Proof

“Sleep is the interest we have to pay on the capital which is called in at death.”

Arthur Schopenhauer

3 a.m. his eyelids grow heavy as he scans the blinking text on the computer screen — the sole illumination in the darkened apartment. The blinds are drawn, closing the room off to the world. He lies bare-chested on his bed; his legs splayed over the edge of the full-sized mattress. His laptop rests on his sternum, rising with each inhalation, then falling. His vision blurs; text loses focus. The machine’s screen dims to conserve power. He considers whispering a quick thank you, but there’s no time for gratitude. The room recedes into the darkness as does he. His eyes grow heavier — his mind begins to quiet; finally, rest.

3:17 a.m. He’s awakened by the tick-tick-tick-tick ticking of the wall clock. Heat from the laptop on his chest underscores the similar sensation in his eyes. He peers into the darkness at the vague outline of the clock. He swipes at his mouse-pad to remove the screensaver and see the time in the bottom right hand of the screen. A pulsating throb courses through his frontal lobes; still not enough time he thinks to himself. He surveys the rest of the 61 square inch screen. His program, a fast-Fourier transform implementation of the Lucas-Lehmer primality test, continues to compute whether 257,885,161–1 is prime. Ineluctably, the algorithm marches along. So must he. Tick-tick-tick-tick. Time for a smoke.

17 minutes. The moon above shines incandescently as if it had just been lit. He chuckles as he exhales, sending pulsating smoke streams from his nostrils. 17 minutes. 7, plus or minus one, hours of sleep are recommended by physicians for a well-functioning body and mind. For the graduate student, sleep means a non-functioning mind, impossible in the search for truth. He takes another drag; the embers at the end of his cigarette glow brightly. 17 minutes in the past 71 hours. His mind trails as it traces the diffusion of his breath. The warm air escapes his lungs and rushes past his pharynx, and, in the night air, its frenetic activity is cooled and the water vapor becomes visible as condensation. He takes another drag as he watches his breath dissipate. His mind had tried slowing the problem down to tease a solution into visibility, but so far all he’d encountered were smokescreens. He mushed the embers of the cigarette against the cold red brick of the wall he’d been leaning against and turned to head back inside.

13 minutes until four. Almost 5 hours until he has to teach his Introductory Calculus class. His eyes quickly scan across the books and papers on his desk — a now coffee stained Über die Hypothesen welche der Geometrie zu Grunde liegen, a stack of student papers he still had to grade, a student ID badge with the name Stanislaw Orlovsky, and textbooks with arcane titles which might hold the key to his secret. He must get back to work. He’d end with the student papers; their silly mistakes would ease the pain of those he’d made during this 13 month journey for truth.

Stan stood out among his fellow graduate students. He had finished the required course work and the qualifying exams in the first year. That summer, he studied statistical mechanics at the Institute for Advanced Studies in Princeton. His peers often looked up to him as an intellectual giant. He was a physical one too. Standing at 6 feet 7 inches, he towered over most people he met, but in the mathematics department where a lack of height correlated with overwhelming intelligence. His massiveness was the glaring exception to the rule. Until recently anyway. His advisor had been the first to notice Stan’s weight loss and the darkening circles around his eyes. He’d made the mistake of cautioning his student about the difficulty of the problem. “You know Stan, I don’t know how productive this is for you; maybe, you should pick a different topic. Even Riemann knew when to move on.” The circle’s darkened as he sharpened his focus, willing his mind to crack the problem.

He would conquer the problem, or it would devour him, and so far The Riemann Hypothesis had been eating him from the inside out. He thought about it all the time. He thought about it while teaching L’Hopital’s rule to still-innocent undergraduates; he thought about it during periodic drives around the perimeter of the campus; he thought about it while imagining sex with the attractive brunette studying functional analysis; he thought about it on long runs through the trails in the nearby nature reserve. He thought that, maybe, all he needed to do was think a little longer; then, he could, finally, rest.

He sat in the back of another boring mathematics talk with his head down, doodling. The speaker droned on about the importance of his work on infinite Abelian groups. The speaker becomes mute to him; Stan sat transfixed by the spiral growing beneath him. He’d written the number one in the center of the page, then a 2 to its right, then a 3 on top of the 2, then a four to the left of the 3. The list grew and he began to circle certain numbers in the list. The spiral on the paper matched the spinning in his head. The numbers seemed to be calling out to him; whispering to him that they were willing to share their secrets if he would only listen — listen more intently.

Later that night he sat at his desk looking at some results about the Hypothesis. He yawned; knowing that it was a false signal, there would be no sleep. Even if he were to lie on his bed, his mind would re-trace the arguments he tried to apply to solve the problem. Time for a smoke. Before he could leave, the phone rang. He considered leaving but decided against it. Some human interaction might do him good.

“Hey, Stan, it’s Mel, did ya’ hear the news?”

“How’s it going Mel? No, what news?”

“They’re saying somebody solved it.”

Oblivious, Stan responded, “Solved what? I don’t know if you can be any more vague Mel. Do you know what time it is?”

“They’re saying some guy solved the Riemann problem.”

Incredulous, Stan retorts, “Get out of here! No way anybody’s closer than I am.”

“I’m sorry Stan, they’re saying the problem’s been solved. They’ll have to check the proof of course but…”

“No way, you have to be kidding me Mel! Somebody solved my problem?”

“Yeah, some Japanese guy — Katsuo or something like that.”

Stan felt the receiver slipping from his hand. Mel’s voice rasped on, “Are you there? You there Stan?” sounding like a plea from a distant corridor. The moisture had already begun to bead on his forehead. His hands felt cold, unattached to his arms. His chest tightened. He thought about the possibility of fading into irrelevance, the possibility of giving talks where students doodled in the background with his voice on mute. His lips, dry and cracked, ached for moisture. His hands reached for the faucet but stopped short. It was pointless; he knew. There would be no satiation. Suddenly, the walls were closing in on him and he needed air.

He dashed out of his apartment in a wild frenzy. He loped right by the elevator as if any stationary moment might be an invitation for Katsuo’s eraser to catch up to him and expunge his existence. He galloped down the stairs, skipping stairs with his long strides. He could almost feel himself escaping effacement. Close to the door, to freedom, to the cool night air that makes the invisible breath visible, he caught one last misfortune: his ankle twisted on the penultimate step. His momentum did not yield as he crashed into the door. A door of solid glass. A final, last misfortune.

He lay in a growing pool of blood in an irregular geometric shape with bits of glass adorning him. His torso — too high on his body. On his face was a peaceful look; the look of one at rest.

The ECG plots a graph of the young man’s beating heart, the rhythmic, eerily periodic beat. A woman sits in the corner looking on as she has for many sleepless nights. She sits stroking his massive right arm with her own dainty little hands; she hopes that her presence, her touch would wake him as it did when he was younger. She’d made a fuss about the size of the bed, but still his legs hung over the edge. Her one consolation was the mathematics of the ECG, the mathematics of her boy’s heart. She wonders if he’s in pain. The doctor walks in, “Ms. Orlovsky, I think I may have some good news for you. It seems that your son has shown signs that he may be exiting the vegetative state.”

She blinked back a tear at the thought that her boy was finally getting ready to wake up. It had been too long; he lies there as the ECG readings prints out the patterns of his heart. She cannot find the words, she searches and then, as if out of thin air she exhales, “13 months. 13 months you’ve been asleep.”