The mathematician André Weil was arrested by the Finnish police in 1939. He had overstayed his vacation in Helsinki while there was a war on, and the police thought he was a spy. The papers in his room didn’t help his case—some of them were letters full of strange notations. Code, perhaps? No, he insisted: It was just math, and his correspondents were other mathematicians. He tried to explain his research to the officers detaining him, but the problem was that—as he would later write to his sister, Simone—“telling non-specialists of my research or of any other mathematical research, it seems to me, is like explaining a symphony to a deaf person.” He was detained, deported from Finland, then imprisoned in France.
The unlucky André Weil is the hero of Karen Olsson’s book, even though she can’t hear his symphony either. “I didn’t go far enough in math,” she writes, “to really understand the Weil conjectures.” (The Weil conjectures are the most famous results of André’s research.) Olsson studied math at Harvard, then abandoned it for writing. Despite loving math’s moments of insight and the strange characters who people its history, she knew she wasn’t good enough to make a career of it. “How little, really, I learned in college,” she muses, “less and less every semester, since whenever I studied one thing, all sorts of further potential studies would reveal themselves, so that instead of making progress I only walked a short way up a sand dune that continually grew larger as I went along.”
Decades later, having become a novelist and a mother, with a son just learning about numbers, Olsson remembers the rarefied pleasures of abstract contemplation with longing and regret. This book is about unrequited love, love for a discipline that remains intractable even as its beauty beckons: “What I wish for now is less the specific math knowledge than a certain constellation of feelings that came with it.”
Olsson explores her theme in a mosaic of anecdotes. In short sections, most only a few paragraphs long, she weaves together memories of her own study, scenes from the lives of André and Simone Weil, and bits and pieces from the history of mathematics. One implication of these juxtapositions is that her own sense of inadequacy toward math is analogous to Simone Weil’s feelings toward her math-genius brother. Olsson loads a lot of angst onto the siblings’ relationship. This choice is the flaw in an otherwise good book, and it is a serious flaw, because it leads Olsson to present a grotesque and caricatured version of Simone Weil.
Like her brother, Simone Weil was a brilliant child who grew up to study at the École normale supérieure, a prestigious graduate institution in Paris. She studied philosophy rather than math, having had the good fortune in high school to encounter Émile-Auguste Chartier, who taught and wrote under the pseudonym “Alain.” This charismatic philosopher, journalist, and political activist considered Weil one of his star pupils and imparted to her his antisystematic method of philosophizing and his interest in intellectual history. After receiving her teaching certification, for several years Weil taught philosophy in schools around France. She dedicated all her spare time to union organizing and political activism. In 1934 she took a sabbatical to spend a year working in a factory, refusing all her family’s worried efforts to ease her experience, trying to gain firsthand knowledge of the working conditions of the French proletariat. It was a shattering experience, but instructive in exactly the way she had hoped. Shortly after this experiment, she abandoned her teaching career to fight fascism in Spain. In 1940, when Germany invaded France, she joined the Resistance. She died in England in 1943, thirty-four years old, because despite being ill she refused to eat more than she imagined was available to those living in occupied France. She effectively starved herself to death out of commitment to her own unsparing ethic.
The writings for which Simone Weil became famous were published after her death—philosophical notebooks transcribed by her parents containing a vast and suggestive universe of fragmentary insight, and various correspondences, such as the letters about Christianity exchanged with a Catholic priest, Father Joseph-Marie Perrin, and published as Waiting for God.
It is this serious and interesting person whom Olsson chooses to depict as the epitome of the inferiority complex. She portrays Weil’s life and work in a series of anecdotes that highlight her ridiculousness, implying that her moral stands, her intellectual projects, her engagement with religion, and her asceticism were all basically responses to the central trauma of not being as good at math as her brother. Here is a characteristic aside: “A photo taken in 1938, in Dieulefit, shows [Simone] standing in front of a doorway with her brother and five other mathematicians. She is the only one looking away from the camera, as though she knows better than to claim a place there.”
Olsson places anecdotes about Simone’s ineptness beside ones about André’s brilliance. On one page she describes how Simone’s students worried that she would set herself on fire trying to light a cigarette, then immediately tells us how André impressed a “distinguished older mathematician” when he visited him in Rome. The intended comparison could not be clearer, but just to make sure we don’t miss it, early in the book Olsson writes:
If this were a fable I might begin: Once there were a brother and a 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.
Even when she is discussing Simone without reference to André, Olsson makes sure to highlight the pathetic. She emphasizes that Simone was clumsy (she injured herself in Spain by stepping in a cooking pot!), sighs over her celibacy (if only Simone had taken a lover somewhere along the way, she would have been so much happier!), and does her best to spin asceticism as masochism. It’s true that Simone Weil was physically awkward, socially abrasive, and sometimes ridiculous, but it is appallingly reductive psychology to attribute every step and misstep in her life to the fact that her brother was better than she at math, just as it is misleading to note all her negative qualities and misadventures without also touching upon her brilliance and originality as a thinker, her empathy and grace.
While Olsson summarizes—or at least adumbrates—André’s mathematical work, she glosses over Simone’s philosophy. The only of Simone’s ideas explored at any length in the book come from the letters she exchanged with André while he was imprisoned on suspicion of spying. Simone objects to the abstractness of modern algebra, stating a preference for geometry, and argues with André about ancient Babylonian and Greek mathematics. In the context of Olsson’s book, these ideas simply function as further evidence that Simone didn’t understand what her brother was doing, and that her inability drove her to arbitrary and silly conclusions: “This animosity toward algebra—where did it come from? Was it that she still resented her brother for leaving her behind, as he launched into the realm of abstraction?”
The most charitable interpretation of the partial and misleading use to which Olsson puts Simone Weil is to assume that all her humiliations of Simone are in fact expressions of personal humility. She identifies Simone’s mathematical inferiority to André with her own failure to understand mathematics as well as she would have liked, so perhaps every aspersion heaped on Simone is a confession of her own feelings of abjection. This is precisely the danger of the hybrid genre Olsson is attempting, a memoir that at the same time recounts the history of other people. The genre can work, as in Sarah Bakewell’s At the Existentialist Café, when the memoiristic bits motivate and prepare a reader for the exposition of philosophical history, but in Olsson’s book, history is twisted to dramatize memoir. Or perhaps Olsson’s love for math and corresponding admiration for André Weil blind her to the independent significance of his sister.
But Olsson may be saying more about her larger subject than she realizes. The subtitle of her book is On Math and the Pursuit of the Unknown. There are subtle distinctions to be made between varieties of the unknown, as her reaction to two kinds of unknowing makes clear. She is bemused by the intellectual products of André and Simone in different ways. Mathematical difficulty tantalizes her; philosophical difficulty merely elicits her scorn.
Olsson tells us that she first encountered Simone Weil’s writings when she was a girl, in an anthology in which she could make no headway. She liked the idea of Weil’s life more than her words. “As a gawky girl, circa 1989,” she writes, “I was less enamored of her writing that I was of Simone herself, the petite French ascetic with cool hair and wire-frame glasses, the political activist / intellectual / mystic who died young.” Returning to Weil’s work as an adult (much as she returned to math as an adult), she continues to find it difficult: “Her prose is dense, at times baffling; I have to bushwhack my way through...clearing back each sentence, each long paragraph, without much notion, as I go along, of where I’m headed.” Later, she resumes the theme: “Much of Simone Weil’s writing is awfully high in fiber, hard to digest…she introduces ideas and relentlessly loops around them.” Olsson’s reaction to this difficulty is quite different from her reaction to the difficulty of André’s conjectures. She seems almost to despise Simone, but she fantasizes about being despised by André: “I imagine that the ghost of André Weil would have something acid to say about all this, that he would have disdained my having ventured to write about him.”
How does one pursue the unknown? What presentiment of truth or pleasure makes some bafflements tantalizing and others tormenting? Ironically, it is Simone Weil who has ideas to offer on this subject. In my favorite of her writings, “Essay on the Concept of Reading,” she addresses the mystery of how, when we look at black marks on a page, we can be affected with the same immediate force as if someone had punched us in the stomach, or as if we had touched something hot:
The mystery is that there are sensations that are pretty much insignificant in themselves, yet, by what they signify, what they mean, they seize us in the same way as the stronger sensations.… We have all experienced, to a greater or lesser degree, the effect of bad news that we have read in a letter or newspaper. Before we have fully taken account of what is going on, we feel ourselves seized and thrown down just as if we had been hit; even much later the sight of the letter remains painful.
This phenomenon, though archetypically encountered in the act of reading a text, is actually spread throughout human experience. We “read” our sensations all the time, experiencing meaning as if it were brute fact, which is how we can have strong feelings for or against the unknown, the not-yet-understood, as Olsson does toward the different unknowns represented by the work of the Weil siblings: “Before we have fully taken account of what is going on, we feel ourselves seized…”
This is all only one strand of a book that includes many other things. The best of these are the anecdotes about various historical mathematicians, glances at their mystic yet hardheaded tribe which include both the famous—Pythagoras, Pierre de Fermat, Georg Cantor—and the relatively obscure—Jacques Hadamard, Goro Shimura, Yutaka Taniyama—glances that really do initiate a reader, like myself, who lacks even an intimation of the pleasures of mathematics, into what it must be like to be a mathematician.
If only Olsson had narrowed her focus to the unknown that she reads as worth her trouble, I could recommend this book without reservation. But explaining what she’s up to early in the book, she writes:
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.
Of these two pieces of unfinished business, only one has been finished in this book.