Chapter 55
The ceremony began.
The director of the Clay Mathematics Institute stood at the center of the stage.
Dozens of cameras scanned the auditorium from all around.
They took in the whole auditorium in a wide shot, zoomed in on the director onstage, and swept across the mathematicians in the front row.
Yu A-yeon's family was seated side by side in the third row.
The star of this ceremony, Yu A-yeon, sat with both hands on her knees, staring straight ahead.
Beside her sat Han Seol-ae, Yu Jinhu, and Yu Arin in a row.
The director took the microphone.
The ceremony was conducted in English.
"Ladies and gentlemen, thank you for attending."
The director's voice filled the auditorium.
"To share in the most special moment in the history of mathematics, we have gathered here today."
A brief silence fell.
"The Clay Mathematics Institute hereby declares that the Riemann hypothesis has been proven and is now formally the Riemann theorem. And we formally recognize Yu A-yeon's achievement in solving the Riemann theorem and declare her a Millennium Prize laureate."
Clap clap clap clap clap clap clap clap clap clap clap clap—!
A huge round of applause erupted in the auditorium.
The applause was so loud.
That no one noticed the little girl seated in the third row laughing with a "hee-hee" sound.
The director raised a hand and quieted the applause.
"Many people have joined us here today. There are mathematicians here, and there are people all over the world watching this moment. For everyone here today, I will explain what the Riemann theorem is, and why this proof is important."
To make it easy for the public to understand, the director began slowly explaining the background of the Riemann theorem.
"Mathematicians have long wondered how prime numbers appear. Prime numbers are numbers divisible only by 1 and themselves, like 2, 3, 5, 7, and 11. At first glance, they seem to be scattered completely at random."
When the director pressed the remote, a screen descended from behind the stage.
"In the early 19th century, mathematician Carl Friedrich Gauss discovered that the number of primes follows a pattern. As numbers get larger, the number of primes smaller than a given number increases roughly like x / log x. What looks random at first glance actually follows a very precise law overall."
On the screen appeared a graph of x / log x and a graph of the number of primes. The two graphs increased in similar fashion.
"But a new question arose. How accurate is this approximation? How large is the error between the actual number of primes and the approximation?
Gauss's student, Bernhard Riemann, answered this question. In 1859, Riemann published an eight-page paper titled 'On the Number of Primes Less Than a Given Number.'"
The director pointed to the screen.
The zeta function appeared on the screen.
ζ(s) = Σ 1/nˢ
"This is a function now called the Riemann zeta function. Bernhard Riemann discovered that this function is directly connected to primes. So he began investigating the points where this function equals zero."
Four points arranged in a line appeared on the screen.
│
│ • 1/2 + 30.4248 i
│
│ • 1/2 + 25.0108 i
│
│ • 1/2 + 21.0220 i
│
│ • 1/2 + 14.1347 i
│
┼─────────
0 1/2 1
"Through complex calculations, Riemann identified four zeros on the complex plane. And when he found that all four zeros lay on a line with a real part exactly equal to 1/2, Riemann left behind a bold conjecture."
Text appeared on the screen.
[All nontrivial zeros of the Riemann zeta function have a real part of 1/2.]
"This is the Riemann hypothesis. But why is it important?"
The director asked the audience.
"If the Riemann hypothesis is true, the error that appears when counting primes becomes almost optimally small. This statement guarantees that the prediction error does not exceed a certain level.
Moreover, thousands of theorems in modern number theory have been proven under the assumption that the Riemann hypothesis is true. Cryptography, computational number theory, algebraic number theory, analytic number theory. Because so many fields are connected to this one problem, it is enormously important."
The director took a breath and went on.
"That is why the essence of the Riemann hypothesis comes down to: 'How predictable is the distribution of prime numbers?' And...
The problem posed in 1859 has today, 167 years later, been solved by Yu A-yeon, a six-year-old mathematician."
✒️✒️✒️
When the director pressed the remote, a photo of Yu A-yeon's face appeared on the screen.
Ayeon Yu (2020)
Since Yu A-yeon always had the habit of raising her fingers to make a peace sign whenever she took a photo.
The photo Clay had been given in advance was also one of Yu A-yeon smiling and making a double peace sign.
And at the cuteness of Yu A-yeon's giant photo on the screen, countless mathematicians smiled with delight.
As a bonus, a chuckling "hee-hee" from some girl in the third row could be heard.
The director went on to explain how Yu A-yeon had proven it.
"Yu A-yeon's proof is based on the Hilbert-Pólya approach. It is an approach that turns the problem of primes into one about the frequencies and energy levels in physics.
If an operator exists, and the eigenvalues produced by that operator match the zeros of the Riemann zeta function, then that would mean the zeros are all on a straight line.
This idea has long been the direction mathematicians have tried to pursue, but actually constructing that operator was an obstacle bordering on impossible.
But Yu A-yeon found a way to construct that operator, and in the end succeeded in proving the Riemann theorem."
The auditorium stirred once again.
"Now I will announce the recipient."
The director held the microphone and, looking at the girl sitting in the third row, slowly said,
"Ayeon Yu."
"Yes-!"
Then the girl in the audience raised her hand high.
The cameraman zoomed in on her.
Black sailor uniform.
Flowing black wavy hair.
The girl walked down the aisle boldly, enjoying everyone's gaze.
Like a superstar, she tossed her hair once with a proud expression.
Pitter-patter-.
Her tiny footsteps rang out in the quiet auditorium.
The girl stepped onto the stage.
Then she gave a little bow.
Toward the audience.
"Hello-! I'm Yu A-yeon!"
Clap clap clap clap clap clap clap clap clap clap—!!
"Ayeon Yu. The question Bernhard Riemann left behind in 1859 has inspired countless mathematicians across generations to take on the challenge.
And today, we are witnessing the moment that long journey reaches fruition.
Your achievement is not merely the solving of a difficult problem.
You have left behind a new mathematical tool, presented a new perspective, and widened the path for the mathematicians of the future.
For decades to come, countless mathematicians will continue their research built on your ideas.
May today's achievement be not the pinnacle of your research life, but another starting point.
We hope that your curiosity will continue to open new horizons in mathematics.
Congratulations."
The director extended his hand, and Yu A-yeon shook it.
The director handed over the prepared plaque with both hands.
Yu A-yeon received it carefully with both hands.
The plaque was quite heavy.
It was too heavy for such a small, delicate child to lift, so Yu A-yeon supported it with both arms just barely.
Then an assistant staff member came over from the side carrying a large panel.
[1,000,000 $]
[Clay Mathematics Institute]
A giant panel indicating that the Clay Mathematics Institute would award one million dollars.
But.
When the staff brought the panel over, Yu A-yeon, who stood at only 112 cm tall, was completely hidden behind it.
Hahahahaha-.
The audience burst out laughing at the mishap.
"Hng."
Perhaps a little embarrassed, Yu A-yeon's face flushed red.
Standing on the platform prepared in advance by the staff, Yu A-yeon could barely poke her face out from behind the giant panel.
"Hee-hee."
Yu A-yeon beamed at the panel that said one million dollars.
The director stood beside Yu A-yeon on the platform.
Camera flashes went off.
Click-click-click-.
"Thank youuu-!"
Yu A-yeon shouted her thanks loudly.
Clap clap clap clap clap clap clap clap clap clap clap clap—!
The applause once again filled the auditorium.
✒️✒️✒️
Beneath the Millennium Prize plaque Yu A-yeon received was engraved the following inscription.
………………………………………………………
The Clay Mathematics Institute
Millennium Prize
Awarded to
Ayeon Yu
For Resolving the Riemann Theorem
A problem that remained unsolved since 1859
And in recognition of an extraordinary contribution
to mathematics and human knowledge
2026
………………………………………………………
A problem left unsolved since 1859
In recognition of the achievement of solving the Riemann theorem
In honor of an extraordinary contribution to mathematics and human knowledge
to Yu A-yeon
the Millennium Prize is awarded
The Clay Mathematics Institute
2026