by Karen Olsson
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.
3.
Having forgotten whatever I once knew about complex functions Fourier series field extensions compact surfaces hyperbolic spaces random walks et cetera, I am left with memories of the Science Center at Harvard, a building with a facade like stair-stepped boxes, constructed around the time I was born, in the early seventies. I attended classes there most days and spent I don’t know how many nights working on problem sets in the library or in vacant rooms. I remember tracking slush through an entry already muddied by hundreds of boot prints, coming and going, descending to the basement computer center or landing in one of the main-floor lecture halls or making my way upstairs to a classroom empty of charm or even the notion of charm. Though elsewhere literature and h
istory were taught in stately old rooms softened by high windows and wainscoting, historically appropriate paint colors, the mossy aura of textual study accompanied by a certain whiff of wealth, the sciences had been paired with austere minimalism, that is to say white walls and black chalkboards and silver conduit pipes leading to clusters of heavy-duty switches. I sat among my fellow students (whizzes, immigrants, nerds, with all their anxious, humming brainpower) in a plastic chair, my backpack at my feet, always afraid that I was about to fall hopelessly behind but also proud that I’d so far managed to hold on to the fast horse of a difficult class. I who, as a white girl from private school, might’ve seemed marked for the humanities but who had wandered over there instead, as though by mistake. Not a boy, not Asian or Indian or Jewish, not from Russia or eastern Europe, not a child of scientists. It seemed as if all the other math kids belonged to one or more of those categories.
As for why I touched down in their midst: I could blame my erratic curiosity, a tendency to follow my nose no matter how many times my nose has led me astray. Or I could say that I was trying to prove myself, to no one other than myself. But after more than two decades, if anything my dalliance with math seems like just that, a past love, one I remember with nostalgia and the kind of echo feeling that adheres to the memory of an old romance. I mean, I had always liked math, but just how it came to consume me in college is a question that I produce a different answer to each time I’m asked—whether it’s somebody else who’s asking or whether I’m asking myself, as I still do from time to time.
An Italian ship takes André from Genoa to Bombay, a two-week voyage, and when the weather is good he strolls back and forth on the deck, reciting lines from a Sanskrit poem. To shield himself from the southern sun, he wears a cork helmet he bought in Paris, and yet, surrounded by sparkling ocean, he burns in no time. His skin peels, and over the course of two weeks he turns the red-brown color of a fox.
mandam mandam nudati pavanah
(gently gently blows the wind upon you)
From Bombay he goes by train to Delhi and then on to Aligarh, where the two men who’ve been sent to greet him titter at his helmet. He’ll settle into an adobe house with a zoologist from Germany: no electricity or plumbing, but high ceilings and a roof terrace and furniture that he has custom-made, according to French designs. His office at the university overlooks a courtyard, which every day fills with students and empties out again, then just before sunset fills with long-tailed birds that speckle the grounds with their shit.
A few doors down is a gnarled old chemistry professor who complains about his idiotic students, about his paltry wages, and especially about the lowlife employees of the railway station who, he’s sure of it, have stolen the shipment of guavas that he ordered from a faraway orchard. He claims he can smell the fruit in the station, that he has found guava seeds near the tracks.
Some of the oldest recorded mathematics comes to us from ancient Egypt, in documents such as the Rhind papyrus, which dates from around 1700 B.C. and contains eighty-five problems and their solutions. The opening line of the papyrus has sometimes been translated as “Directions for Attaining the Knowledge of All Dark Things.”
It was a dark thing, perhaps, to find the volume of a truncated pyramid, as in this problem: “If you are told: A truncated pyramid of 6 for the vertical height by 4 on the base by 2 on the top. You are to square this 4, result 16. You are to double 4, result 8. You are to square 2, result 4. You are to add the 16, the 8, and the 4, result 28. You are to take a third of 6, result 2. You are to take 28 twice, result 56. See, it is 56. You will find it right.”
My freshman year, during the first week of classes, when you could attend a lecture or two before committing yourself, I visited a daunting, yearlong math course meant for prospective math majors. By the time I found the room, a narrow auditorium with a sloped floor, the seats were already taken. I stood in the back and peered down at the professor, who seemed really far away, not only because he was in the front of the lecture hall and I was in the rear but because of his thick glasses, and the way he spoke in damp, guttural torrents inflected by what might’ve been a mild speech impediment, not to mention the very energy in the room. A geeky electricity.
CONSIDER A BALL IN N DIMENSIONS, the professor said.
Below me, a pack of heads bobbing, nodding, while he chalked a mysterious inequality up on the blackboard. A ball in n dimensions? I had no idea what that meant, much as I would’ve liked to think it referred to a fancy-dress occasion in an alternate universe. I left and took a computer science class instead.
But I turned out to be lousy at computer science—I had no patience for debugging programs—and at the beginning of my sophomore year I went back to the same math class. Which was muleheaded of me, since in the prior semester, in addition to bombing out of second-semester computer science, I had not done especially well in a multivariable calculus class meant for physics and engineering majors. I’d pretty much decided to leave all that behind and major in philosophy. But I can remember reading Hamlet at nineteen and understanding even that play as essentially a story of a fellow adolescent who, like me, was indecisive. And there were other factors, forces that drew me back. Before that second semester came to its sorry end, I’d signed up for a math summer program, and there I learned that the math that professional mathematicians do has a different tenor from multivariable calculus for physics majors, more abstract and more rigorous. That summer I also began an epistolary romance via a platform called Pine, an early form of e-mail used mostly by science people (and all too perfectly named, for a facilitator of epistolary romance), which would lead to an actual romance with someone studying physics and math. In other words, I found some social support for the whole endeavor. In other words, I fell in love. And then there was the very fact that I’d felt defeated—I wanted to prove those other classes wrong.
By that time I had overcome my fear of the ball in n dimensions, and I knew that the course split into two classes after the first exam: one faster-paced and directed at the sort of kids who seemed to have all met one another already at International Math Olympiad competitions; the other, while still challenging, accessible to more ordinary people who happened to like math. I took that other class, which as it turned out was the best class I ever took in anything.
Though André is a twenty-three-year-old foreigner in his first proper job, he’s nonetheless been made chairman of the department. Right away he is saddled with a complicated subtraction problem: he must produce a report on the staff of his department and in effect choose which of his three colleagues should be fired. None had made a good impression. “Pathetic characters,” he’ll call them in his memoir, “devoid of merit.”
One of them short and obsequious. One of them with a long beard he dyes red, known for his willingness to help students. One who claims to be studying a copy of an ancient Arabic manuscript, yet no one besides the man himself has ever laid eyes on the putative document. If André knew where to find decent replacements, he would happily fire them all.
The best class I ever took in anything, not just because I was entranced by the math itself but because we were encouraged to work on the difficult weekly assignments in groups, and I had never collaborated like that before: arguing my way through problems with three or four or five other people into the wee hours of the night. We were a small band of students giddily, exhaustedly trekking through an abstract moonscape, helping one another across patches of ice or fighting over which direction to head next. The egos, the insecurities, the unabashed nerdiness! I miss it still.
Also, at nineteen, so much is up in the air, open to question, unreliable. I think part of what I liked about math was simply that it seemed like a sure thing, as sure as a thing could be, a solid mass of true and rigorous and irreproachable knowledge that I could grab like a pole on a bus.
See, it is 56. You will find it right.
I’ll just go ahead and say, in case it’s not already clear, that André can be pretty
abrasive. He is arrogant, impatient, short with people. Wound tight.
As the house has no electricity and hence no electric fans, a boy is paid a pittance to stand on the veranda and pull at the string that sets in motion the panka, a piece of cloth hung from the ceiling, so that the air might circulate while André naps. Sometimes the boy dozes off, and André wakes up in a sweat and shouts “Pankevale!” to rouse him.
(His sister not only would’ve refused to nap under those conditions but surely would’ve insisted upon yanking the string herself, while someone else—the boy—slept.)
A caustic sense of humor. A hatred of flattery.
But he loves India. Everything is brighter or else darker than it is in France, louder or else more opulently silent, more fragrant or more foul. Oleander bursting in front of the house, mangoes rotting in the back. He loves it. He loves the spicy food. He loves to read the railway timetable in bed and take trips on the weekends.
On a full-moon night he and two friends are lent a car and driver by a university benefactor, and they travel to Fatehpur Sikri, where in the latter part of the sixteenth century the Mughal emperor Akbar built magnificent palaces of red sandstone for himself and his courtiers, only to abandon them because of a lack of water. There are no gates or guards or hours of operation, and under the light of the moon André and his friends wander through the abandoned imperial city, through courtyards and galleries and harems where, in the blazing moonlight, lattices within the windows cast honeycombs of shadow on the floors.