Under warm lighting, four people sit facing one another.
BBC’s The Planet.
It is the science and liberal arts program with the largest viewership in the world. For a show dealing with mathematics and science, it is an exceptional achievement. The secret to its popularity lies in the host Evan’s masterful presentation and his ability to book guests. And he possesses an almost animal instinct for never missing whatever topic is gaining momentum at the time.
With a gentle smile, he greets the viewers.
“Good evening. This is Evan Clark of The Planet.
Today, we will be discussing a story that no one has yet been able to verify. First, let me introduce our guests. Please give us a brief greeting.”
The scholars seated at the table introduce themselves in turn.
“I’m Anton Bauer of the Clay Mathematics Institute.”
“My name is Clara Wiss. I study molecular biology at Johns Hopkins.”
“I’m Marcel. I teach cognitive science and philosophy at Oxford.”
All three are figures with high public recognition in their respective fields. Evan nods with a satisfied expression.
“In my opening, I called this an as-yet unverified story. Even so, there is a reason we have invited world-renowned scholars here today.
It is because of a very famous mathematician—the prover of the Riemann Hypothesis, now the director of Apex Lab Korea. A week ago, in a small café in Korea, the equations he left on the wall are said to be shaking the academic world.”
A photograph of the café appears on the screen.
Equations densely fill a wall covered in large sheets of paper. Some images were taken with smartphones, but footage shot by a 4K camera has been edited in as well.
“First, let us hear from those who were at the scene.”
A short video clip plays.
A plump-looking man in his thirties appears, his name and occupation displayed in captions.
[Lee Chanseong, Professor of Mathematics at KAIST]
He shakes his head with a despairing expression and says,
“It is not a complete proof. The entire process has been omitted. But if this is correct…”
He stops breathing for a moment. As though even putting the words out into the world is a burden.
“This is no longer merely a mathematical problem. We will have to consider from where, exactly, we must begin rewriting modern science.”
The screen returns to the studio.
A brief silence.
Evan smoothly receives that silence. He turns his head slightly and looks at the panelists.
“That was quite a strong statement, wasn’t it? That we must rewrite modern science. Dr. Anton, I’ll ask you first. I understand you actually went there yourself.”
Anton nods with a stiff expression.
“I wanted to see the atmosphere at the scene for myself, as part of an investigation.”
“The Clay Mathematics Institute is the organization that oversees the Millennium Problems. Is there an official position on this incident?”
As if he had expected the question, Anton smiles.
“Of course, it is still far too early. But I do have a personal opinion. There has been much discussion over whether the equations Seoha left in the café solved the P versus NP problem, but that is by no means the core issue.”
Evan shrugs.
“Judging by the reaction in the mathematics community, I hear he didn’t even address that problem directly.”
“That’s right. Seoha did not solve that problem.”
“Did not solve it? Please explain a little further.”
“In an interview, he said that Turing’s theory of computational complexity cannot encompass the entirety of the universe. Just as no matter how precise a map you draw on a flat surface, it cannot fully represent the Earth.”
Marcel naturally takes up his words.
“It must be similar to when non-Euclidean geometry appeared.”
“Exactly. Euclid was not wrong. He was complete only on a plane. To express the broader world of curved surfaces, entirely different rules were needed. That is what Seoha is pointing out.”
The host asks with a small laugh,
“Doesn’t that require considerable courage?”
“It does.”
After taking a sip of water, Marcel continues.
“Perhaps our society could have developed fifty, or even a hundred years faster. If only one giant had found the courage.”
“Oh! And who would that be?”
Evan’s eyes light up as he asks about the sort of historical anecdote viewers would enjoy.
“Carl Friedrich Gauss. The man revered as the Prince of Mathematicians.
In the early nineteenth century, roughly two hundred years ago, Gauss discovered a shocking fact during his research. That even if the parallel postulate were denied, there existed a geometry without logical contradiction. In other words, he realized Euclidean geometry was not everything.”
“Two hundred years ago?”
“Yes. But Gauss did not publish it. It was discovered after his death; the research remained in his letters and notebooks. The reason can be guessed from words he left behind himself.”
“What did he say?”
“I fear the clamor of the Boeotians.
Boeotia was a real region in Rome, and its people were notorious for being stubborn and ignorant. In other words, Gauss hid it because he feared criticism from the ignorant masses.”
“Was it such a big deal that he had to hide it?”
He shakes his head.
“Goodness, the greatest problem was the group that revered Kant. In Kantian philosophy, Euclidean geometry was regarded as a truth inherent in our cognition. Something like an axiom of mathematics. If you shook that foundation, wouldn’t a fierce reaction come back?”
“Ah… So it wasn’t only a problem of mathematics.”
“That’s right. Gauss avoided that fight. Later, two scholars reached similar conclusions, but after publishing their papers, they were ridiculed.
This is the part I find regrettable about Gauss. Even if he did not publish it himself, it would have been good if he had said something in support of them.”
“Now that I hear it, that does seem true. Then when did it come to be accepted?”
“A turning point came in 1854. Bernhard Riemann, who had been Gauss’s student, directly denied Euclid. Gauss was among the audience, and it is said that he was deeply moved upon hearing the lecture. But at the time, Gauss was elderly, and not long after the lecture ended, he died.”
“Oh dear… In the end, he left without saying a word.”
“That is why it is so infuriating. Even Riemann’s geometry was accepted in that era as a mathematical amusement.”
“Even Riemann’s?”
“It was only after Einstein appeared that it was revealed to be the language describing the actual universe. Riemannian geometry was the mathematical foundation of the general theory of relativity.”
“Then how long did it take, exactly?”
“The general theory of relativity was published in 1915. But it was widely accepted much later still.”
“And yet Gauss knew this a full century earlier.”
“What I want to say is that academia and society are that conservative.
If the shock and resistance the public and mathematicians felt when non-Euclidean geometry appeared lasted a hundred years, what will happen this time?
Seoha has not touched only mathematics. Computer science, philosophy, engineering, medicine, pharmacology… The affected fields are countless. In every field written in Turing’s language over the past century, there will be fierce backlash.”
Evan turns to Clara.
“I hear the reaction in biology has also been heated.”
Clara laughs softly. She looks somewhat tired.
“To be honest, I haven’t slept properly for the past few days. For biotechnologists, there are several problems that are like long-cherished aspirations.
Protein folding, the mechanisms of memory storage and retrieval occurring in the brain, the origin of the genetic code, the secret of cellular regeneration, how the immune system distinguishes self from non-self—problems like these.”
“They sound difficult just hearing about them.”
“The interesting part is that many of them fundamentally share the same question.”
“What is that?”
“How on earth do living systems find optimal solutions so efficiently? These are all problems that must find the correct answer from among astronomical numbers of possibilities. With Turing’s theory of computation, we could never find an answer.”
“You mean the limits were clear.”
“When I saw Seoha’s theory, I felt it. That perhaps we had been using the wrong language all this time.
The simultaneity of uncountable space.
We have not yet interpreted all of the equations, but the concept Director Yu presented explains the parts that Turing’s theory had blocked off with astonishing neatness.”
“That’s difficult. Please give us an example.”
“There is some material I obtained with great difficulty. It is an early conceptual diagram of the theory. In Seoha’s computational theory, it says that paths not suited to the purpose are not supplied with resources and disappear. Then what about cancer cells? What if they are stealing resources from our bodies while deceiving the purpose?”
“Ah!”
Evan lets out a cry of surprise.
“I cannot state anything definitively, but the direction fits so well it gives me chills.”
“The laboratories must be in an emergency. I understand why you stayed up all night. What is the reaction like in the mathematics community?”
The host asks, looking at Anton.
“Mathematics is slow by nature. Not because mathematicians are lazy, but because that is the nature of the discipline itself. Before a formal paper comes out, there is hardly anything to respond to.”
“Come to think of it, Seoha hasn’t formally published a paper either, has he?”
“That’s right. All he did was leave equations on the wall of a café. Naturally, it is not a complete proof, and there has been no peer review. It was not even a presentation he intended.”
Evan asks with an expression of incomprehension.
“Then isn’t that a little strange? Why is the academic world making such a fuss?”
The three look at one another, meeting each other’s eyes. Then, as if by prior agreement, they speak at the same time.
““Reliability.””
Anton continues his explanation in a calm voice.
“As you know, Ramanujan received almost no formal education. Even so, he wrote down more than 120 formulas and sent them to Hardy. Only the results, without proofs. Naturally, Hardy could not believe them at first.”
“It must have seemed absurd.”
“But what was the result? It was revealed that Ramanujan was correct, with only a very small number of exceptions. Today, those formulas are used in elliptic functions and modular theory. They are also the foundation of black hole entropy and phase transition theory in physics. As a mathematician, I can say with certainty that this was an ability possessed by only one person in history.”
“Still, there were some that were wrong.”
Anton shakes his head.
“The expression ‘wrong’ is not precise. Most of the problematic formulas lacked rigor. He intuitively saw the answer first, but did not have the technique to package it carefully in mathematical terms. There was no case where the intuition itself was wrong.”
“Ah! Then that means…”
“They do not say it aloud, but there must be no small number of scholars who think the same thing I do. That Seoha is the second Ramanujan to appear in five thousand years of mathematical history.”
Evan’s eyes grow wide.
“Wh-what do you mean by that!”
“Despite his young age, Seoha has solved many difficult problems so far. The number of papers he has published is not small either. Among them, not a single line—no, not a single word—has been wrong.”
Anton looks straight into the camera, as if gazing into the eyes of the viewers.
“This is something that can only be explained by assuming that Seoha possesses the same intuition as Ramanujan. Moreover!”
Gulp.
As though nervous, Evan swallows.
“He is a Ramanujan who grew up in an ideal environment, no less. Not only did he receive proper formal education, his body is healthy as well!
So how could we possibly ignore this?”