Two brilliant siblings and the curious consolations of math

This was a lament, not a boast. How austere advanced mathematics can seem to the layperson — a confluence of the intimidating and the irrelevant. It’s easy to forget that math has been vaunted as a source of pleasure, even consolation. In the Symposium, it is described as a source of the most sublime eros, second only to the Platonic ideal of beauty. Late in life, Thomas Jefferson reported that its contemplation was a balm against the despair of aging.

Karen Olsson’s beguiling new book, “The Weil Conjectures,” arrives as a corrective, describing mathematics — its focus, abstraction, odd hunches, blazing epiphanies — as a powerful intoxicant, a door to euphoria. She twines her arguments around the story of the Weil siblings: André and Simone, the philosopher and secular saint — “the only great spirit of our time,” according to Camus.

The precocity of the Weil siblings is the stuff of legend. At 9 years old, André was tinkering with doctoral-level math. By 12, he had taught himself Sanskrit, become a proficient violinist and taken his younger sister’s education in hand. The pair spoke to each other in rhyming couplets and Ancient Greek. Their idea of play was to recite long passages of Racine and Corneille aloud to each other, with any errors earning a hard slap across the face. (That’s one alternative to “screen time.”)

When Simone, barely into her teens, felt hopelessly outpaced by her brother, she contemplated suicide. “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 later wrote. “I preferred to die rather than live without that truth.”

Her genius was for the moral imagination, for empathy so extreme it flirted with self-erasure. At 5, she gave up sugar in solidarity with French troops stationed at the front of World War I. It’s not merely that she was preternaturally attentive to the suffering of others, she was determined to cast her lot with them — to live without heat and keep strict rations, to fling herself into factory work and volunteer in mines and fields — often with disastrous results. Her parents, marvels of forbearance, frequently had to swoop in to save her from her noble, quixotic ambitions. In 1936, she made it to the front lines of the Spanish Civil War, posing as a journalist. She could barely handle her heavy gun — and promptly stepped in a pot of boiling cooking oil. The skin came off her foot along with her sock; she required weeks of convalescence and care.

“The Weil Conjectures” takes its title from a series of propositions written by André that led to the development of modern algebraic geometry. “The word ‘conjecture’ derives from a root notion of throwing or casting things together,” Olsson writes. To the story of the Weil siblings, she adds her own infatuation with mathematics, which she studied briefly in college before turning to fiction (she is the author of two novels). Those years spent swotting away at equations retain a special sheen in her memory: “We were a small band of students giddily, exhaustedly trekking through an abstract moonscape,” she writes. “The egos, the insecurity, the unabashed nerdiness! I miss it still.”

As a “midlife mother of two,” she is perplexed to find herself returning to math, watching university lectures online, finding comfort in the steadiness of numbers “given our present-day world’s particular instabilities and alternative facts.”

The book unfurls effortlessly, loose and legato. There are no real revelations — the subjects are well-known and long dead. There are no stakes; there is no suspense. I was riveted. Olsson is evocative on curiosity as an appetite of the mind, on the pleasure of glutting oneself on knowledge. André “gorges himself” on mathematics and Sanskrit. Simone crawls between her books arrayed on the floor, “leans over Descartes like an animal drinking.”

What’s curious is that we never learn why she was reading Descartes so intently (or that he later became one of her prime philosophical sparring partners). There are slow pans of André at his desk, his cat perched on the edge, but we are rarely privy to the work itself. Olsson remains breezy on the finer points of their intellectual interests, perhaps to keep the narrative from being bogged down.

The glamour of mathematics is what excites her, its colorful stories. The book advances in fragments, historical divagations that drift by, smoothly as clouds: Hippasus of Metapontum supposedly flung off a ship for his discovery of irrational numbers, or the unearthing of the Rhind papyrus of 1700 B.C., one of the oldest mathematical documents, with an insuperable opening line: “Directions for Attaining the Knowledge of All Dark Things.” Olsson is drawn to anecdotes that emphasize the role of beauty and chance. Why do we represent the unknown with x? Credit René Descartes’ printer, who was running out of letters while producing copies of the treatise “La Géométrie.” X, y and z remained, and the printer settled on x, the least used letter in French.

If there is an x in this book, it is Simone Weil.

For all of Olsson’s skill at untangling knotty mathematics, she is baffled by Simone, insensible to her charisma and put off by her prose — “awfully high in fiber,” she describes it, and lacking in style. It is a freakish version of the thinker she offers us, a gaunt catastrophe in wide skirts. “The more I learn,” Olsson writes, “the more I begin to wonder whether his sanity somehow implicated his sister’s extremity, whether in the Weil family, the two roles were divided between them: He would be the great mathematician, and she would come unhinged.”

The issue of Weil’s mental state has long preoccupied and divided her biographers. She died at 34, from tuberculosis, aggravated, it is said, by prolonged malnutrition from restricting herself to children’s wartime rations. “Unhinged” is a crude diagnosis, especially in a book that gives short shrift to her work and influence. From “The Weil Conjectures,” it’s difficult to discern how rich and various her 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.

The mathematician Henri Poincaré, a mentor to André, imagined that thoughts lived in the mind like static particles, “as if hooked to a wall,” Olsson writes. Thinking liberated them and allowed them to crash into and attach to one another. Her book is full of such moments of connection, combustion and surprise. And if x goes unsolved, there is something apt and beautiful there, too. For all the riddles of mathematics, there is also the ordinary and eternal mystery of other people’s minds.

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Publication Notes:

“The Weil Conjectures: On Math and the Pursuit of the Unknown”

By Karen Olsson

214 pages. Farrar, Straus & Giroux. $26.

This article originally appeared in The New York Times.