The Weil Conjectures

by Karen Olsson

  After I went to college my dreamy notion of becoming an expatriate journalist seeped underground, but from time to time some version of it would bubble up, even as I skirted around the math department. Most of my math courses followed a standard format—lectures pegged to a given textbook, problem sets, exams—but I took one class, a seminar on dynamical systems, that attempted to combine the mathematics and the history of the subject. We were assigned to write a paper, in addition to solving problems. One day I found myself in the professor’s office. I don’t remember whether I’d gone there on purpose or just happened by the office while he was sitting there with the door open, but I think it was the latter: I walked past and he called me in to talk. He complimented the paper I’d written and asked whether I was planning to apply to graduate school in math. I assumed he was encouraging me because the math profession could use more women, but what he said next was that the math profession could use more writers. “We need people who can explain this stuff,” he said.

  I gave a noncommittal answer, I wasn’t sure, maybe, but what I remember thinking was: I want to be a real writer. I’m not going to write about math.

  Very early one morning, policemen knock on the door of the Marseilles apartment. Selma Weil answers, then goes to wake up her daughter, who rouses herself and dresses quickly. As Simone sips the coffee her mother has made, the police ask about the local Resistance network, which she recently joined in hopes of being sent to England. She tells the men she doesn’t really know the others in the network, doesn’t recognize the people in the photos they show her, doesn’t remember names. She says she learned about the group from a person at a bus stop whom she never saw again. The police search her room, which is so full of manuscripts that Selma finds herself feeling sorry for them.

  On three occasions Simone is summoned to the police station for questioning. Each time, in the belief that she’ll be arrested, she brings a valise packed with clothes and a copy of the Iliad; each time her parents accompany her and wait across the street at a small café while she is inside the station. Her interrogators leave her in a corner and speak to her only occasionally, issuing vague threats of what might happen if she doesn’t inform on other members of the Resistance. She stalls and stalls.

  At last an asthmatic officer tells her she’s a little bitch.

  You know I could have you thrown into jail with a bunch of whores, he says.

  She can see her parents out the window, anguishing over plates of untouched food.

  I’ve always wanted to know that environment, she replies. Which is the absolute truth. She returns the policeman’s stare, and in the end she is let go.

  What was I thinking in that professor’s office, what did I mean by “a real writer”? I remember a conversation I had with a fellow student in the math summer program I attended after freshman year, a computer and math nut who always wore tracksuits and who’d grown up on an island off the coast of Washington State, who’d only ever been to the movies on group excursions during this summer program, an American singularly removed from American culture. We were eating lunch or maybe dinner in a university cafeteria, and I found myself arguing with him, pestering him to admit that he hoped to write a novel eventually, which I believed everyone secretly did. He explained that, to the contrary, his intention was to pursue a Ph.D. in math.

  “But after that,” I was saying, “surely one day you want to write a novel . . .”

  “No!” he said, exasperated. “I want to be a mathematician!”

  Finally, reluctantly, I was persuaded that he had no interest whatsoever in writing a novel. Only after this conversation did I begin to think that my desire to be a writer was something particular to me, that even if many other people also wanted to be writers, and even if there was a part of me that recoiled at the whole soggy notion of being an aspiring writer, nevertheless I was, already, an aspiring writer.

  According to one scholar’s thesis, it was the invention of writing that gave rise to number as an abstract concept. The prehistoric people of the ancient Near East, exchanging sheep or grain, originally recorded what they’d traded using clay tokens that represented the thing traded; in time they began storing the tokens in a type of envelope, marking the envelope to designate what was inside of it. Eventually they dispensed with the tokens, in favor of the marks.

  Simone has arranged to meet, at a café in Avignon, a writer-farmer: that is to say, a self-taught philosopher who owns twenty acres of land with a stone farmhouse where he lives with his wife and his father. This man, Gustave Thibon, is a devout Catholic and a meticulous diarist. Sitting near the café’s entrance, he waits for her and notices the rot at the bottom of the doorframe that she has yet to walk through, the wobble of the table. He’s uneasy about the whole thing, about this woman who wants to be hired to do manual labor. Yet his friend Father Joseph-Marie Perrin asked him to consider bringing her on, and in deference to the priest he has agreed to host her for a few weeks.

  A philosophy teacher from Paris, the priest told him, living in Marseilles for now. An intellectual, a woman of faith. Thibon said he couldn’t understand why she would want to work on a farm.

  Truth be told, I don’t entirely understand it myself, the priest said.

  When she enters the café it seems to him as though a moderately strong wind could spirit her off. A shipwreck of beauty, he will later recall her as, careworn and concave. She’s barely over thirty but looks much older and at the same time ageless. In spite of the summer heat she has on baggy wool pants and a jacket over her shoulders. An untended mass of black curls. Her eyes, scanning the room and then finding his, startle him, and right away he thinks: She’s possessed. Her very presence causes him a peculiar kind of pain.

  She disagrees with him about everything, countering whatever he says in an oddly monotonous voice, until he’s practically drained of speech. Two hours they spend hashing out the terms of her employment, which she fears are overly generous.

  I don’t care to have any privileges the other workers don’t enjoy, she insists.

  All I meant to say is that they have more experience, and if you become exhausted you must—

  I will keep on. I’ll take my breaks when the others do, or less often if necessary.

  If necessary?

  To do my share.

  He avoids putting her to work until she insists he stop treating her as a friend. In the fields she’s an even less promising laborer than he anticipated, blundering and overeager. More than that, she’s a source of worry. How much can she take? What if she collapses? Yet she has a doggedness, a will to keep toiling—and there’s something about that pure gaze of hers that makes him respect her.

  In the evenings, they read Plato in Greek together.

  She refuses to accept a bedroom in the farmer’s house, protesting that it’s too comfortable for her. Instead she settles into a tumbledown cottage at the edge of the woods, its dirt floor scattered with old rat droppings.

  (All it lacks is a door of tar.)

  She calls it her fairy-tale house, and so becomes the sort of figure—a sprite, a witch, a shapeshifter—who would live in one. She fetches her water from a nearby spring, sweeps out the droppings, clears weeds outside, gathers wood, makes fires. She eats very little, wishing she could be like one of those hibernating animals who require no food. She sleeps on the dirt floor.

  “I continually see the light of the sun shine in a different way on the valley and the hills,” she writes in a letter, “and then, at night, vast stretches of starry sky.”

  Her parents come to visit and encounter an old woman who, not knowing their identities, exclaims that the man who owns the vineyard has taken a mistress: “She is a crazy woman who lives in a hut!”

  There is something tempting, albeit ultimately unsatisfying, about the theories of the semioticians, those who would leave reality out of it and explain math as simply a language, a sign system, an intersubjective method of persuasion. If only for selfish reasons—then I could c
onceive of what I did in college not as a random detour but as a specialized kind of writing, a strange and unnecessary but not entirely irrelevant preamble to all the other writing.

  André has taken an underpaid instructorship at a college in Pennsylvania, a position he considers beneath him and would not have accepted but for the fact that he has a family to support, a baby on the way, and no better option. (Although a mathematician of rare talent, he is also a Jewish foreigner—it hasn’t been easy to secure an American job.) The college is a second-rate engineering school that trains young men to go to work for Bethlehem Steel. A diploma machine: he becomes a cog. His colleagues know nothing of genuine mathematics; their task (and his) is to feed formulas to narrow-minded students, young men he considers mediocre, dismally incurious—he isn’t exactly sensitive to the fact that none of them grew up with his privileges, they are working-class kids trying to make their way up the ladder, now with the draft hanging over them. He doesn’t foresee that some of them will be sent to his own country to fight in the war that he escaped.

  Once in a while he forgets where he is, forgets the dull colleagues, the rows of blank faces in the classroom, the clicking of the mechanical pencils, the steel mills and their black smoke. He launches into a proof, an argument he finds beautiful and, flicking his wrist like an orchestra conductor, he marks out lines of symbols on the chalkboard, losing himself in the chain of reasoning.

  This completes the proof, he concludes, still holding his stub of chalk up in the air, still in his bubble of contentment as he turns back to the students.

  A vast silence follows.

  Are there any questions? he asks.

  Always the same one. Is that going to be on the exam?

  In an interview posted to YouTube, the mathematician Maria Chudnovsky discusses how she and three colleagues developed a 150-page proof of something called the strong perfect graph theorem: “You know, when you work on a problem like that where the solution is long, first you just try in the dark, you try different things. And then you start to get an idea of how things should go. And then sometimes you think you’ve got an idea, but in fact you’re wrong. But then there comes a time when you imagine some sequence of steps in your mind, and you’re able to take all the steps.”

  You try in the dark, you develop an idea that’s maybe the wrong idea, indeed you might run down a bunch of wrong ideas, but then (if you’re lucky) another, better idea comes and you’re able to imagine your way to a solution. That is the fundamental narrative of the creative process in any field. And of writing in particular, because (like math) it is so interior, theoretical, on some level a game with symbols. However much these games depend on an external reality, receiving inspiration from and following rules imposed by the world outside our heads, they require barely any equipment, they can be played by a person alone at her desk.

  At her request, Thibon helps Simone get hired at another farm for the grape harvest. There she will kneel and cut grapes with an old pair of steel clippers, laboring for hours, past what should be her breaking point, eventually so depleted that she lies down under the vine trunk but still reaches up to tug another bunch toward her face. (Sometimes I am crushed by fatigue, she admits to a friend, but I find in it a kind of purification. She writes to her parents that the work brings her great joy.) When she goes to sleep at night, it’s as though she is still at work, cupping the fruit and snipping the stems. Her body becomes sticky and stained from grapes that have burst, and her fingers won’t fully extend, as though they’ve been snared in a gummy purple web, but she must go on with her cutting, go on inching down the rows with her back in the dirt, her hair in the dirt, dragging her wooden basket along, the marvel of everything made—the basket, the clippers, her shoes, her hands—not lost on her even as she is picking grapes in her sleep.

  One day, as she’ll tell the farmer, she wonders whether she hasn’t died and gone to hell without noticing, hell having turned out to be an eternal grape harvest.

  She memorizes the Greek text of the Lord’s Prayer, recites it to herself until the words tear her thoughts from her body and deliver them to a place that seems to be outside of perspective or point of view, outside of space itself.

  People who encounter her during this time, old friends and strangers alike, are struck by her presence. A nun, one Sister Colombe, would recall meeting her—how she entered a room wrapped in a navy-blue cape and stood quietly behind a companion—and would remember the indelible impression made by her manner of silence, the quality of attention that radiated from her at first sight.

  For a spell she becomes unhitched from any regimen or routine. She writes, “I have fallen into a kind of abyss in which I’ve lost the idea of time.”

  It’s probably best to leave analogies between math and writing in the semi-obscure territory that André Weil described in his letter to his sister—that realm of intuition, furtive caresses, mental courtship. But I think back to the conversation I had with the young mathematician who I believed must want to write a novel, and while it’s funny to me now, the way I projected my own secret hope onto someone sitting across from me at lunch, I think another reason I was convinced that a math person would wish to write fiction is because he was a math person, already inclined to probe and to help extend a kind of alternate universe. I wonder whether mathematicians and fiction writers might be people for whom the lure of alternate worlds is particularly strong. And then I wonder whether this is just a natural consequence of abstract representation itself, that once you start putting words or numbers on paper you are already beginning to piece together a kind of parallel universe, which you then want to access, discover, flesh out. I might go so far as to conjecture (too broadly, too tentatively) that even hash marks on ancient clay envelopes contain the seeds of this desire.

  André, across the Atlantic, has become more tightly roped to the idea of time, as the expansion of Eveline’s stomach reminds him. His wife has become so large he’s sure there must be a giant baby in there, or three babies, no other pregnant woman has ever been this huge, he’s convinced, though in reality he’s just never paid much attention to pregnant women, much less shared a bed with one.

  Once the baby is born she seems to him as little as Eveline was big. Sylvie, they call her, not actually intending to recombine pieces of her mother’s and her aunt’s names, yet there will be times in her life when André starts to address her as Simone before he catches himself.

  While mother and baby are still in the hospital, his friend Chevalley, one of the Bourbaki crowd who’s now teaching at Princeton, drives over to help out at the house and talk mathematics. As André washes dishes Chevalley stands at the drying rack, listening to André discuss the problem of counting solutions to polynomials, which he punctuates by waving a soapy glass in the air, letting off a flurry of suds. His stepson, now twelve, watches as André hands that same glass to Chevalley without having rinsed it off, then plunges his sleeve into the dishwater, not noticing until after he’s finished saying what he’s been trying to say about Dedekind’s generalization of the Riemann zeta function. Quite a few plates and cups and pots, washed after previous meals, are sitting on the countertops, as André has not bothered to put them away, in some cases doesn’t even remember where they go.

  When he brings Eveline and their daughter home, the baby seems like something else he might all too easily lose track of, her forehead still wrinkled, her hair a matted black skullcap. Her arms flail and her tiny fingers curl. Her doll’s lips are wet. When he picks her up she is all but weightless, how can it be, a living human.

  One evening, a few days before Easter, Simone travels by train to the town of Carcassonne to visit a writer named Joë Bousquet, who during the First World War took a bullet to the spine that completely paralyzed him. For twenty-two years he’s been confined to bed; he continues to live with great physical pain.

  The night is lit by a low yellow moon. Simone reaches the house very late and pushes gently on a door that Bousquet’s mother
left open, finding a clean, spare house with almost no furniture, only two chairs and a table and a lamp in front, and beds in the bedrooms, one of which belongs to Bousquet.

  He is awake. He never sleeps for more than a few hours at a time, he whispers. He’ll need to be moved but sometimes there’s no one to move him, and then all he can do is meditate on the crushing pains in his legs and in his sides and in his back where the bullet shattered his vertebrae.

  Simone is on her knees. She asks him to tell her more, to describe his pains to her. He meets her eyes and calmly obliges. Sometimes I am shot again, he says, I feel the bullet rip into my spine again. Sharp glass splinters explode all through my body, I am cut everywhere. Sometimes my joints feel like they’re on fire, a fire deep inside my legs. Or nails are driven into my hip bones. Every day and every night is different, he says.

  It must be torture, she says, as much in fascination as in sympathy.

  It is, but I’ve learned how to observe pain. I see it happening in myself.

  What is it like, to watch?

  It has . . . I can’t put it into words. I can only watch.

  I wish I could know what you feel. Maybe it sounds naïve.