“Hey! Wasn’t the person who just went in last year’s New Horizon winner?”
“There are seniors who got the Schrödinger Scholarship and the Marie Curie Fellowship, too. This is insane. Did they seriously issue some kind of full mobilization order?”
The department’s famous names wandered the corridor with faces like death.
“Are they not letting us join?”
“They said volunteering is fine, didn’t they? We can at least make coffee and take out the trash.”
Seeing the seniors’ hollow eyes, the overflowing pizza boxes, and the murderous equations filling the boards, the undergraduates smacked their lips.
It was probably a major event that would never come again in their lifetimes.
The classmate beside him nodded. He, too, was a prodigy who had entered MIT after being called a genius in his own right, but there was nothing he could do in this colossal affair.
“I snuck in yesterday and looked at the board. It seemed like they were dealing with L-functions, but I gave up trying to read it.”
“Whew. Yeah. It feels kind of lousy, like we’re being left out, but what can we actually do?”
There were no undergraduate names on Whitman’s draft list. It was not for some romantic reason, like children being unable to go out onto a battlefield. The dean had simply judged that they would be of no help.
Even so, among the undergraduates, the desire to take part in this war spread like wildfire. They volunteered to take out trash and ceaselessly carried coffee and doughnuts.
Hugo, a math department postdoc who had received the New Horizon Prize, looked around and said,
“Math department, listen up. If we get pushed around by the physics kids, from tomorrow on you’ll be doing that work, too. The Riemann Hypothesis is our home ground.”
Laura, a Marie Curie Fellowship scholar listening from the side, chuckled.
“How interesting. Then shall we have the math department wait on us? All right, physics! Let’s pick up the pace.”
At Laura’s provocation, Hugo’s brow twitched.
“Hmph! Says the one whose side can’t even filter out noise properly and ends up producing operator errors.”
“What did you say? You people are the ones using statistical models whose ergodicity hasn’t even been properly verified. Do you even understand the process of replacing the zeros of the Riemann zeta function with a physical spectrum?”
“Are you stupid? That’s the theory our department’s Seoha created.”
“In our department’s quantum laboratory, you mean. Physics contributed a lot to that paper!”
At the two’s savage banter, the graduate students flinched. The undergraduates carefully collected the pizza crusts and paper cups that had fallen at their feet.
Whitman and Leonard split Felix and Arthur’s paper into twenty modules and distributed them to each lab. And the most suspicious parts were assigned to Hugo and Laura, the aces of the two departments.
On the large screen placed in the center of the conference room, a collaboration tool was running in real time.
The drafted graduate students and postdocs all let out sighs.
“Whew, this is no joke. How long do we have to do this?”
“I got dragged out while I was writing my own paper.”
“You people, watch your mouths! The dean is smiling over there. I can see it in his eyes. That benevolent smile that says, ‘If you don’t participate, you won’t get your degree either.’”
At Hugo’s warning, everyone gauged the mood and returned to their seats.
‘This is strange.’
One week, two weeks, time passed.
At first, it had been a project they were forced to join against their will, but as verification progressed, the equations began to feel alien.
For days, Hugo had been glaring at the modular transformation formula written on the chalkboard. Algebraically, there seemed to be no flaw at all. Every term was closed, and the variables were perfectly controlled as well.
“It’s too perfect, isn’t it? To the point that it feels unpleasant.”
Laura, too, tore at her hair as she watched the values from the simulations she had run match Felix’s predictions like a carbon copy.
“Hugo, if there’s an error here, I don’t think it’s a data problem.”
“But there’s definitely a problem. If it isn’t the data, there’s only one answer. Probably the coordinate system…”
“Interesting. You felt that too? The deeper we dig, the more it stinks. Doesn’t this feel like something huge?”
Laura stuck out her tongue and smacked her lips.
In her mind arose an image of condemning the heretics who had built a false tower. It would cause an enormous stir not only in academia, but socially as well.
A thrill ran through her when she imagined her own name engraved on the front of it. The heretics would be executed. And the one preparing the guillotine to sever their heads would be none other than herself!
Hugo and Laura’s eyes gleamed greedily.
“Let’s report it first.”
“Of course.”
The eyes of the two deans sank coldly as they read the report they had submitted.
“A topological mirage…”
“A difficult part to verify. Even comparing hundreds of thousands of cases at once won’t make it easy to grasp.”
Even in mathematics, there existed expressions that satisfied every algebraic condition yet could not actually exist.
“There is a high possibility that it is a structure that is perfect locally but does not hold globally.”
“Mm… the Penrose triangle.”
It was a figure devised by Roger Penrose, the British mathematician and Nobel Prize-winning physicist.
If one examined each line individually, there was no problem, but when viewed as a whole, it had a geometrically impossible structure. As if their opinions had aligned, the two looked at each other and nodded with grave expressions.
Whitman looked at Hugo and Laura and asked,
“Do you know what the most terrifying form of verification is in modern mathematics and physics?”
“Pardon?”
“Uh… well. Wasn’t verification always terrifying?”
He wore a pleased expression.
“A complete survey and cross-verification.”
Their faces turned white.
“Y-you can’t mean!”
“You’re joking, right?”
“Once we know where to dig, what comes next is simple. From now on, we will dismantle the paper’s coordinate system down to the atomic level.
Every equation, every transformation, every assumption will be reverified independently. Whether there were any missing conditions or implicit premises. Whether the choice of coordinate system was justified.”
Laura cautiously raised her hand.
“Dean, if we do that, won’t it take at least several months?”
At present, all the researchers had temporarily put aside what they had been doing and come to assist. But they could not maintain this state forever.
Common sense dictated that a wartime total mobilization order had to end quickly.
“You underestimate MIT.”
Whitman’s eyes flashed sharply.
“Several months? That would be the case if only a handful of people were fighting in solitude. But right now, countless talents are gathered here, are they not? From this point on, we will switch to a war of annihilation.”
It was a large-scale mission unprecedented in MIT’s history—or perhaps in the history of universities.
Hundreds of renowned graduate students and postdocs were mobilized to verify a single page of a paper.
“Asymptotic Behavior, Analytic Continuation near Singularities. We dig relentlessly into every part Felix passed over as obvious.”
“Laura, examine the corresponding relationship of the quantum energy levels.”
Not only personnel, but all of MIT’s computational resources were mobilized as well.
Every available workstation, and even the supercomputer The Core—every bit of computing power rushed toward a single target.
Watching this, all the undergraduates clicked their tongues in awe.
Gulp.
‘It feels like something incredible is about to happen.’
‘Am I actually standing in a historic moment?’
Postdocs ran roughly through the corridors.
Even when night fell, the lights in the building did not go out. Since the deans did not leave work, no one could go home.
‘How dare you try to browbeat us with data? Felix, Arthur. If you have truly solved the Riemann Hypothesis, then your proof should be able to withstand this level of verification.’
“Dean, Section 14 has passed. Its algebraic accuracy is perfect as well.”
“The numerical analysis results also match the paper’s predictions to twelve decimal places.”
Each time a report came in, disappointed sighs flowed from the researchers.
Whitman gritted his teeth. If he had not had Seoha and Elijah’s certainty, he might have given up by now. But if he knew the answer, then all that remained was to keep pushing forward with tenacity.
“Continue. Thoroughly, without leaving even a single gap.”
There was no wavering in his voice.
Exactly forty-two days after the total mobilization order had been declared.
The night was deep, but the buildings of the two departments still shone like lighthouses in the darkness.
It was then.
“Huh?”
In a corner, Hugo, who had not slept for seventy-two hours and had been glaring at the sheets, sprang up from his seat.
Crash—
His chair toppled over with a loud noise, but no one cared.
“I… I found it.”
Hugo’s voice trembled.
In an instant, the conference room became so silent one could hear a pin drop. Whitman and Leonard approached him as though drawn by magnets.
“Where is it?”
With a trembling hand, Hugo pointed at the equation on the screen.
It was the part dealing with one of the paper’s most fundamental premises: the irreversibility of the operator.
“Look at the mapping process from the T-plane to the S-plane here. Felix assumed that this transformation had the same orientation at every level. Algebraically, there’s no problem at all. But…”
Hugo looked at Laura.
Quick on the uptake, she began hammering at the keyboard like a madwoman and expanded the simulation’s scale down to the Planck level.
“It’s twisted… ever so slightly.”
The geometric structure displayed on the screen wavered like a jellyfish, then slowly began to distort.
Laura covered her mouth with her hand as if she were about to scream.
“Arthur and Felix hid a non-Euclidean gap in an extremely ingenious way. Below a certain threshold, the topology of the equation tears. It’s a very small error, but even this is enough for the theoretical consistency they claim to collapse.”
Silence flowed.
“……”
“……”
A single point of error.
In that instant, Laura thought she might be able to understand Felix.
What if MIT had not thrown all its human and material resources at it? Nine times out of ten, it would have been accepted as orthodoxy. And it probably would not have been broken for decades.
Whitman wore a sorrowful expression.
At the moment Felix became certain that he had proved the Riemann Hypothesis, he had discovered a tiny impurity. If he only covered that up, it was all but certain that his name would be left in human history.
Felix had failed to overcome that momentary temptation. And the instant he compromised, he died as a scholar.
“Hugo, Laura!”
At Whitman’s call, both of their shoulders stiffened.
“What happens if this error is expanded globally?”
Laura quickly entered the numbers and pressed the Enter key.
Tatatatak!
At that moment, the dazzling graph on the screen shattered as though a glass had broken. All that remained was a heap of random data with no order whatsoever.
“It’s over.”
Leonard murmured in a low voice.
It was the moment the forty-two-day hellish march came to an end. Some wiped away tears, and some cheered in the thrill of victory.
“Yes!”
“We did it! We did it!”
“Ha, damn it. Thank God.”
Hugo smiled with hollow eyes and said,
“We won, Dean.”
Whitman shook his head with his eyes closed.
“No. Truth has won.”
Dawn began to break outside the window.
Hugo and Laura came walking out into the corridor, staggering like zombies. They felt grimy, having not even showered, let alone changed clothes, for days. But their faces shone with the exhilaration of paladins who had condemned wicked heretics.
“Laura, that effect when the graph shattered earlier was killer. Ugh, the sheer satisfaction…”
“Don’t talk to me. I feel like half my brain cells are dead. First thing I’m doing when I get back is lying down in bed and sleeping for thirty hours.”
As they spoke, Hugo tilted his head and looked toward the corner.
Someone was fidgeting anxiously. He tried to come toward them, then backed away again; then he tore at his hair and changed direction once more.
The two of them chuckled and approached him.
“Seoha! What are you doing here?”
His shoulders flinched, and he slowly turned to look at the two of them.
“I was wondering if there was anything I could help with.”
Seoha’s eyes shook, unable to settle.
He found it difficult to face the researchers’ wretched appearances. They had thrown aside even their own research to come here. He felt uncomfortable, thinking that an official notice like that had gone out because of what he had said to the dean.
“Seoha, do you happen to remember me?”
“Yes. You were in the quantum laboratory before.”
Laura’s face brightened instantly.
“I’m grateful to you. Thanks to you, I got a good opportunity. And you don’t need to worry about us. We finally found a counterexample.”
Seoha’s eyes sparkled.
“Really?”
“Yeah. But, you know…”
“Yes.”
Laura shuddered as though sickened.
“If you think you owe us even the tiniest bit, then repay it by solving the Riemann Hypothesis. That thing was a truly absurd monster. We only dug into a fragment of it for a short while, and yet…”
She swallowed with a gulp.
“…it was terrifying. What we saw was a failed proof. At the same time, it was also the remnants of a possibility that had been torn apart in a truly miserable way. The Riemann Hypothesis is a demon. I honestly can’t bring myself to believe that humanity will be able to solve it.”
Hugo added his agreement.
“Ah, I think I know how that feels too. The demon of Riemann went slurp and devoured Felix and Arthur. It was refreshing, but also a little painful.”
Seoha’s eyes widened, and then he changed his expression and smiled brightly.
“Don’t worry about that. I’ll make sure to execute it.”
His smile looked far too pure. The conviction dwelling within it was so chilling instead that the two of them felt goosebumps rise all over their bodies.