by Karen Olsson
At the sight of the photo an interior seam splits, and it comes rushing back to me, how intimidated I was by them. The true math people, I mean, the wunderkinds, the superstars. This included my professors—I was terrified of all of them—and a number of my quote-unquote peers. Along with their myopic half smiles, their awkwardness, their naïveté, their sandals, their hacky sacks and ping-pong paddles, they had, or seemed to have, a solid confidence, an inner compass pointing directly to a university math department. They struck me as happily at home in that world, they had arrived, whereas any time I had reason to venture into the math department I would scurry in and out as quickly as I could. From those exceptional kids I detected (or at least imagined) some mix of snobbery and pity toward someone like me, smart enough to get by, but just the ordinary type of smart. Much as mathematics came with a democratic ideology, according to which it was a realm of rarefied knowledge open to anyone who wished to work her way along its paths, there also seemed to be an unstated but obvious hierarchy. If math to me was a dark place where I went groping around on my hands and knees, here were these other people with killer night vision who could see everything at once, go prancing from one topic to the next.
Weeks pass before I actually write to the mathematician. During this time I mention to a few people that I’m thinking of trying to interview a math professor but have been reluctant to contact him because I’m intimidated and also not entirely clear about what I’m asking, and they all say the same thing: I’m sure he’d be flattered to hear from an interested person outside his field, I’m sure he’d love to talk to you—but I’m not sure. In my mind I am that deaf person, nagging a composer to explain a symphony. One day as I’m driving I think I catch sight of the very man, that mathematician, on a bicycle, crossing a street up ahead, but I’m not close enough to get a good look.
At last I compose an interview request, not as an e-mail but as a document that I save to my computer. The next day I tinker with it, save it again. I revise it once more the following afternoon. It’s a Friday when I paste the text into an e-mail and hit Send, and in that instant I’m already sure that I’ve made a mistake.
I keep checking, into the evening, for a reply, fully expecting him to put off an interview or turn me down outright. Nothing that day, nothing over the weekend. On Monday I suppose he’s returned to work and will reply soon, but still nothing comes. Nothing all week. Nothing at all.
Never mind the possible explanations for this—an aggressive spam filter, or an in-box so jammed with other e-mails that mine was lost in the mix, or just the ordinary pileup of life that would outweigh a near-stranger’s request, or some ordeal that would eclipse it entirely—I’m quick to interpret the lack of response as confirming the scorn I always suspected was there, disdain for the tourist.
A lot of Simone Weil’s writing is awfully high in fiber, and it can be hard to digest, just as it is in her college essay on Descartes. Much as she critiqued her brother’s mathematical abstractions, her prose is often quite abstract. She introduces ideas and relentlessly loops around them. At times her propositions have hardly any more meaning to me than the Pythagoreans’ Justice = 4, only without the whimsical concision of Justice = 4. Yet her work is also sown with passages of wisdom and beauty, so that right when I’m tempted to start skimming, something will hook me, and I dog-ear the page so that I can return to it later.
I assume that I would experience Simone as I do her writing, that at times I would find her too earnest, an exhausting companion, saying the same thing over and over, obsessed with that day’s obsession, yet at other times she’d be spirited and generous. An unexpected mischief would surface. This is the Simone who, having at last secured passage on a Swedish freighter bound for Liverpool, gathers the small group of fellow passengers every evening and, under an overcast sky that seems to reflect their collective foreboding, entertains them by telling folktales.
And here she is at the Liverpool clearing center, where she is detained for two and a half weeks while the British perform their background checks: she learns to play volleyball, of all things. Someone’s put up a raggedy net on a dirt lot behind the cafeteria, and often she’s the first one there. She comes dressed in baggy pants and a button-down shirt and a hat that she removes before playing. Aiming for the brick wall of the building, she tries to teach herself to serve. She almost knocks out a window.
Honestly I think I understand anyone else’s dislike of math better than I understand whatever hold math has had on me. In response to the person who asks, “But what’s the point of all this?,” I don’t have a good answer. In fact I sometimes am that person, can muster only a peevish respect for, let’s say, Monsieur Pierre de Fermat, royal councillor at the parliament of Toulouse, who, when he wasn’t engaged in the dreary business of regional administration, would turn his attention to another convoluted system of rules, searching for laws governing the whole numbers.
An uncredited portrait of Fermat, reprinted in a book I took out of the library, renders the great seventeenth-century amateur in an ample black cloak, with flowing dark curls and a pencil mustache. He looks, to me, rather fat and supercilious. In 1658, apparently, he presided over the trial of a defrocked priest and sentenced him to be burned to death. Meanwhile he laid out his results in letters to his contemporaries, to Mersenne, to Carcavi, to Pascal. Here’s one: every prime number that can be expressed in the form 4k + 1 can also be expressed uniquely as the sum of two squares, a2 + b2.
In college I was never tempted to take a course in number theory, which considers questions like this one, because it seemed to me too insular, a kind of numerical navel-gazing. I am pretty much unmoved by the fact that certain prime numbers can be written uniquely as the sums of two squares, and although now I believe that number theory is much more interesting than I gave it credit for, I imagine that many (if not most) humans feel about math the way I felt then about number theory. It’s remote, it’s not about anything but itself except by a series of happy accidents.
“Fermat lived temperately and quietly all his life, avoiding profitless disputes,” claims the mathematician E. T. Bell in his book Men of Mathematics, a hoary classic of math history published in 1937. “We shall understand his even, scholarly life if we picture him as an affable man, not touchy or huffy under criticism,” Bell asserts, and then in a confusing juxtaposition he adds that Fermat was “without pride, but having a certain vanity.”
Humble, but haughty? Then again, E. T. Bell was paying tribute to his heroes. Over the years it has emerged that Men of Mathematics is not always the most reliable source.
A slight woman, plainly dressed, pushes open the door to an office in London. The boss thinks at first that this lady has come begging, that somewhere there are curly-haired pauper children to feed, but then she introduces herself, she’s the new hire, Simone Weil, and still all he can think to do, since she seems on the verge of collapse, is to help her to the nearest chair. She slumps over herself. Her long black skirt bunches on the floor. He wonders whether she has fallen asleep, until she starts to speak. With hardly any preface she announces that her mission, of which the highest authorities have been made aware, is to drop herself into battle by means of a parachute. She has trained as a nurse, she adds.
The boss offers her a glass of water. She scans the room, tells him again that she has medical training.
For a few days the question of what to do with Simone hangs over the Free French office in London, until somebody finally says, well, she’s a writer, let her write. They give her a small room with a desk. Various proposals have been made regarding how to reorganize the French government once the war ends, and they ask her to evaluate these schemes.
Far-fetched as the parachute idea seems to everyone else, she won’t let it go, keeps mentioning it, and at the same time she works harder than the boss would’ve imagined anyone could, much less this woman. She writes day and night, page after page; it becomes obvious she’s not just analyzing parliamentary structure.
Having refused the offer of a typewriter, she composes everything in her careful, neat hand: well-formed letters that stand up straight and rather prettily on the lined page. It’s as though she’s taking dictation from a sourceless voice that speaks slowly, steadily, incessantly.
Rather than hand over her work in person she leaves it at the boss’s door. Included in her typescripts are reflections about truth on a higher plane, about the idea of a good in the universe that is not just a human construct but an objective reality. The boss shows it to his assistant, who as he reads moves the paper farther and farther away from his face, wincing, and then asks, “But why doesn’t she concentrate on something concrete?”
She’s trying to learn to drive, they discover. She gets her hands on an aviation manual and studies it carefully. She obtains a parachutist’s helmet.
The essence of powerful speech, according to Simone, lies in “bare simplicity of expression.” Writing should be stripped-down and impersonal, thought scrubbed of any trace of the thinker. The greatest creations of Western culture, to her mind, are ones that achieve this transcendent anonymity: the Iliad, geometry, Gregorian chant.
Naturally, then, she doesn’t insert herself directly into what she writes; her texts proceed by force of argument, unconcerned with style. Shortly before leaving France she passed off her notebooks to Thibon, suggesting to him that some of the material from them might be published under his name, since what mattered to her were the ideas they contained, not the fact that she was the one who wrote them down. Yet these notebooks, hundreds of pages of fragments, will eventually constitute a key part of her literary legacy—that is to say, the very pages from which she was ready to delete her name will, later on, help make her name. Unpublished during her lifetime, they’re full of quotations and precepts, philosophical and religious and critical meditations, a working out of the principles of her own mental ex perience. They seem like notes for some hugely ambitious future book, a Bourbaki-like survey of existence as she knew it, starting from first principles.
For Simone, impersonality is not just a writerly ideal but an existential and religious one. She wants to bring about her own undoing. What she aspires to is a state of selfless perception, in which her mind wouldn’t be limited to the data of her own senses. Rather, by suspending her own imagination and holding herself at attention, she thinks she might receive divine wisdom from the material world the way a blind person is informed by a cane: “May the whole universe, in relation to my body, be to me what to a blind man his stick is in relation to his hand. His sensitivity is no longer really in his hand but at the end of the stick.” The universe would become an instrument. Through it she would know God.
The lecture room where André is installed that fall and winter is drab, and the acoustics are poor. It’s as though the room’s soundscape were partitioned into disjoint subsets, a well of his own words pooling around the lectern where he stands, and other, more agile noises floating above the students in eddying currents of their own murmurs and the timbre of the pipes. Every day but Friday, groups of army recruits are led into the room by their noncommissioned officers. The soldiers are silent and well-mannered young men for as long as they’re in line, but as soon as they spread out and take their seats they revert to boyhood, unable to stop wiggling and stretching and whispering and snorting. Little did André ever think he’d miss the dull grinds from the year before, and yet these kids care even less for math. Really they don’t have any use for it at all. They’ve been awaiting orders to deploy, and their commanders, searching to occupy them in the meantime, have dispatched them here to learn algebra and analytic geometry. It’s make-work for both the troops and the colleges, which have plunged into poverty for lack of students.
They barely take note of the algebra that André is presenting—off the cuff, having not bothered to prepare a lesson. The interlocking machinery of simple equations, the formulas that delighted him at the age of nine, can’t breach the hard shells of their brains. The army boys imitate his voice under their breath, then grow bolder and start to talk among themselves. One of them sneezes twice, and even that seems aggressive, such loud sneezing. André has to ask an officer to settle them down.
When it’s calm, a boy raises his hand.
“But I don’t understand what x is.”
André smiles to himself. If only he could deliver a real response, convey something of the scope of the question. He could devote a lecture just to the history of mathematical symbolism, to Diophantus, Viète, Descartes.
A thousand images come to mind—himself as a boy with his algebra book, the half smile of his teacher Hadamard. Eveline as she was that summer in Finland. His prison cell. What is it? What is x?
He returns to this room, these boys, and starts to explain (again) the use of the variable.
O men of mathematics!
In the middle of watching the twenty-first online algebra lecture, I hit a wall, stricken with a sudden exasperation as much physical as it was mental, as though my head, my shoulders, part of my spine, were itching from the inside. While Professor Gross was elaborating on the Sylow theorems, as he was saying that “any two Sylow p-subgroups H and H' are conjugate,” I became instantly tetchy, I couldn’t take it any longer. Who cares? I am a midlife mother of two, I thought morosely, and this is the most pointless thing I could possibly be doing.
Though on second thought it was no more pointless than anything else I would be using the Internet to do. One day I’d opened YouTube and seen featured there, under the heading “Watch It Again,” a row of five videos I’d recently viewed. In the middle of the row were stills from algebra lectures, a trio of Professor Gross action shots—Gross writing on the blackboard! Gross gesturing at the blackboard! Gross gazing at the blackboard!—and flanking those were a pair of 1980s music videos by New Edition.
That said, I paused the lecture.
At the same time it occurred to me that maybe the problem wasn’t too much math but rather too little, a lack of immersion, since I only watched these lectures once or twice a week, if that. In the interim, I would forget about Sylow p-subgroups entirely (even as New Edition’s “If It Isn’t Love” stayed intractably stuck in my head).
“This is not like an everyday job which one can interrupt any minute and resume again,” said Gauss of math. “One always has to invest a lot of effort and has to have much free time to again bring everything to one’s attention.”
I didn’t have the free time, the attention. It had been months since I started watching the lectures, and I was only a little ways past the midpoint of the semester, and it was far from clear to me what would be the merit in continuing with the class, other than whatever merit comes from finishing what you’ve started.
On a cloudy spring day, at a convent outside of London, a nun greets two young Frenchwomen, Simone and a friend, who have appeared at the gate. What can she do for them? Simone mumbles and trips over her words, and it takes some back and forth before the nun understands that they wish to camp on the grounds. The nun looks at the sky—thunderheads loom in the distance. Are you sure? she asks.
Well after vespers it begins to pour. Straining to see from her room’s window, she can’t make out anything and decides that the women must have left, but after adjusting her vision she finds their slick and collapsing tent. Sighing, she puts on her rubbers and runs out to them, urging them to come inside, as her umbrella pulls away from her and rain hits her slantwise, but only one of them agrees to follow her back to the building. The other, the one who asked permission to camp there, insists on staying in the tent, which is hardly any different from staying out under nothing at all, so bent up and abused and waterlogged is the canvas. Shivering wildly even as she refuses. The nun recognizes it, this love of misery, she’s known fellow nuns who angle toward suffering like plants to the sun, but she pleads with the woman. You’ll catch your death out here, she shouts. Catch my death! the woman repeats, as though she hasn’t heard this turn of phrase before. Catch my death
, she says again, and stays out there all night long.
My exasperation with the Sylow theorems echoed the way I’d begun to feel about math in general by the time I was a senior in college, as though I’d been squeezing myself into a container I no longer wanted to stay inside of, which was also the way I’d come to feel about my relationship with my boyfriend, even though these were good containers and had been very good to me and maybe I could’ve lived my whole life, another life, comfortably within them. But I grew restless, I threw all that away, just to see what I could see.
“There is a reality located outside the world, that is to say, outside space and time, outside man’s mental universe, outside the entire domain that human faculties can reach,” Simone writes while she’s in London. “Corresponding to this reality, at the center of the human heart, is a longing for an absolute good, a longing that is always there and is never satisfied by any object in this world.”
Beyond the quotidian real world and everything we know, an inaccessible goodness: for her, every search is a search for this, doomed to failure in the sense that these searches can’t attain their end during this lifetime, but then again the quality of a life derives from the quality of its searching.
The mathematical conjecture, labeled as such, is a creature of the twentieth century; while there were always open problems and speculations and hypotheses, the spread of conjectures as a genre of math is a recent development. Barry Mazur—a Harvard mathematician I once took a class from but never dared speak to—calls these contemporary proposals “architectural conjectures,” meaning they lay out the basis of a theory, a core set of expectations believed to be true, a foundation and a design that waits for others to come along and construct the rest of whatever is being built, maybe redeveloping the surrounding area in the process. The driving force behind all this conjecturing, Mazur writes, has been analogy, as in the case of the Weil conjectures. What the architects have been designing are bridges.