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—who, 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.
Hausdorff rose to fame (mathematical fame, at least) for his work on set theory, which helped lay the groundwork for modern topology. He was a professor in Leipzig, then Bonn, then the Baltic city of Greifswald, and then Bonn again.
Though Jewish by birth he had assimilated; his wife, Charlotte, the daughter of a Jewish doctor, had converted to Lutheranism, and they baptized their daughter. Believing that they could keep their heads down and get by unnoticed, they reacted too late to the rise of the Nazis. On November 9, 1938, the day after Felix’s seventieth birthday, came the pogrom known as Kristallnacht. A mob gathered outside his house.
“There he is, the head rabbi,” they shouted. “Just watch out. We are going to send you to Madagascar, where you can teach mathematics to the apes.”
As I understand it, André and Simone Weil’s last name is pronounced something like “vay” but every time I read it I hear the word wail. André wail. Simone wail.
After Kristallnacht, Hausdorff searched for a means to emigrate to America. He never found one. In 1942 he, Charlotte, and Charlotte’s sister took lethal doses of poison in order to avoid the camps.
“I am sorry to cause you yet more effort beyond death,” Hausdorff wrote in a farewell letter to Hans Wollstein, who was his friend and estate lawyer, and who himself later died at Auschwitz. “Forgive us our desertion! We wish you and all our friends to experience better times.”
A masochistic student, Simone spreads out her books on the floor of her unheated apartment and shambles on her knees from one text to another, the winter wind blowing through the open windows as she turns the pages.
She crawls about the room, then leans over Descartes like an animal drinking, her vertebrae bulging through the back of her shirt. Then it’s on to Kant, to Chardin. There is damp laundry hanging on lines strung between the walls, stiffening in the cold, a banner that she forgets about when she pushes herself up and stands on tingling feet. For a moment her face is shrouded in her underwear.
Or she bows over a geometry book at a quay of the Seine where large blocks of stone are unloaded from boats, kneeling on the ground here too, in love with stone, with everything that’s hard.
“I studied mathematics, which is the madness of reason,” announces the narrator of Clarice Lispector’s Água Viva.
While in college André learns enough Sanskrit to read the Bhagavad Gita, with the help of an English translation contained in an anthology called Sacred Books of the East. He is smitten with the poem, and it becomes his guide, as much of a faith as he will find in his life. Later on it will also help him to intuit something of the way his sister thinks.
His copy of the Gita is a small volume covered in red velvet, the pages coarse and pulpy. The black script bleeds in places. He mutters lines to himself, undulations of syllables.
O Sanjaya, what did my sons desirous of battle and the sons of Pandu do after assembling at the holy plain of Kuruksetra?
He meets—in Paris, at the home of a French scholar of Indian studies—the minister of education for the state of Hyderabad, a tall, laughing man who says he’ll soon be appointing new professors to the Aligarh Muslim University, not far from Delhi. The minister is to become president of the university and wants to establish a chair of French civilization. André, who yearns to go to India on any terms, volunteers for the job. Later that fall he receives a cable: IMPOSSIBLE CREATE CHAIR FRENCH CIVILIZATION. MATHEMATICS CHAIR OPEN. CABLE REPLY.
Long ago, in the prehistory of civilization, the human mind was crude, a basic animal mind—or so conjectured Simone in “Science and Perception in Descartes,” a long essay she wrote during her final year of the École Normale. This strange paper contains in embryo some of the questions and themes that would obsess her throughout her life. Hardly a conventional academic work, it starts off with a speculative tale of how science came to be: In some ancient era, she imagines, people had no access to broader concepts and abstractions, yet they had an inkling that other forms of thought were possible, and so they invested priests and kings with power, because they believed them capable of this higher knowledge. And then along came Thales, an early Greek mathematician. His development of geometry was “history’s greatest moment,” she writes—(!!!)—a revolution that overthrew the absolute authority of the priests.
But to what end? she asks. Did that revolution merely replace the false rule of priests and kings with a (truer, yet still unjust) rule of mathematicians and scientists? Or did it bring equality, by revealing that the purest thought is also ordinary thought, that we might all live by the light of our own minds?
Recently I sought out this essay, and I’d hardly begun reading before it became obvious to me why I never made much headway into The Simone Weil Reader. Her prose is dense, at times baffling; I have to bushwhack my way through “Science and Perception in Descartes,” clearing back each sentence, each long paragraph, without much notion, as I go along, of where I’m headed. Many of her claims are more bold than they are convincing. Surely a professional historian would reject the essay out of hand. But as I read it, I picture its author, a twenty-one-year-old philosophy student still struggling to step out of her brother’s shadow, and I find even her oblique flights of theorizing more fraught, more poignant, than I would have as a younger reader, since now I take this parable to be informed by Simone’s own youth. I remember the specter of her older brother’s genius, her own crisis of identity, and I think of course she associates power with some inaccessible type of cognition.
Once she’s done with her imaginary history, André’s invisible pull on the essay seems all the stronger. For Simone then launches into a critique of present-day math, or as she puts it, “the absolute dominion that is exercised over science by the most abstract forms of mathematics.” Math has drifted too far away from us; it has become disconnected from the real world. Eventually she’ll take this up with André directly and tell him outright that contemporary mathematics, his beloved vocation, is too removed from life.
She wants to reconcile the abstract and the concrete, to make philosophers and mathematicians of us all, but how that would work is never clear. Math, as Simone sees it, ought to function as a kind of passageway between the mind and the world: “I am always double: on the one hand, a passive being who is subject to the world, and on the other, an active being who has a grip on it; geometry and physics help me to conceive how these two beings can be united, but they do not unite them.” Only through action—“real action, indirect action, action that conforms to geometry”—can reason seize hold of the world.
Action that conforms to geometry? What could that be? During the year she worked on the essay she barely consulted her adviser, the philosopher Léon Brunschvicg, who in the end did not think much of “Science and Perception in Descartes.” He gave it the lowest possible passing grade: a ten out of twenty.
But here’s another line from the essay: “I must be tricky, cunning, I must hamper myself with obstacles that lead me to where I want to go.”
Who could say what that line has to do with Descartes, still I think to myself, Yes, exactly—this is how a writer must be. All these years I’ve spent throwing obstacles down in front of myself, coming up with problems too twisted to solve.
Everything in life comes too late.