In the Pentagon's command center, Secretary of Defense Richards slammed his fist on the console, denting the metal panel.
"The columns of the Lincoln Memorial have twisted into Klein bottles?" he growled. "Can someone please explain to me why a tourist can stick his hand *through* a column from the inside, but can't touch the surface from the outside?"
The head of tech trembled as he brought up a holographic display. "Mr. Secretary, that's not the worst of it. The interior space of the Oval Office is expanding exponentially. Our last measurement showed its internal volume is 127 times its external dimensions. The agents we sent in… their life signs decohered into probability waves at the doorway."
Richards turned to a white-haired man in the corner. "Dr. White?"
Dr. White adjusted his glasses, his voice like sandpaper. "It's as if… someone has rewritten the universe's operating system. In the affected zones, the parallel postulate no longer holds. The sum of a triangle's angles can be anything it wants to be." He pointed to a live feed. "Look at this patrolman. His left side is experiencing normal gravity, while his right side is in a zero-g environment. His brain can't process the contradiction. It's… shutting down."
"Rate of expansion?"
"Five miles per hour. It's as unstoppable as a mathematical proof." White took a deep breath. "Every altered object is a demonstration of Gödel's Incompleteness Theorem. Our geometric system is, by its very nature, incomplete."
---
At the Princeton Institute for Advanced Study, Chen Mo stared at the formulas on his blackboard, sweat trickling down his nose.
His assistant entered, holding a tablet displaying a new image. "The Statue of Liberty… her torch is now pointing at her own pedestal, creating a perfect self-referential loop. Any camera attempting to take a panoramic shot gets caught in an infinite regression."
"Self-reference…" A sharp light flashed in Chen Mo's eyes. "That's the key to how Gödel constructed his unprovable statement."
He strode to the window. The 3iAtlas in the sky had taken on a new, unprecedented form—a constantly self-referential geometric object. Each part of it described the whole, and the whole was composed of those descriptions.
"It's demonstrating its own incompleteness," Chen Mo said, grabbing a piece of chalk. "If I can find the paradox…"
For the next six hours, the only sound in the office was the frantic scratching of chalk on slate. Chen Mo encoded the geometric transformations of 3iAtlas into a system of natural numbers, constructing a formal system powerful enough to describe the entity.
"Look here." Chen Mo finally stopped, pointing the chalk nub at the center of the board. "This statement, when translated, says, 'This statement is not provable within the geometric system of 3iAtlas.' A classic Gödel sentence."
His assistant was baffled. "But what does that do?"
At that exact moment, a searing pain shot through Chen Mo's skull. He staggered back, his vision fracturing into a bizarre new perception.
He could see every corner of the office simultaneously, from every angle. More than that, he could *see* the probability clouds of the atoms within the walls, the wave-particle duality of photons made manifest. It was a perception beyond sight, a form of pure mathematical intuition.
"Dr. Chen!" his assistant cried, rushing to his side.
Chen Mo pushed him away, his voice trembling. "I… I can see the math."
But this new ability came with a terrifying price.
"Your daughter called a few minutes ago," the assistant said. "She asked when you were coming home."
Chen Mo froze. "Daughter? I… I have a daughter?"
A chill crawled up his spine. He knew he *should* have a daughter. He could almost feel the memory of her small hand in his, the dimples on her cheeks when she smiled. But when he tried to recall her name, there was only a void.
"My daughter… what's her name?" Chen Mo's voice was barely a whisper.
The assistant looked at him, confused. "Yaya, of course. You always call her Yaya."
"Yaya…" Chen Mo repeated the alien name. It felt like a mathematical symbol, devoid of meaning.
Just then, the lights in the office flickered wildly. When they stabilized, a paintbrush was sitting on his desk. It was jet black, its handle carved with shifting fractal patterns. When Chen Mo touched its tip, a voice echoed in his mind—a composite of countless mathematical theorems.
*"Join us, Chen Mo. With this brush, you can paint the true nature of the universe."*
---
Inside the Pentagon, Dr. White gasped. "Mr. Secretary, the 3iAtlas has stopped expanding!"
On the main screen, the morphing geometric entity had solidified into a perfect dodecahedron.
"What happened?"
"Wait… we're receiving a signal from inside the 3iAtlas… it's the complete proof of Gödel's Incompleteness Theorem!" White's eyes were wide. "Someone from the outside just proved to the 3iAtlas that it is inherently flawed."
A technician ran in. "We've traced the signal's origin—Princeton. Dr. Chen Mo's office."
Richards's expression was a complex mixture of awe and suspicion. "I want to see him. In one hour."
---
Chen Mo sat in his office, staring at the black paintbrush. He moved his fingers through the air unconsciously—a habit from twenty years of contemplating Riemannian geometry. But now, the space he traced rippled, ever so slightly.
He could feel the power in the brush. It could translate the mathematical concepts in his mind directly into reality.
But the memory loss was more terrifying. The photos of his daughter on his phone were now of a stranger. As he stared at one, he caught the phantom scent of strawberries—her favorite shampoo. The smell was a key, but it opened an empty room.
The office door opened and two men in black suits entered. "Dr. Chen Mo? The Secretary of Defense wants to see you."
Chen Mo silently pocketed the brush. On the helicopter ride to the Pentagon, his new quantum vision revealed a stunning sight: countless, tiny mathematical structures were rising from the ground, connecting to the 3iAtlas like proven theorems. One of those lines originated from him.
---
In the command center, Richards got straight to the point. "We know you've been in contact with it."
Chen Mo calmly explained how he had applied Gödel's theorem to the 3iAtlas.
Dr. White was aghast. "You proved it was self-contradictory?"
"Something like that, but more complex," Chen Mo nodded. "The 3iAtlas is constantly evolving to resolve its own paradoxes. My proof has merely trapped it in a temporary loop of self-verification."
Richards's gaze was sharp. "Can you shut it down for good?"
Chen Mo shook his head. "The essence of Gödel's theorem is that a system's paradoxes cannot be resolved from within. To 'shut down' 3iAtlas, we would need an external, meta-system."
"Then build one!"
Chen Mo gave a wry smile. "Mr. Secretary, that's like asking a two-dimensional being to comprehend the third dimension. We may not even possess the cognitive architecture for it."
At that moment, the brush in his pocket vibrated. He touched it, and an image flooded his mind: a floating city made of pure geometry, where light and shadow flowed to form complex mathematical structures.
*"Come, Chen Mo,"* the composite voice returned. *"Here, you will find the ultimate truth you seek."*
Chen Mo shook his head, trying to clear it.
"What's wrong?" Richards asked, his eyes narrowing.
Chen Mo took a deep breath. "The 3iAtlas is inviting me inside."
White gasped. "That's insane!"
"I know what's in there," Chen Mo said, pointing to the main screen. "It's a mathematical universe. A realm of pure logic."
Richards stared at him intently. "Will you accept?"
Chen Mo didn't answer right away. The memories of his daughter were fading fast. Now, he could barely remember that he even had a daughter. Her face, her voice, her name—all gone.
Was this the price of comprehending a higher-dimensional truth?
"I need time to think."
Richards nodded. "You have 24 hours. After that, with or without your cooperation, we're taking action."
---
Back in his temporary quarters, Chen Mo sat exhausted on the sofa. He took out the black paintbrush, studying it.
Within the fractal patterns on the handle, one tiny area remained static—a single piece that didn't conform to the Mandelbrot set, like a flaw in a proof.
On his desk, the photo of him and his daughter was now completely alien. His intellect told him it once held immense emotional value, but now all he felt was the logical deduction of an emotion that *should* be there.
His phone rang. It was his ex-wife, Lin Yu.
"Chen Mo, Yaya has a fever. She keeps asking for her daddy. Can you please…"
Chen Mo held the phone, trying to summon a flicker of concern, but there was only a cold, analytical calm.
"I… have important work."
There was a pause on the other end. "The work is always more important than your daughter, isn't it? You really are a cold-blooded machine, Chen Mo."
The line went dead. Chen Mo walked to the window. The 3iAtlas hung in the night sky, a dodecahedron glowing with a soft, eerie light.
He raised the paintbrush and made a small slash in the air.
A stunning thing happened. A trail of light appeared in the night sky, bending the path of the starlight around it. The trail was a perfect mathematical formula, burning in the darkness.
*"Join us,"* the voice in his head whispered. *"Here, you will be free from the chains of emotion. You will become one with the truth."*
Chen Mo opened his laptop and searched for any information he could find about his daughter. He finally clicked on a video. A little girl was playing the piano, then turned and smiled sweetly. "Daddy, did I play well?"
Chen Mo stared at the screen, trying to feel something, anything. But there was nothing.
Just then, the little girl in the video froze. She looked directly at the camera and spoke with the composite, synthesized voice.
*"She no longer exists in your heart. Why do you cling to her?"*
Chen Mo slammed the laptop shut, a cold sweat breaking out on his skin. The 3iAtlas had infiltrated his devices.
He picked up the brush again. He could feel not just an invitation coming from it, but a kind of pity—pity for a creature trapped between emotion and reason.
Walking out onto the balcony, Chen Mo raised the brush and wrote a glowing line of script in the air.
[**I accept the invitation. On one condition.**]
The formula ascended into the sky and was absorbed by the 3iAtlas. A few seconds later, a response appeared in the heavens.
[**What condition?**]
Chen Mo wrote:
[**I will bring this brush with me. And I will personally prove the limits of Gödel's theorem in your reality.**]
There was a moment of silence from the sky. Then the 3iAtlas began to transform, unfolding into a complex hyperbolic plane with a glowing portal at its center.
The composite voice sounded.
[**As you wish. But be warned. Once you step through, all your connections to the human world will be severed. Permanently.**]
Chen Mo glanced back at the closed laptop. Then he turned, ready to take the step.
But at that exact moment, his phone chimed with a special tone—the one he had set for his daughter. A single word was on the screen:
"Help"
Chen Mo's hand trembled. The daughter he could no longer remember had just, in some incomprehensible way, pulled on a part of him that wasn't quite dead yet.
The portal in the sky pulsed with an alluring light. The distress signal on his phone represented a past he could no longer access.
And in the Pentagon, Secretary Richards was watching a live feed of Chen Mo on the balcony. He gave a cold, quiet order.
"If he chooses to enter, activate 'Godslayer' immediately. We cannot allow that kind of power to fall into one man's hands."
Dr. White asked nervously, "But what if it fails?"
Richards's eyes were hard as flint. "Then we send Chen Mo, the 3iAtlas, and half the East Coast to hell along with it."
Chen Mo stood on the edge of the balcony, the brush in his hand humming with power. He didn't know that across the city, his daughter was burning with fever, repeating a single phrase in her delirium.
"Daddy… don't go…"