held it out to Seoha.
Seoha hesitated for a moment, then accepted the box. Then he bowed deeply to the old professor.
“Thank you.”
That night, Orsen quietly offered a prayer to a God he had never sought in his life.
Please, let me live only until I can see that boy’s growth.