by Karen Olsson
THE WEIL CONJECTURES
For Andrew
ALSO BY KAREN OLSSON
Waterloo
All the Houses
Contents
Also by Karen Olsson
Part One
One
Two
Three
Four
Part Two
Five
Six
Part Three
Seven
Eight
Part Four
Nine
Ten
Part Five
Eleven
Twelve
Thirteen
Fourteen
Acknowledgments
A Note About the Author
PART ONE
1.
Small for her age, she takes up maybe a third of the operating table, from her folded-over socks to the crown of her head. Every so often a nurse places a towel soaked in chloroform over her nose and mouth. While the doctor cuts into her abdomen she babbles, sings Christmas songs, recites names from ancient legends. She seems not so much asleep as bewitched.
It’s 1912. Simone is three.
With a snip and a pinch Dr. Goldmann fishes out her swollen appendix. “We are not interested in luxury,” the tiny patient announces, and the forceps nearly fall from his hands. As though she’s been possessed by some restless soul—the things she says! Afterward he tells her mother that she is too extraordinary to go on living.
She recuperates in a drafty room in the hospital annex. Although her mother urges her to lie still under a pile of blankets, Simone makes a game of kicking off the covers and trying to wriggle out of bed. As a young woman, Selma had wanted to study medicine, but her father, Simone’s grandfather, forbade it, and instead she married a doctor, drew a magic circle around her family, and lavished herself upon them. Now Selma brings a basin to the bed so that Simone can wash her hands for the fourth time. Now she tries to pin down her daughter by telling her a story called “Marie in Gold and Marie in Tar.”
Once there was a girl named Marie who was sent by her stepmother into the forest to look for food. In the middle of the forest she came to a house, and there she heard a voice asking whether she would like to enter through a door of gold or a door of tar.
“Tar is good enough for me,” she said, and all at once she was showered with gold pieces. She brought them home to her stepmother, who promptly sent her own daughter, also named Marie, into the forest. This second Marie arrived at the same house and was asked the same question. She, however, picked the door of gold. As soon as she walked through it, she was deluged with tar.
I am left wondering whether the first Marie ever found any food.
Whether the second Marie died of asphyxiation.
At any rate, Simone would later say that the story had a profound influence on her. All her life, it seems, she went looking for tar doors.
Though the doctor couldn’t have meant it literally when he judged her unfit for this life, he would be proved right. She was extraordinary, and at thirty-four she died a very strange death—an extraordinary death, the end product of her extraordinary manner of thinking and living.
Her older brother, André, is also extraordinary. A few years after Simone’s appendectomy, when he’s about nine, he discovers an algebra book, its own kind of door. He races right through, enters a house full of equations, and begins to tinker with them, rearranging terms, expanding here, factoring there. Sometimes when he finishes a page of calculations he’ll hold it up above his face and admire the sheer density of what he’s written, everything in alignment. The superscripts, the equals signs, the variables: x after x after x.
This worries his mother. “We can’t help but be a trifle annoyed and anxious, my husband and I, at the absorbing passion André shows for algebra,” Selma writes in a letter. “Some way or other he got hold of a book . . . and he is so happy that he has given up all play and spends hours immersed in his calculations.”
A month earlier, he’d been just as obsessed with croquet.
One day, coming down the stairs, he stumbles and falls. As he sits on the floor, clutching his knee, Simone, aged six, rushes to find his algebra book and then brings it to him, because she’s sure it’s the thing that will comfort him most.
His parents try taking away his paper and pencil, so that he might spend more time outside, but soon they find him using a pebble to scratch equations into the sidewalk.
A head for numbers.
Episodes of graphomania turn up in biographies of other mathematicians; take for instance Archimedes, who, it is said, would rake the ashes out of a fire and draw shapes in them. Who after bathing and oiling himself would trace diagrams upon his skin with a fingernail.
Or Karl Weierstrass, who in the 1840s and ’50s taught school by day and reimagined the field of mathematical analysis by night. Give him a pencil, said one of his sisters, and he might start to scribble his mathematics on any surface—on wallpaper, on a shirt cuff.
Weierstrass would later write of the “infinite emptiness and boredom” of his years as a schoolteacher, before he achieved renown as a mathematician just shy of forty.
About his success he would say, “Everything in life comes too late.”
The scrape of the rock across the pavement as the boy works out his calculations. His delight as terms fall away and roots reveal themselves, as he begins to hang formulas and number relationships around the new rooms in his mind. He takes shelter there while autos throttle past and cannons fire in the distance—the country is at war. The family has followed Dr. Weil to Neufchâteau, where he attends to soldiers wounded in battle and to victims of a typhoid epidemic. For the sick patients the preferred treatment is to plunge them into ice-cold baths. Most of them die.
André still plays with his sister, usually tutor to her pupil. He teaches her to read, delivers astronomy lectures on the bus. A know-it-all in short pants and a doll of a girl in a sailor dress, her hair in ringlets, egging him on with questions: oh, how they irritate the other passengers with their precocity! Something they don’t yet know is that they are Jewish, since their parents have turned away from religion and never discuss it, but there’s bound to be at least one old bigot on the bus who presumes by their appearance. Who huffs, I can’t stand listening to children parrot things they don’t understand.
Simone and André memorize long sections of verse by Corneille and Racine, and they recite them in turn, staring bug-eyed at each other. It’s a contest: although they smirk as they call out the lines, every time one of them misses a word or mangles a phrase, the other delivers a hard slap to the face.
They look alike, an older boy version and a younger girl version of the same child, with abundant black hair and eyes full of dark intensity, hungry to know everything. Churning brains appended to small, floppy bodies. They’ll shout a phrase in ancient Greek and take off running. Or fall so deep into their novels as to forget lunch. Or cackle loudly at some joke that only they find funny, tumbling into each other, their laughter a pulse that bounces back and forth between them. Their mouths gaping, their noses practically touching: ha ha ha ha ha!
Or: from another room Selma will hear odd shuffling sounds, and when she comes in to investigate she finds them pinching, kicking, grabbing each other by the hair. Their faces have gone white with rage.
One winter, André decides that he is done with knee socks, he wants to tough it out bare-shinned, and, naturally, Simone follows his lead. Over their mother’s protests they go sockless; worse, they’ll board a bus with her and shiver theatrically and chatter their teeth and complain that their parents refuse to buy them socks. One day another passenger hurries out of the bus after them, points at Selma, and denounces her: “Yo
u wretch!”
Children’s games, but in adulthood, too, Simone would be eager to deprive herself, to go without heat, food, sleep. And an inner voice would lash at her, You wretch!
“La Trollesse” is her childhood nickname within the family. The (feminine) troll, as though she were not quite a girl, yet not not a girl. And not quite of this world, though not belonging to any other: a lumbering creature from a fairy tale.
Once there were a brother and sister who devoted themselves to the search for truth. A brother who spent his long life solving problems. A sister who died before she could solve the problem of life.
2.
It was a conversation with his printer that led René Descartes to choose x to represent unknowns in his 1637 treatise La Géométrie, or so the story goes. Running out of letters, the printer offered Descartes the choice of x, y, or z to indicate unknown quantities in equations. When Descartes replied that it didn’t matter to him which one they used, the printer selected x, because x was used less frequently in French than y and z. In other words, a practical suggestion by a seventeenth-century typesetter lies behind all the x’s in algebra, and maybe some other x’s too. One way or another, x has come to stand for what we don’t know, what we’re seeking, for sex shops and invisible rays and the marked spots where treasure lies hidden.
Was the choice strictly pragmatic, I wonder, or was there always something erotic about x?
To compress the unknown into a single symbol was very powerful, for it made algebraic manipulation easier and more legible, and after Descartes it was widely adopted. Powerful in a broader sense, too, this naming the unknown: x, neither alive nor dead, took on an existence of its own, outside of time, worming its way into an infinitude of equations, of propositions. The unknown as a thing.
What is my unknown? My x?
“An insect tries to escape through the windowpane, tries the same again and again, and does not try the next window which is open and through which it came into the room,” writes the mathematician George Pólya in his book How to Solve It. “A man is able, or at least should be able, to act more intelligently. Human superiority consists in going around an obstacle that cannot be overcome directly . . .”
But I feel for the insect, because I’m a person who tends to be drawn to the glass, the banging—banging my head against a see-through wall, banging instead of solving, a way of forever putting off the solution. Then again I think there’s an intermediate condition, a mode that is more than banging and less than solving. It’s this in-between state I like, as I buzz my way across the window glass, not quite bent on escape.
Simone on the verge of adolescence: a slip of a girl half hidden by boxy clothes, glasses, that curly mass of hair. Skinny legs and small, uncouth hands, like buds reluctant to bloom. Her mother favors boys—the “forthrightness” of boys, she once explained in a letter, as opposed to the “simpering” of girls—and for a while Simone wishes to be treated as a boy. Her family calls her Simon; she signs letters to her parents “your respectful son.”
By the age of thirteen or fourteen, it becomes much harder for a girl to play at being a boy, and that’s not the only illusion that won’t hold up. Simone enters into a period of what she’ll later call “bottomless despair.” A sinkhole of self-doubt and shame. She decides she isn’t especially smart, not smart like her brother is, and sees no point in living if she’s merely a normal person.
She thinks about killing herself. “I didn’t mind having no visible successes, but what did grieve me was the idea of being excluded from that transcendent kingdom to which only the truly great have access and wherein truth abides,” she will later recall. “I preferred to die rather than live without that truth.”
Why should her brother be admitted to the kingdom and not she? What else was there?
Then, after weeks, months, of self-loathing, she discovers a way forward. A tar door. When one hungers for bread, one does not receive stones. Anyone who is sufficiently patient may achieve a kind of transcendence, provided that he “longs for truth and perpetually concentrates all his attention upon its attainment,” she’ll write. She arrives at an idea of strenuous faith, a discipline of attention. It’s a crucial epiphany for her: the only way she can rescue herself, that is to say the only way she can (on her terms) lead a life that is not worthless, is to devote herself wholly, with every ounce of her energy, to the truth—an impossible goal, really, but she would stay dedicated to it.
Her brother, by this time, is a student at the renowned École Normale Supérieure, a temple of learning where he gorges himself on mathematics and also on languages, among them Sanskrit. He’s rarely home, and when he is home he has no time to explain anything to her.
Her relations with her lycée classmates are not bad, but they’re not especially good either, and while she endures their pranks and shares meals with them, she invents a secret friend. This friend is, curiously, distant and hidden, a friend who she hopes will be revealed to her one day. She has made up a friend who won’t keep her company.
I know I wasn’t the only high-school girl to check The Simone Weil Reader out of the library. Saint Simone, herself an imaginary friend to who knows how many lonely teenagers of a certain era. In her own way, a severe and elusive one.
Did I actually read The Simone Weil Reader? Or did I just flip through it, lying on my bedroom carpet, depressed and restless, listening to cassette tapes? As a gawky girl, circa 1989, I was less curious about her writing than I was about Simone herself, the petite French ascetic with cool hair and wire-frame glasses, the political activist / intellectual / mystic who died young. Casting about for role models, I chose the most outlandish ones, women who’d lived lives I would never lead, who’d suffered in ways I never would, uncompromising and bold and pure while I was none of those things.
Maybe Simone and I have some unfinished business, that is to say, I’m moved by André Weil’s story in part because he was the brother of Simone Weil, the luminous mystery behind a book I failed to read. But I could also say that I’m drawn back to Simone Weil because she was the sister of André Weil, one of the great mathematicians of the twentieth century—math representing, for me, another piece of unfinished business.
Beginning in 1897, the mathematician Felix Hausdorff published literary essays under the nom de plume Paul Mongré, and in one of them he laments that two genders are insufficient. He wishes for a third: “Everything is thus, but must it be thus? . . . Could there not be a crystal space, where one could see around the corner and sense one’s way into another I? . . . Or why not three genders . . . Men, Middlers, Mothers . . .”
Never mind the dubious setup—that is, “men” at one pole and “mothers” at the other—I like his notion of “middlers.” I think of myself as a middler, or used to think of myself that way before I became a mother. Once I was a tall boyish girl who liked math—which, much as it was a field dominated by men, struck me even more so as a field dominated by middlers, by which I mean that in the aggregate its people seemed more androgynous than the general population.
Mongré = mon gré, French for “my taste” or “my liking.” Under that name Hausdorff also published poetry, a play, a book of aphorisms, and a book-length philosophical essay titled Chaos in Cosmic Selection.
Simone enters the École Normale Supérieure herself in 1928 to study philosophy, one of a handful of women enrolled there. She smokes constantly, loves to stay up all night talking and arguing in a café, though what she’d prefer to be doing (or at least thinks she’d prefer to be doing) is manual labor. She wants to work on a farm. She believes it would’ve been better to be born poor. Once, while walking with a fellow philosophy student named Camille Marcoux, she passes a wine market and decides to apply at once for a job putting corks into wine bottles. Marcoux has to steer her away.
Like Simone, Marcoux is interested in mathematics, and he lends her a geometry textbook by Jacques Hadamard, a beloved professor at the École Normale and an outstanding mathematician—wh
o, as it happens, would become the supervisor of André’s doctoral thesis on Diophantine equations. When she returns the book, it has been all but torn apart, with some pages marked up and others ripped out. Hadamard, she informs Marcoux, has committed crimes against geometry.
(What these crimes might’ve been, I don’t know.)
Then there’s a vacation on the Normandy coast in 1931. Simone is captivated by the fishermen there and begs them to let her join one of their crews. They all reject her, until one of them, Marcel Lecarpentier, sees her “running along the shore like a madwoman,” as he’ll later recall, then “going into the sea with her wide skirts,” and turns his boat around. He allows her onboard to work. When a bad storm hits, she refuses to be tied down.
“I’m ready to die,” she declares. Her voice is peculiar, a low monotone and yet full of fervor. “I’ve always done my duty.”
My own earliest math-related memory dates to around second or third grade, when “function machines” appeared on worksheets. These were cartoon machines, tall and narrow and amiable, that turned numbers into other numbers. Each machine contained a two-column grid, partially filled with numerical inputs and outputs. On top of the grid was a space for a rule, like “Multiply by five,” in which case the number in the first column times five would give you the number in the second column. The task was to supply the blank parts of the grid, to write the machine’s output for a given input, or vice versa. Or sometimes you’d have to guess the rule from the numbers given. All of which is just to say that I remember being pleased by the machines; I liked the idea of a multiply-by-five contraption. It was an early step back from numbers themselves, a shift of emphasis toward the dynamics of it all, from the stolid nouns to the freewheeling verbs that connected them.
And a little green shoot in my mind: there must have been something tantalizing to me about abstraction itself, even if I couldn’t have said as much at the time. I remember in that same year discovering a pleasure in writing that was in no small part physical, delighting in the way I could move a pencil across my notebook and fill line after line, entire pages! Of course I didn’t recognize how I’d begun to reposition myself, how ready I was to disappear into a piece of paper—how the representation of a thing could seem more alluring than the thing itself.