Proving the Riemann Hypothesis
Regardless of how people might react to her proof of the Riemann Hypothesis, Yoo A-yeon picked up the microphone and began her lecture. Her cute, bright voice rang out loud and clear across the entire auditorium.
Yet the words coming from the mouth of this adorable little girl were anything but childish.
“First, since some of you may not specialize in number theory, I’ll start from the definition of the Riemann zeta function! The Riemann zeta function looks like this!”
Her small, delicate hand gripped the chalk.
Tap-tap-tap.
On the blackboard, in the cute handwriting one might expect from a child, appeared formulas that would be difficult for non-specialists to understand.
ζ(s) = Σ(n=1 to ∞) n⁻ˢ
ζ(s) = ∏ₚ (1 − p⁻ˢ)⁻¹
ζ(s) = (1 / Γ(s)) ∫ (0 to ∞) [xˢ⁻¹ / (eˣ − 1)] dx
ζ(s) = 2ˢ πˢ⁻¹ sin(πs/2) Γ(1−s) ζ(1−s)
The definition of the Riemann zeta function. The Euler product over primes. Analytic continuation. The functional equation.
Formulas derived from the Riemann zeta function gradually filled the blackboard.
“The Riemann zeta function, defined as the sum of the reciprocals of s-powers of all natural numbers for a complex number s, can be analytically continued to the complex plane. By transforming this function in various ways, we can obtain its representation as an infinite product over primes. Through the structure of the Riemann zeta function, we can indirectly read the distribution of primes!”
Yoo A-yeon then repeated the Korean explanation in English.
“The Riemann zeta function is basically the sum of one over n to the s, taken over all positive integers n, for a complex number s—”
One sentence at a time. Her English pronunciation was far from perfect, but she enunciated each word clearly and deliberately without shortening anything. It was what English speakers might call an honest pronunciation, clear enough that even mathematicians from abroad could follow the lecture without difficulty.
The audience’s emotions, which had begun with confusion, gradually shifted to wonder and awe.
“There are many approaches to solving this problem, but I used the Hilbert–Pólya approach! The idea is to interpret the zeros of the zeta function as eigenvalues of some operator! In other words, a mathematical problem transforms into a problem in quantum mechanics! That’s why there are theoretical physicists among you sitting here today!”
At first, they had thought it was a joke. When Yoo A-yeon began her presentation, they assumed the child was simply reciting a memorized script. They thought whoever had planned this surprise must be out of their mind. They had even resolved to voice their displeasure the moment the act ended.
But the more they listened to Yoo A-yeon’s explanation, the more they had to abandon those irreverent thoughts.
This can’t be real… How can a child that young explain concepts even a PhD student would struggle with?
A number theorist in his forties alternated his gaze between the printed copy of Yoo A-yeon’s paper and the girl writing on the blackboard.
Her explanations were remarkably sharp. There were no hesitations, no stumbles. Moreover, the dual presentation in Korean and English was a performance no one could believe came from a child. Even he, when lecturing to undergraduates, doubted he could explain so fluidly without notes.
“And this part! The section I wrote in the paper might be a little hard to understand, so I’ll explain it step by step!”
Yoo A-yeon kindly elaborated on the parts not detailed in the paper—the finer points of the logical development that he himself had not fully grasped.
That meant this tiny child understood the paper far better than he, a professor of number theory, did.
Is this child truly the author of the paper, Yoo A-yeon…?
Was she really the author? If so, how had she studied modern mathematics at such a young age? How had she managed to prove the Riemann Hypothesis?
Questions flooded his mind. He felt an urge to raise his hand and bombard her with questions at the top of his voice. Yet he soon shook his head. Everyone among the roughly one thousand people seated here likely held the same doubts. The reason they remained silent and continued taking notes was because they were scholars. Because they wanted to witness the moment the Riemann Hypothesis was solved with their own eyes.
What was I thinking… A mathematician should judge by mathematics alone.
Who the author was, how old they were, what they looked like—none of it mattered. A true mathematician communicates through the logic on the blackboard. And the logic Yoo A-yeon presented on that blackboard was breathtakingly elegant and beautiful.
Flip-flip.Scratch-scratch. The soft sounds of pages turning and pens scribbling filled the auditorium.
At some point, everyone who had harbored doubt or displeasure vanished. They focused entirely on Yoo A-yeon’s writing and her words, as if trying to etch this moment into memory. If history remembered this occasion, they wanted to be able to boast that they had been present.
Thirty minutes had passed since Yoo A-yeon began her presentation.
Outside the lecture hall, the live MeTube stream showed viewer numbers that had soared from around ten thousand before the lecture to fifty thousand—and they were still climbing.
The person who solved one of the seven great mathematical problems was actually an incredibly cute little girl?!
It was the kind of gossip no one could resist checking out immediately. Shocked by the news, viewers began spreading it rapidly across communities, social media, messengers, and even to family and friends in real life.
The rumor spread like wildfire, drawing in even those with no interest in academic issues. For them, the content of the lecture didn’t matter. Riemann Hypothesis or whatever—it was all headache-inducing. What captivated them was simply the sight of a small, adorable girl presenting difficult material before elderly professors. That image alone was enough to flood them with dopamine.
Meanwhile, on Twitter:
In English-speaking communities:
Before she knew it, the time had come to end the lecture. An hour had already passed. Speaking continuously without rest had left her mouth completely dry.
Phew… I’m so thirsty.
She supposed it was inevitable that talking a lot would dry out one’s saliva. Yoo A-yeon gulped down the bottled water her mother handed her.
Still, maybe it’s because they’re all adults who’ve lived long enough. Everyone’s so well-mannered.
She had prepared several countermeasures in case someone interrupted the flow by asking a ridiculous question, but fortunately none had been needed. For the first five minutes they had watched her with skeptical eyes, but now everyone was listening attentively with compliant gazes. She felt truly grateful.
“—Therefore, I was able to show that the operator H I proposed in the paper satisfies these three conditions! In other words, the Riemann Hypothesis is true! Ta-da! With that, I conclude the proof!”
Bow. Standing on the platform, Yoo A-yeon bent at the waist and expressed her gratitude to everyone who had listened to her lecture for nearly an hour.
I wonder what kind of reaction they’ll show…?
She felt a flicker of anticipation mixed with tension. There might still be people who hadn’t let go of their doubts. If so, they could direct aggressive questions at her and her mother. She needed to be prepared for that. Gulp. As she thought this and looked out at the audience, someone began to clap.
Clap.
Clap.
Clap-clap. Clap-clap-clap-clap.
The professor in the front row stood up first. Then the professor beside him followed. The wave spread instantly. People in the next seats, people in the back rows—roughly one thousand people rose to their feet and began applauding her.
Clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap-clap!!!