The Solitude of Prime Numbers

by Paolo Giordano

  2760889966649. He put the lid back on the pen and set it down next to the paper. “Two thousand seven hundred sixty billion eight hundred eighty nine million nine hundred sixty six thousand six hundred and forty nine,” he read out loud. Then he repeated it under his breath, as if to take possession of that tongue twister. He decided that this number would be his. He was sure that no one else in the world, no one else in the whole history of the world, had ever stopped to consider that number. Probably, until then, no one had ever written it down on a piece of paper, let alone spoken it out loud.

  After a moment’s hesitation he jumped two lines and wrote 2760889966651. This is hers, he thought. In his head the figures assumed the pale color of Alice’s foot, standing out against the bluish glare of the television.

  They could also be twin primes, Mattia had thought. If they are . . .

  That thought suddenly seized him and he began to search for divisors for both numbers. 3 was easy: it was enough to take the sum of the numbers and see if it was a multiple of 3. 5 was ruled out from the beginning. Perhaps there was a rule for 7 as well, but Mattia couldn’t remember it so he started doing the division longhand. Then 11, 13, and so on, in increasingly complicated calculations. He became drowsy for the first time trying 37, the pen slipping down the page. When he got to 47 he stopped. The vortex that had filled his stomach at Alice’s house had dispersed, diluted into his muscles like smells in the air, and he was no longer able to notice it. In the room there were only himself and a lot of disordered pages, full of pointless divisions. The clock showed a quarter past three in the morning.

  Mattia picked up the first page, the one with the two numbers written in the middle, and felt like an idiot. He tore it in half and then in half again, until the edges were firm enough to pass like a blade beneath the nail of the ring finger of his left hand.

  During his four years of university, mathematics had led him into the most remote and fascinating corners of human thought. with meticulous ritualism Mattia copied out the proofs of all the theorems he encountered in his studies. Even on summer afternoons he kept the blinds lowered and worked in artificial light. He removed from his desk everything that might distract his gaze, so as to feel truly alone with the page. He wrote without stopping. If he found himself hesitating too long over a passage or made a mistake when aligning an expression after the equals sign, he shoved the paper to the floor and started all over. when he got to the end of those pages stuffed with symbols, letters, and numbers, he wrote “QED,” and for a moment he felt he had put a small piece of the world in order. Then he leaned against the back of the chair and wove his hands together, without letting them rub.

  He slowly lost contact with the page. The symbols, which only a moment before flowed from the movement of his wrist, now seemed distant to him, frozen in a place that denied him access. His head, immersed in the darkness of the room, began to fill with dark, disorderly thoughts and Mattia would usually choose a book, open it at random, and begin studying again.

  Complex analysis, projective geometry, and tensor calculus had not managed to diminish his initial passion for numbers. Mattia liked to count, starting from 1 and proceeding through complicated progressions, which he often invented on the spur of the moment. He allowed himself to be led by numbers and he seemed to know each one of them. And so, when it came time to choose his thesis topic, he went with no doubts to the office of Professor niccoli, professor of discrete calculus, with whom he had never even sat an exam and about whom he knew nothing other than his name.

  Francesco niccoli’s office was on the fourth floor of the nineteenth-century building that housed the mathematics department. It was a small room, tidy and odorless, dominated by the color white—the walls, shelves, plastic desk, even the cumbersome computer on top of it, were white. Mattia drummed softly on the door and from inside Niccoli wasn’t sure if the knocking was for him or for the office next door. He said come in, hoping he had not made a fool of himself.

  Mattia opened the door and stepped into the office.

  “Hello,” he said.

  “Hello,” replied niccoli.

  Mattia’s eye caught sight of a photograph hanging behind the professor, which showed him, much younger and beardless, holding a silver plate and shaking hands with an important-looking stranger. Mattia narrowed his eyes, but couldn’t read what was written on the plate.

  “Well, then?” Niccoli urged, studying him with a frown.

  “I’d like to write a dissertation on the zeros of the Riemann zeta function,” said Mattia, staring at the professor’s right shoulder, where a dusting of dandruff looked like a little starry sky.

  Niccoli made a face, an ironic smile.

  “Excuse me, but who are you?” he asked without concealing his disdain and locking his hands behind his head as if wanting to enjoy a moment of fun.

  “My name is Mattia Balossino. I’ve finished my exams and I’d like to graduate within the year.”

  “Have you got your record book with you?”

  Mattia nodded. He slid his backpack off, crouched on the floor, and rummaged around in it. niccoli stretched out his hand to take the book, but Mattia preferred to set it on the edge of the desk.

  For some months the professor had been obliged to hold objects at a distance to get them properly into focus. He quickly ran his eyes over the sequence of high grades. not one flub, not one hesitation, not one try that had gone wrong, perhaps on account of a love story that had ended badly.

  He closed the book and looked more carefully at Mattia. He was dressed anonymously and had the posture of someone who doesn’t know how to occupy the space of his own body. The professor thought he was another of those who do well in their studies because they are unable to make much headway in life. The ones who, as soon as they find themselves outside the well-trodden paths of the university, always reveal themselves to be good for nothing.

  “Don’t you think I should be the one to suggest a topic for you?” he asked, speaking slowly.

  Mattia shrugged. His black eyes moved right to left, following the edge of the desk.

  “I’m interested in prime numbers. I want to work on the Riemann zeta function,” he replied.

  Niccoli sighed. Then he got up and walked over to the white bookshelf. As he ran his index finger along the spines of the books he snorted rhythmically. He pulled out some typed pages stapled in one corner.

  “Fine, fine,” he said, handing them to Mattia. “You can come back when you’ve performed the calculations in this article. All of them.”

  Mattia took the stack of pages and, without reading the title, slipped it into his backpack, which leaned against his leg, open and slack. He mumbled a thank- you and left the office, pulling the door shut behind him.

  Niccoli went and sat back down in his chair and thought about how over dinner he would complain to his wife about this new and unexpected annoyance.

  22

  Alice’s father had taken this photography business as the whim of a bored little girl. Nonetheless, for his daughter’s twenty-third birthday, he gave her a Canon SLR, with case and tripod, and she had thanked him with a beautiful smile, as impossible to grasp as a gust of icy wind. He had also paid for her to take evening classes, which lasted six months, and Alice hadn’t missed a single lesson. The agreement was clear if implicit: university came before everything else.

  Then, in a precise instant, like the line separating light and shade, Fernanda’s illness had gotten worse, dragging all three of them into an increasingly tight spiral of new tasks, drawing them toward an inevitable cycle of apathy and mutual indifference. Alice hadn’t set foot in the university again and her father pretended not to notice. A feeling of remorse, the origins of which belonged to another time, kept him from imposing his will on his daughter and almost kept him from talking to her at all. Sometimes he thought it wouldn’t take much, all he would have to do was go into her room one evening and tell her . . . Tell her what? His wife was disappearing from life like
a wet mark drying on a shirt and, with her, the thread that still connected him to his daughter was slackening—it was already scraping the ground—leaving her free to decide for herself.

  With photography Alice liked the actions more than the results. She liked opening the back of the camera and unrolling the new film a couple of inches, just enough to catch it in the runner, and thinking that this empty film would soon become something and not knowing what, taking the first few snaps into the void, aiming, focusing, checking her balance, deciding whether to include or exclude pieces of reality as she saw fit, enlarging, distorting.

  Every time she heard the click of the shutter, followed by that faint rustle, she remembered when she used to catch grasshoppers in the garden of their house in the mountains when she was a little girl, trapping them between her cupped hands. She thought that it was the same with photographs, only now she seized time and fixed it on celluloid, capturing it halfway through its jump toward the next moment.

  During the course she had been taught that the strap of the camera is to be wrapped around the wrist twice. That way, if someone tries to steal it they’re forced to tear your whole arm off along with it. Alice ran no such risk in the corridor of our Lady’s Hospital, where her mother was being cared for, but she was used to carrying her Canon like that anyway.

  As she walked she grazed along the two-tone wall, brushing it with her right shoulder from time to time to avoid touching anyone. Lunchtime visiting hour had just begun and people were pouring into the hospital like a liquid mass.

  Aluminum-and-plywood doors opened onto the wards, each with its own particular smell. Oncology smelled of disinfectant and gauze soaked in methylated spirits.

  Alice entered her mother’s room, which was the second to last. She was sleeping a sleep that wasn’t her own and the gadgets to which she was connected didn’t make a sound. The light was faint and drowsy. on the bedside table red flowers were arranged in a vase: Soledad had brought them the day before.

  Alice rested her hands and the camera on the edge of the bed, where the sheet, lifted in the middle by her mother’s outline, flattened out again.

  She came every day to do nothing. The nurses already took care of everything. Her role was to talk to her mother, she imagined. Lots of people do that, acting as if the patients were capable of hearing their thoughts, able to understand who was standing there beside them, and conversing with them inside their own heads, as if illness could open up a different channel of perception between people.

  It was not something that Alice believed in. She felt alone in that room and that was that. Usually she would just sit there, waiting for half an hour to pass, and then leave. If she met a doctor she asked for news, which was always the same anyway. Their words and raised eyebrows meant we’re only waiting for something to go wrong.

  That morning, however, she had brought a hairbrush. She took it out of her bag and delicately, making sure not to scratch her face, combed her mother’s hair; at least the hair that wasn’t squashed against the pillow. She was as inert and as submissive as a doll.

  She arranged her mother’s arms on top of the sheet, extended and parallel, in a relaxed pose. Another drop of the saline solution in the drip ran down the tube and disappeared into Fernanda’s veins.

  Alice moved to the end of the bed, resting the Canon on the aluminum bar. She shut her left eye and pressed the other to the viewfinder. She had never photographed her mother before. She pressed the shutter and then leaned a little farther forward, without losing the frame.

  A rustling sound startled her and the room suddenly filled with light.

  “Better?” said a male voice behind her.

  Alice turned around. Beside the window a doctor was busying himself with the cord of the venetian blinds. He was young.

  “Yes, thanks,” said Alice, a little intimidated.

  The doctor stuck his hands in the pockets of his white coat and went on looking at her, as if waiting for her to continue. She leaned forward and snapped again, more or less randomly, as if to please him.

  He must think I’m crazy, she said to herself.

  Instead the doctor came casually over to her mother’s bed. He took a glance at her chart, narrowing his eyes as he read, reducing them to slits. He went over to the drip and moved a wheel with his thumb. The drops started to come down more quickly and he watched them with satisfaction. Alice thought there was something reassuring about his movements.

  The doctor came over to her and grasped the bed rail.

  “The nurses are obsessed,” he remarked to himself. “They want darkness everywhere. As if it weren’t already hard enough in here to tell day from night.”

  He turned and smiled.

  “Are you the daughter?”

  “Yes.”

  He nodded, without condescension.

  “I’m Dr. Rovelli,” he said. “Fabio,” he added, as if he’d been thinking about it.

  Alice shook his hand and introduced herself. For a few seconds they stared at the sleeping Fernanda, without exchanging a word.

  Then the doctor tapped twice on the metal bed, which sounded hollow, and walked away. As he passed by Alice he leaned slightly toward her ear.

  “Don’t say it was me,” he whispered, winking and pointing at the light-filled windows.

  When visiting hours were over Alice descended the two flights of stairs, crossed the entrance hall, and left through the automatic glass doors.

  She crossed the courtyard and stopped at the kiosk for a bottle of fizzy water. She was hungry, but was used to keeping the impulse in check until she had erased it almost entirely. Fizzy drinks were one of her tricks. They were enough to fill her stomach, at least long enough to overcome the critical moment of lunch.

  She looked for her wallet in her purse, hampered slightly by the camera that hung from her wrist.

  “It’s on me,” said someone behind her.

  Fabio, the doctor whom she had met just half an hour before, held out a bill to the man in the kiosk. He smiled at Alice in a way that stripped her of her wish to protest. Instead of the white coat he wore a blue short-sleeved T-shirt and a strong aftershave that she hadn’t noticed before.

  “And a Coke,” he added, turning to the man.

  “Thanks,” said Alice.

  She tried to open the bottle, but the top slipped through her fingers without moving.

  “May I?” said Fabio.

  He took the bottle from her hand and opened it using only his thumb and index finger. Alice thought there was nothing special in the gesture, that she could have done it herself, like anyone else, if only her hands hadn’t been so sweaty. And yet she found it strangely fascinating, like a small heroic feat performed specially for her.

  Fabio gave her back the water and they drank, each from their own bottle, glancing stealthily at each other as if contemplating what to say next. Fabio’s hair was short, with chestnut curls that shaded into red where the sun struck them directly. Alice had a sense that he was aware of the way the light played on his hair; that in some way he was aware of everything he was, and all the things around him.

  They moved a few feet away from the kiosk, together, as if by common agreement. Alice didn’t know how to say good-bye. She felt indebted to him, partly because he had given her the water and partly because he had helped her to open it. She wasn’t even sure she wanted to go so quickly.

  Fabio understood.

  “Can I walk you to wherever you’re going?” he asked cheekily.

  Alice blushed.

  “I’m going to the car.”

  “To the car, then.”

  She didn’t say yes or no, but smiled, looking in another direction. Fabio made an obsequious gesture with his hand that meant after you.

  They crossed the main road and turned into a smaller one, where the sidewalk was no longer sheltered by trees.

  It was from Alice’s shadow, as they walked side by side, that the doctor noticed the asymmetry of her gait. Her right shoulder,
weighed down by the camera, acted as a counterpoint to the line of her left leg, which was as hard as a stick. Alice’s unsettling grace was exacerbated in her oblong shadow, making it look one-dimensional, a dark segment branching out into two proportional and equal mechanical prostheses.

  “Have you hurt your leg?” he asked.

  “What?” said Alice, alarmed.

  “I asked if you’d hurt yourself,” he repeated. “I saw you were limping.”

  Alice felt her good leg contracting too. She tried to correct her walk, leaning on her faulty leg as much as she could, until it really hurt. She thought of the cruelty and precision of the word lame.

  “I had an accident,” she said. Then, as if by way of apology, she added, “A long time ago.”

  “Car?”

  “No, skiing.”

  “I love skiing,” Fabio said enthusiastically, sure that he had found an opportunity for a conversation.

  “I hate it,” Alice replied crisply.

  “That’s too bad.”

  “Yes, too bad.”

  They walked side by side not saying anything more. The young doctor was surrounded by an aura of tranquillity, a solid and transparent sphere of security. His lips were pursed in a smile even when he wasn’t smiling. He looked at ease, as if he met a girl in a hospital room every day and chatted to her as he walked her back to her car. Alice, on the other hand, felt like a piece of wood. Her tendons were on the alert, she was aware of the creaking of her joints, the stiff muscles sticking to her bones.

  She pointed to a parked blue Seicento, as if to say that’s it, and Fabio spread out his arms. A car passed along the road behind them. From nothing, its noise grew and then faded away again, until it finally disappeared.

  “So, are you a photographer?” said the doctor, to buy some time as much as anything else.

  “Yes,” Alice replied instinctively. She immediately regretted it. For the moment she was a girl who had quit university and was wandering around the streets snapping photographs more or less at random. She wondered whether that was enough to make her a photographer; what was the boundary between being and not being someone?