IN A 1941 ESSAY penned for Cahiers du Sud, Simone Weil wrote that a key responsibility of writers is the ability “of awakening us to the truth”; those writers who succeed “give us something in writing that is equivalent to the depth of reality.” The exchange that follows ventures to discover some of that depth. It comes in the aftermath of my review of Karen Olsson’s The Weil Conjectures: On Math and the Pursuit of the Unknown (2019), which appeared in the Washington Independent Review of Books in August.
Olsson’s book received considerable attention in the press, which is unusual given that its contents are mostly cerebral though occasionally coated with autobiographical glosses. One of the reviews was authored by Parul Sehgal, a book critic at The New York Times, who characterized Olsson’s work-craft as “[b]eguiling.” According to Sehgal, the book’s treatment of mathematics — “its focus, abstraction, odd hunches, blazing epiphanies” ― depicts the discipline “as a powerful intoxicant, a door to euphoria. […] Olsson is evocative on curiosity as an appetite of the mind, on the pleasure of glutting oneself on knowledge.” In short, the book entices minds drawn to wrestling with truths, both mathematical and biographical.
But Sehgal’s appraisal included a cautionary note related to the way Olsson portrayed Simone Weil, one of the two main characters in her book. In Seghal’s view, Olsson’s depiction of Weil was unfair at times, particularly her use of the word “unhinged.” Such terminology and synonymous terms offer “a crude diagnosis, especially in a book that gives short shrift to her work and influence” — a judgment with which my own review-essay agreed. Sehgal added that Olsson’s treatment made it “difficult to discern how rich and various [Weil’s] life truly was; or to grasp her political shrewdness and the intellectual concerns and the style that has irrigated the work of Maurice Merleau-Ponty, Iris Murdoch, Giorgio Agamben, Elizabeth Hardwick, Susan Sontag.” Indeed!
The Weil Conjectures left me in a reviewer’s quandary. On the one hand, I valued the creative cast of the book and its tug-and-tumble of ideas; on the other hand, I felt an injustice had been committed in its portrayal of Weil, a woman not without her problems but also deserving of a real measure of respect. My review alone, however, seemed inadequate to address this issue, so I had an idea: perhaps the author might agree to a digital Q-and-A with no punches pulled. Much to my surprise, Karen Olsson graciously accepted my invitation. Even though my review had raised some questions about her book, she volunteered to participate in this open and frank exchange of ideas; she went along with it, bringing her own case to the court of public judgment. For that generosity, I sincerely thank her.
RONALD COLLINS: Your career has been impressive, spanning journalism and fiction. The Weil Conjectures is your first nonfiction book, though you wrote in an essay for Granta that the original project began as a novel, a fictional work cast in the shadows of André Weil, the renowned mathematician.
Why the shift from fiction to nonfiction? And is this shift total? On that point, Professor E. Jane Doering of Notre Dame University asked me to pose this question: “To what extent did your imaginative fictional writing enter into the composition of Conjectures?”
KAREN OLSSON: For most of my career I’ve written nonfiction and fiction, but the balance has shifted over the years. First, I was a journalist writing (unpublished) fiction on the side, then I published a novel [Waterloo, 2005] and continued to work for magazines, then I had kids and did less work for magazines while publishing a second novel [All the Houses, 2015] and beginning a third. As you note, that third novel, about mathematicians, morphed into this book, which broadly speaking is nonfiction, but there are scenes in the book that are speculative — based on factual material about André and Simone Weil, but invented — as well as dreams I imagined for them.
I gather that your editor at Farrar, Straus and Giroux was Emily Bell, a creative and respected figure in the publishing world. Can you give us a sense of how she figured into the weave of Conjectures?
Emily is a wonderful editor — she’s extremely smart but doesn’t try to impose her own vision onto a book. In this case, the manuscript she first read was fairly close to the final version, but she encouraged me to add more about myself and to begin weaving in the memoir sections closer to the beginning of the book.
There are a lot of conceptual, psychological, and biographical dots to be connected in Conjectures. What was your method? How did you chart out such a multidimensional book?
It was less charting than collage — not a random arrangement, but an intuitive one. I had certain constraints, in that I wanted to alternate among the stories of the Weils, my own experiences, and other anecdotes of math history, and I wanted all of those to be roughly chronological. And then I looked for pieces that would resonate when juxtaposed, passages that seemed to speak to each other.
You majored in mathematics at Harvard. Would it be fair to say that Conjectures is your way of trekking back in time, of reconnecting with the puzzling yet enticing world of numbers?
Yes — I’d say reconnecting more than going back in time.
Your book intermingles a good measure of autobiography by way of 31 or so paragraphs of personal digression. Why? How does that fit into the stratagem of your writing experiment in Conjectures?
I wanted to write a book about math for people who wouldn’t be inclined to read a book about math, and I wanted to try to explain to those people the appeal math had for me, in part by telling the story of how I fell into studying math in college.
The jacket art, a wheel with 30 pairs of multicolored spokes (with one bowed), is by the Austin-based artist Jessica Halonen — it’s titled “Target 17” and, I gather, is science-related. Do you know the artist? How did this cover come to be?
Jessica is a friend and neighbor, and I have always loved that painting. I’ve never discussed the genesis of it with her — it just seemed right for the book, and I was thrilled she gave permission to use it.
Conjectures has no table of contents, no index. Why?
In its design, it’s closer to an essay than it is to a standard work of biography or history.
Similarly, Conjectures has no notes or sources, though in the acknowledgments you mention your reliance on “Simone Weil’s essays and letters,” Sylvie Weil’s book, and Simone Pétrement’s biography, among other works. Regarding Simone’s opus, did you consult the French collected works and the French biographies? Or did you rely instead on the works available in English?
I consulted the French collected works for Simone’s letters, in particular the ones she and André exchanged while André was in jail in 1940. That exchange is central to the book, and with my high school French and a dictionary I could muddle my way through it, but for the most part I read books in English.
You set the tone in the first three paragraphs, which are quite dramatic. You describe a scene in which three-year-old Simone is about to undergo an appendectomy. You have her “sing[ing] Christmas songs” and “recit[ing] names from ancient legends. She seems,” you write, “not so much asleep as bewitched.” Shortly thereafter, you add: “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.”
This makes for a captivating introduction, but how does it square with what we know of the actual medical scene in 1912? In Simone Pétrement’s biography (the authoritative work), there is no reference to Simone singing any Christmas songs or reciting the names from any legends during surgery. Regarding the quote in which you have her talking about luxury: it is not associated with Simone’s surgery but rather with something she said at another time to her cousin when she said: “I do not like luxury.” I asked some colleagues about Pétrement’s two-volume French edition and they informed me that Simone was not singing, naming figures from ancient legends, or talking about “luxury” during or shortly after her medical procedure. Moreover, in Gabriella Fiori’s Simone Weil: An Intellectual Biography (1987), all we have is this: Dr. Goldmann “listened to the discourses of the little child under the effects of chloroform.”
Can your depiction be documented, or is it offered up in an emblematic way, to give some impressionistic sense of what occurred in 1912 when this young girl had her appendix removed?
I think this is a good example of my technique in the book. What I’d read in Pétrement’s biographies was that Simone astonished the doctor by saying very precocious things while she was knocked out — what exactly is not specified — and that, at the same age of three, she’d announced, “I do not like luxury.” In writing the scene, I wanted to make it more dramatic and specific, by conjuring what she said during surgery, but I wanted to stick with something plausible, something she might well have said at that age.
There are a lot of dream scenes in chapter seven: “Simone dreams of Crete”; “André dreams he is on a ship”; “Simone dreams her brother is a tooth”; “André dreams of a bucket”; “André dreams himself back to the École Normale Supérieure”; “Simone dreams she has developed a new physical theory”; “Simone dreams she is in a refugee camp”; and “André dreams he can no longer dream.” Do these so-called dream accounts refer to actual dreams, or are they utilized as a sort of literary device in the service of something beyond the demonstrable realm?
A literary device. I don’t know anything about their actual dreams.
In a word, how would you describe André? And what was it about him that caught your interest?
I can’t come up with a single word that captures him. He was brilliant, of course, passionate about math and disciplined in his approach. As I imagine him, he could be very caring with his family, but he didn’t suffer fools gladly. I was captivated by the story he tells in his own memoir and by the fact that he was Simone’s brother.
You write: “I imagine the ghost of André Weil […] would disdain my having ventured to write about him.” Why did you say this?
He was contemptuous of biographies of mathematicians written by non-mathematicians. I don’t think he would care to be written about by someone who can’t fully appreciate the work he did.
You have said you were first drawn to Simone in high school but more to her biography than to her philosophy. Later you came to view her through a different lens (more about that in a minute). What work of hers or what idea, if any, was most meaningful to you, and why?
I would say that there are lines of hers that are meaningful to me, moments of great lucidity in her writing, and certain nets that ensnare me, as I try to untangle them, like the line from her college thesis that I quote in the book: “I must be tricky, cunning. I must hamper myself with obstacles that lead me to where I want to go.” I’m also drawn to her ideal of attention and fascinated by her analogy of the blind man’s stick, which I understand as a mystical idea of the universe as a vehicle of perceiving. (“Let the whole universe be for me, in relation to my body, what the stick of a blind man is in relation to his hand.”)
Finally, I think her critiques of political ideology and force, the way she wrote about the dangers of objectifying other people, particularly in her essay on the Iliad, remain all too relevant.
In reading your book, I sensed a real and recurring impatience with Simone compared to a relatively indulgent and often admiring attitude toward André. Am I mistaken?
In one sense, I feel upset with Simone, because I think her eccentricities and blind spots ultimately contributed to her death at a young age. While I don’t think it’s quite right to call that death a suicide, I do think her disregard for her own body — which verged on a desire to not have a body — shortened her life. At the same time, I feel more sympathetic to her than I do to André, because, much as I admire his great intellect, he seems more arrogant, less vulnerable than she was.
You write that Simone has been dismissed as “a nutjob”; later, you characterize her as “unhinged.” Though her work should stand or fall on its own merits, it is nonetheless true that this same woman has been hailed by the likes of Albert Camus, T. S. Eliot, Dorothy Day, Iris Murdoch, and by philosophers such as Peter Winch and Mario Von Der Ruhr. Are these notable thinkers simply wrong? Was Susan Sontag wildly off the mark 57 years ago when she asserted that “anything from Simone Weil’s pen is worth reading”? After all, this was a woman who penned learned and mind-opening essays on Plato and Homer, on the nature of force, on the curse of political parties, on the power of words, and on the philosophical and spiritual dimensions of attention. Given all that, is it intellectually legitimate to portray Simone Weil as “a nutjob” or “unhinged”?
I never say (nor do I think) that she was a nutjob. What I wrote was: “Simone was more often quasi-canonized as a kind of genius or dismissed as a nutjob than she was recognized as something in between, as human.” I’m certainly not allying myself with the canonizers or those who dismiss her there; I think both characterizations are wrong. In that passage, I’m saying that she’s hard to write about without veering toward one pole or the other. In part, that’s because she lived at extremes, and it’s hard for us, as middle-of-the-road people, to comprehend that kind of life without resorting to oversimplifications.
As for “unhinged”: this is from a passage in which I discuss the cultural archetype of the mad mathematician. We have this idea of the best mathematicians as crazy and/or autistic geniuses, when many great mathematicians, like André Weil, have been conventional in the way they lived, eminently sane. At first, he seemed to me a counterexample to the stereotype, but as I wrote about André and Simone I wondered whether, in the Weil family, there was a kind of psychological splitting of the job, in which he was deemed the great mathematician and she the great eccentric. “Unhinged” here refers to a role within the family, rather than an absolute, the “crazy” sibling versus the “genius” one. It might be too strong of a word — I was thinking, maybe too literally, of a door starting to come off its hinges, and not of complete derangement.
Incidentally, I don’t think a person’s being a great writer and attracting a legion of admirers would, in itself, demonstrate that the person isn’t crazy. At any rate, Simone wasn’t crazy in the sense of clinically insane, but she was well outside the norm in her disregard for herself and the ways in which she sometimes tried to put her ideals into practice. To be as fixated as she was, toward the end of her life, on a plan to parachute herself into the front lines of battle: that to me is nuts. Poetic, but nuts. So I’d say she had some crazy ideas and did some crazy things, but that is different from saying she was a madwoman.
Though highly unorthodox, Simone was a deeply spiritual person — a devotion expressed, among other ways, in her appreciation for Pythagorean mathematics and mysticism. While, as you note, André did read works such as the Bhagavad Gita, do you see him (as reflected in his life and writings) to be a spiritual person?
He doesn’t strike me as one, though it’s possible that he was simply private about his spiritual inclinations and didn’t leave a record of them.
In the acknowledgments, you note: “Writing this book was an unexpected journey down a rabbit hole.” I’m interested in learning more about that journey. For example, the publisher’s promo for your book states: “The Weil Conjectures tells the story of the brilliant Weil siblings ― Simone, a philosopher, mystic, and social activist, and André, an influential mathematician.” Yet the title nowhere mentions them. So, too, with the subtitle: “On Math and the Pursuit of the Unknown.” In light of this, would you say that your book is primarily about André and Simone? Or are they employed for some larger conceptual enterprise related to that “rabbit hole”?
It is primarily a book about math and about math as an example of creative endeavor.
Toward the end of your book, you write: “Maybe the dream of pristine writing, in which the writer is present but not present, masked behind the light of her brilliant transmission, is realized in […] works I only dream of reading.” Can you elaborate?
Written language, or spoken language for that matter, seems to me always imperfect, a rough approximation of something unspoken — though sometimes, in the process of approximating, we arrive at some unforeseen idea, so that’s part of the beauty of language too.
Mathematical expression is more precise. When I talk about “the dream of pristine writing,” I’m speculating that in, for example, the statement and proofs of the Weil Conjectures (one of André’s great achievements in math, though too advanced for me to follow) there is a kind of beautiful exactness that I’ll never be able to appreciate.
You state, “[T]he longer I go on writing, the more I sense its limitations.” Can you tell us more about these “limitations” and how they figured into your thinking in authoring the book?
As I get older, life in some ways seems more mysterious and less intelligible than it did when I was young, and in that way it seems less directly amenable to explanation. I still believe in the power of writing to evoke complexities and mysteries, but often you can’t do that in a direct, journalistic way. More has to be left to the line breaks, to what’s not said.
To tease out the last question a bit more: Might your style of writing as presented in Conjectures be seen as a sort of meditation on the power of writing to convey truths? If so, does that relate to the way André communicated truth in the language of mathematics and how Simone did the same in her essays and notebooks?
That’s certainly one thing I was chewing on. As I noted above, math for me represents a different and more precise form of expression than ordinary language, but it can only convey its own particular truths. When it comes to Simone, I think of Anne Carson’s characterization of her as a person who, on the one hand “wanted to get herself out of the way so as to arrive at God” and who, on the other hand, was a writer driven by “the brilliant self-assertiveness of the writerly project.” A writer has to have a self! But she seems to have wanted to write toward her own unmaking, and in that sense maybe the mathematical demonstration was for her a model of a kind of beautiful thinking that, once it has been produced, seems unauthored.
In her notebooks, Simone wrote: “Method of investigation: as soon as we have thought something, try to see in what way the contrary is true.” How does the concept of contradiction play out, if at all, in André’s conjectures on mathematics?
I’d guess that most mathematicians think about counterexamples when trying to understand or prove an idea; moreover, a classic mathematical tactic is proof by contradiction, a.k.a. the law of the excluded middle — assume that a proposition is false, show that the assumption leads to an absurdity, then conclude that the proposition is true. This stands in contrast to what Simone seems to be writing about, namely that for some types of thoughts and ideas, the idea and its contrary both convey some sort of truth.
For Simone, philosophy was an activity to bridge the mind ever more directly to the world, to link thought to action, and to come to grips with the realities of this world and the contradictions they create. In this regard, Simone wrote of a “new way of conceiving mathematics,” one in which the theoretical and practical value of analyzing a problem “would no longer be distinct.” It was that separation — what she tagged the “trick” of modern science — that troubled her. Years later, in a letter to André while he was imprisoned in Rouen, Simone wrote: “Present day mathematics, considered either as science or as art, seems to me to be singularly far from the world.”
On the one hand, André seemed taken by math’s “solidity.” On the other hand, Simone was far more concerned with math’s relationship to “the facts of the universe” and in attempting to bridge the gap between math and “daily life.” What do you think about this? And how do you suppose André would respond to Simone’s critique of modern science and modern math (especially algebra)?
We know how André responded to Simone’s critique — he sent her a 16-page letter explaining his work by putting it in historical context. (“If the critique of art is a futile, empty genre, the history of art is maybe possible,” he’d written in a previous letter, implying that he felt the same way about math.) He was a great mathematician who loved what he did, so I can’t imagine he was bothered by her idea that contemporary math is too far removed from what she took to be the ideal, which was ancient Greek math.
In a 1933 letter to Émile-Auguste Chartier, Simone wrote about the importance of analogical thinking. In this regard, might there be some bridge between the thought of Simone and André? If so, it seems that the two of them employ such thinking for different purposes. What do you think?
Sure, I think the two of them had various habits of mind in common — both were steeped in classics, both sought out underlying principles, both were fierce arguers, and yes, both were brilliant analogy-makers.
In the first chapter of your book you refer to André as the “brother who spent his long life solving problems.” And then you refer to Simone as the “sister who died before she could solve the problem of life.” Mindful of that, let me turn to something you say later on and invite you to compare and contrast these various statements.
Of André you write: “The flicker of a parallel, the suspicion of a connection, excited him, more so than nailing it down, working out the details. As though knowledge itself were a bit of a letdown: it’s being on the cusp that brings the greater thrill.” Three chapters later, you write of Simone:
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.
As you understand them, how were their searches similar, and how were they different?
I think of André as a more lateral thinker — drawing connections between different areas of math — and Simone as more vertical, seeking something ineffable, divine. To oversimplify a bit, Simone was searching for God, and André was searching for a way to prove the Riemann hypothesis.
There are 15 printed pages of drafts of 1940 letters Simone penned for André, which you reference in your book. These letters, as you know, primarily concern mathematics, ancient and modern, and are rather complex in places. They are also chock-full of philosophic observations. For example:
This [Platonic] conception of number as forming a sort of mean between unity (which is the property of thought) and the limitless […] quality which is presented in the object is singularly luminous. The prescribed direction (one →many →infinite) entirely precludes what we call induction and generalization. It is remarkable that this method was scrupulously followed by Greek science.
In the same way, with regard to things seen, proportion enables thought to grasp all at once a complex variety in which, without the aid of proportion, would lose itself.
Two things about such a passage: (1) It reflects a serious and informed engagement with André regarding mathematics, and (2) it addresses the higher principles suggested by mathematics. Yet this engagement, profound as it is in places, does not seem to come through in your book. Rather, you claim that much of what André wrote in his long letters to Simone “flies right over her head” or was simply “beyond her.” How so? And what about Simone’s responses to André and his appreciation of her arguments?
You are quoting me out of context! What I describe as “beyond her” are not his 1940 letters but the deliberations of mathematicians at a Bourbaki conference in 1938. For Simone, as for any of us who don’t have a graduate degree in the field, the discourse of professional mathematicians at a conference would not be terribly intelligible.
And what “flies right over her head” is the elaboration of his own work in the 16-page letter I reference above. It dives into advanced contemporary math. She herself wrote back that she’d understood none of it. That’s separate from her keen interest in ancient mathematics, which was not over her head. I do write, for example on the pages you reference, about her engagement with the ancients and her debates with André in those letters. To delve into the specifics was beyond the scope of my book; what matters to me is the importance math had for her — she felt that geometry as practiced by the ancients was a supreme art.
In the 1940s, André gave staying power to the idea of finite fields and how they might be tapped to answer certain problems about numbers. To this day, that insight continues to open doors in mathematics, as evidenced by a new article in Quanta magazine. For André, did such insights figure into any larger philosophy of life? Or did they float mainly in the ether of higher mathematics?
I didn’t come across any material relating how they might’ve figured into a larger philosophy of life.
On a related front, Professor Lawrence Schmidt of the University of Toronto asked me to pass along this question: “The most important philosophical question raised by Simone and André’s dialogue about algebra and geometry was: In what sense is algebra a monster of modernity, something which has destroyed human scale and dehumanized our culture?” How would you respond to that?
This question is raised more directly in the writings collected under the heading “Algebra,” in Weil’s 1947 book Gravity and Grace. Algebra, along with money and mechanization, there represents the signifier cut loose from the signified, and she sees all three as dangerous. For her, it’s dangerous when we turn to playing games with symbols, or making symbols ends in themselves. It’s akin to the critique she makes in her essay about the Iliad, in which she discusses how we lose our way by turning people into things.
For André, meanwhile, the symbolic constructs of algebra are the means to beautiful truths about numbers. Really, when it comes to algebra, he and his sister are talking past each other: for him it’s an art and a passion and a fundamental part of his profession, while to her it’s a menace to civilization, an abstraction that distances us from meaning.
One final question: Early on in your book, in connection with calculating, you take notice of the wedge-shaped stamps used by the “Babylonians to mark a clay tablet before it dried.” And then, in the very last entry on the final page, you write: “Thirty-five hundred years ago, a Babylonian presses a wedge into clay. One, two, three times. Then leaves a gap. Then presses again.” What a conceptual cliffhanger of an ending! At the expense of asking you to reveal your writer’s hand, what more can you tell us about why you ended the book the way you did?
I’m sorry to say I don’t have a very illuminating explanation. But I’m moved by the fact that humans have been trying to solve math problems for thousands of years, and by the way that those efforts are intimately linked to writing.
Let me conclude by thanking you again, Karen, for taking the time and making the effort to respond to my questions and to call me out when I was off the mark. Perhaps someday we might share our respective thoughts in a lively public conversation, one not cabined by the confines of printed words.
Thank you, Ron! I hope so.
Acknowledgments: I happily acknowledge and sincerely appreciate the guidance of Eric Springsted, Larry Schmidt, and E. Jane Doering in developing some of my thoughts for this Q-and-A, this even though they may take exception to a few of my wayward words.
Ronald Collins is a retired law professor and co-director of the History Book Festival and book review editor for SCOTUSblog. His review-essay covering Karen Olsson’s The Weil Conjectures: On Math and the Pursuit of the Unknown (2019) appeared in the Washington Independent Review of Books.