Chapter 212
Translator: Dreamscribe
Four people sat facing one another under warm lighting.
BBC's The Planet.
It was the science program with the largest viewership in the world. An unusual achievement for a show dealing with mathematics and science. The secret to its popularity lay in the deft hosting and booking skills of its presenter, Evan. And he had an animal instinct for never missing a topic while it was heating up.
With a gentle smile, he greeted the viewers.
"Good evening. This is Evan Clarke, with The Planet.
Today we're going to discuss something that no one has yet been able to confirm. Let me introduce our guests first. If you could each say a quick hello."
The scholars seated at the table introduced themselves in turn.
"Anton Bauer, from the Clay Mathematics Institute."
"My name is Clara Wyss. I research molecular biology at Johns Hopkins."
"I'm Marcel. I teach cognitive science and philosophy at Oxford."
All three were figures with high public recognition in their respective fields. Evan nodded with a satisfied look.
"I said in the opening that this story hasn't been confirmed yet, and yet there's a reason we've gathered world-class scholars here to discuss it.
It's because of the man who proved the Riemann Hypothesis, an extraordinarily famous mathematician who now serves as Director of Apex Lab Korea. A week ago, at a small cafe in Korea, he left a set of equations on a wall, and word is that they are shaking the academic world to its foundations."
A photograph of the cafe came up on screen.
Equations packed edge to edge across a wall covered in sheets of poster paper. It was a picture taken on a smartphone, but 4K camera footage had been edited in alongside it.
"Let's begin by hearing from the people who were there."
A short video clip played.
A slightly plump man in his thirties, his name and occupation displayed in a subtitle.
[Professor Kim Chan-sung, Department of Mathematics, KAIST]
He shook his head, his expression despairing, and said,
"It isn't a complete proof. The entire process has been left out. But if this is correct...."
He stopped breathing for a moment. As if even letting the words out of his mouth was more than he could bear.
"Then this is no longer a matter for mathematics alone. We're going to have to work out where on earth to begin rewriting modern science."
The feed returned to the studio.
A brief silence.
Evan received that silence smoothly. He turned his head slightly and looked at his panel.
"Rather strong words, weren't they? That modern science must be rewritten. Let me put this to Dr. Bauer. I understand you actually went there yourself."
Anton nodded, his face stiff.
"I wanted to see the atmosphere on the ground for myself, as part of looking into it."
"The Clay Mathematics Institute is the body that oversees the Millennium Prize Problems. Do you have an official position on this affair?"
Anton smiled, as though he had expected the question.
"It's far too early for that, obviously. But I do have a personal opinion. There's been a great deal of talk about whether the equations Seo-ha left in that cafe solved the P vs NP Problem, and my view is that that is not remotely the point."
Evan shrugged.
"From what I've seen of the reaction in the mathematics community, he didn't even touch that problem directly."
"That's right. Seo-ha didn't solve that problem."
"He didn't solve it? Could you explain a little further?"
"In an interview, he said that Turing's theory of computational complexity cannot contain the whole of the universe. Rather like how, no matter how finely you draw a map on flat ground, you can never fully represent the Earth."
Marcel picked up the thread naturally.
"So it's much the same situation as when Non-Euclidean Geometry first appeared."
"Precisely. It isn't that Euclid was wrong. He was only complete on a plane; to describe the wider world of curved surfaces, an entirely different set of rules was required. That's what Seo-ha is pointing out."
The host laughed softly and asked,
"Isn't that the sort of thing that takes a great deal of courage?"
"It is."
Marcel took a sip of water and continued.
"Our society might well have advanced fifty, perhaps a hundred years faster. If just one towering figure had found the courage."
"Ohh! And who would that be?"
Evan's eyes gleamed at a piece of historical gossip his viewers were sure to enjoy.
"Carl Friedrich Gauss. The man revered as the king of mathematics.
In the early nineteenth century, so roughly two hundred years ago, Gauss discovered something shocking in the course of his work. That even if you deny the Parallel Postulate, there exists a geometry with no logical contradiction in it. In other words, he realized that Euclidean geometry was not the whole story."
"Two hundred years ago?"
"Yes, but Gauss never published it. It came to light after his death; the research was there in his letters and notebooks. As for why, we can guess from words he left behind himself."
"What did he say?"
"I fear the clamor of the Boeotians.
Boeotia was a region that actually existed in Rome, and its people were notorious for being stubborn and ignorant. In short, Gauss hid his work because he feared the abuse of an ignorant public."
"Was it really so serious that he had to conceal it?"
He shook his head.
"Oh, the crowd who worshipped Kant were the biggest problem of all. In Kantian philosophy, Euclidean geometry was regarded as a truth innate to our very perception. Something like an axiom of mathematics. And if you shake a foundation like that, wouldn't you expect a violent response?"
"Ah.... So it wasn't purely a mathematical matter."
"Exactly. Gauss avoided that fight. Later, two other scholars arrived at similar conclusions, but they were mocked once they published their papers.
This is the part where I find Gauss disappointing. Even if he wasn't going to announce it himself, it would have been good of him to speak up in their support."
"Now that you say it, yes. So when did it finally win acceptance?"
"The turning point came in 1854. Bernhard Riemann, who had been Gauss's student, stood up and rejected Euclid head-on. Gauss was among the audience, and it's said that he was deeply moved by the lecture. But Gauss was an old man by then, and he died not long after it ended."
"Oh dear.... So he went to his grave without ever saying a word."
"Which is exactly what makes it so maddening. Even Riemann's geometry was received as a mathematical plaything in its own time."
"Riemann too?"
"It only became clear that this was the language describing the actual universe once Einstein came along. Riemannian Geometry was the mathematical foundation of general relativity."
"So how long did it take, all told?"
"General relativity was published in 1915. But it was another good while before it was widely accepted."
"And yet Gauss knew all this more than a century before that."
"My point is simply that academia and society are that conservative.
If the shock and resistance that the public and mathematicians felt when Non-Euclidean Geometry emerged lasted a hundred years, what do you suppose it will be like this time?
Seo-ha hasn't only touched mathematics. Computing, philosophy, engineering, medicine, pharmacology.... The fields affected are beyond counting. There will be fierce resistance from every domain that has been written in Turing's language for the past century."
Evan turned to Clara.
"I hear the reaction on the biology side has been heated as well."
Clara laughed softly. Her face looked rather tired.
"Honestly, I haven't slept properly in days. There are a handful of problems that biotechnologists have longed to crack for generations.
Protein folding, the mechanism by which the brain stores and retrieves memory, the origin of the genetic code, the secret of cellular regeneration, how the immune system distinguishes self from non-self. Problems of that sort."
"Just hearing that list makes them sound difficult."
"The interesting part is that a great many of them fundamentally share the same question."
"And what is that?"
"How on earth do living systems find optimal solutions so efficiently? Every one of these requires locating the correct answer among an astronomical number of possibilities. With Turing's computation theory, there was simply no way to get there."
"So the limits were clear-cut."
"Looking at Seo-ha's theory, it struck me. That perhaps we have been using the wrong language all this time.
The Simultaneity of Uncountable Space.
We haven't managed to interpret all of the equations yet, but the concept Director Yu has put forward explains the places where Turing's theory got stuck with astonishing cleanness."
"That's difficult. Do give us an example."
"There's a document I obtained with a great deal of difficulty. It's an early conceptual diagram of the theory, and it states that in Seo-ha's computation theory, any path that doesn't serve the purpose is denied resources and dies out. So what about cancer cells? What if they're deceiving the system about their purpose while stealing resources from our bodies?"
"Ahh!"
Evan let out a startled cry, almost a shriek.
"I can't declare it as fact, but the direction alone fits so well it gives me chills."
"Your lab must be in a state of emergency. I can see why you've been up all night. And how has the mathematics world responded?"
The host asked, looking at Anton.
"Mathematics is slow by nature. Not because mathematicians are lazy, but because that's the character of the discipline itself. Until a formal paper appears, we hardly respond at all."
"Come to think of it, Seo-ha never formally published a paper, did he?"
"Correct. Leaving equations on a cafe wall was the whole of it. It's certainly not a complete proof, and there was no peer review. It wasn't even an announcement he intended to make."
Evan asked with a look of bafflement.
"In that case, isn't this a bit odd? Why on earth is academia making such a fuss?"
The three of them glanced at one another, eyes meeting. Then, as if by prior agreement, they spoke at the same moment.
""Reliability.""
Anton continued his explanation in a calm voice.
"As you know, Ramanujan had almost no formal education. Even so, he wrote out some hundred and twenty formulas and sent them to Hardy. Results only, with no proofs. Naturally, Hardy couldn't believe them at first."
"I imagine it must have seemed absurd."
"And how did it turn out? With only a very few exceptions, Ramanujan was shown to be right. Those formulas are used today in elliptic functions and modular theory. They're also the foundation of black hole entropy and of phase transition theory in physics. As a mathematician, I can state without hesitation that this was an ability only one person in all of history has ever had."
"Still, some of it was wrong, then."
Anton shook his head.
"'Wrong' isn't quite the right word. The formulas that caused trouble mostly lacked rigor. He saw the answer intuitively first, but he had no knack for packaging it up neatly in mathematical terms. There was never a case where the intuition itself was wrong."
"Ah! Which means...."
"They don't say it out loud, but there are by no means few scholars who think as I do. That Seo-ha is the second Ramanujan to appear in five thousand years of mathematical history."
Evan's eyes went round.
"Wh-what are you saying!"
"Young as he is, Seo-ha has already solved a great many open problems. And he's published no small number of papers. In all of them there has not been a single line, no, not a single word that was mistaken."
Anton looked straight into the camera, as though gazing into the eyes of the viewers.
"This is a thing that can only be explained by assuming Seo-ha possesses the same intuition Ramanujan had. And on top of that!"
Gulp.
Evan swallowed, as if tense.
"He is a Ramanujan raised in ideal conditions, no less. One who not only received a proper formal education but is sound in body as well!
So how could we possibly ignore this?"
*****
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