As a girl, I too was attracted to Simone Weil. How could anyone not be? Mystical, intense and crazy, Weil radiates the kind of posthumous aura that dazzles youth and seduces young women. In The Weil Conjectures: On Maths and the Pursuit of the Unknown, Karen Olsson, herself a mathematics graduate from Harvard, traces the entwined lives of two siblings: Andre Weil, the great mathematician, and Simone Weil, the French philosopher.

Most interestingly, Olsson associates mathematical thinking with the craft of writing, thus providing a common constellation of ideas that interrelates the siblings’ otherwise wildly different life trajectories. For example, Andre Weil not only revered the Bhagavad Gita and read Sanskrit, but he also served as the Mathematics Chair at Aligarh Muslim University.

The Weil Conjectures is above all an interdisciplinary work of mathematics and literature in the sense that Olsson uses the presuppositions and methods of each discipline to apprehend the other. For example, Olsson pursues the meaning of “conjecture” in mathematics to discuss the style of discursiveness innate to writing. A conjecture is a “reasoned wager about what’s true”. It is a “root notion of throwing or casting things together”, but it can be good or bad thinking; a smart speculation or merely a “reckless mental leap”.

Self-reflexive intensity

From the very title of the book, which takes its name from Andre Weil’s algebraic conjectures, we glimpse what Olsson thinks of “conjecture” in the life of the mind. She modifies her views on what writing means through such a prism. Writing is not only a quest for the mot juste or an attempt to exactly transcribe thought. It is not just an attempt to bring mental insights and dormant intuitions into conscious existence. Like in mathematics, it is not the ironclad proof that promises a solution which is thrilling, but the feeling of being on the verge of grasping something.

As Olsson’s meandering, digressive, aphoristic text shows, she herself abandons strictures of form for a self-reflexive intensity. We deem good writing to have a certain transparency and accessibility: “something clean and powerful as the best mathematical proof”.

To undercut this supposition, she explores the widely-held assumptions that maths is unassailable in its proofs and theorems and that it is the result of the private minds of geniuses. This “solidity” of mathematics is, however, illusory. Though typically seen as an “austere architecture” of eccentric geniuses, Olsson shows us how mathematics is actually a “giant math ant colony” of complex systems of relationships.

Work versus image

For the author, the very modality of the disciplines influences the Weils’ outlook to life. Simone constantly questions Andre about Mathematics that has become so specialised and abstract that it is inaccessible to the common man. In many ways, Simone’s distrust of abstraction guides her quest for meaning. Rejecting theory, she chooses to directly investigate the streams of life.

It also viscerally shapes her political activism, leading her to side with the Anarchists in the Spanish Civil War and to work in factories to see what the working conditions there are like. What Simone wants more than anything else is to transcend the limits of her own self, and achieve a kind of impersonality that will help her attain a ‘selfless perception’.

As Olsson notes, it is ironic that Simone’s public persona threatens to overshadow her work, whereas Andre’s work has nearly erased his celebrity. In the beginning, Olsson captures Simone’s masochistic devotion to truth but downplays her mysticism to set it as a foil for Andre’s mathematics. But, anybody who reads Simone would find it hard to uphold such a distinction for she was mystical as well as practical. There are indirect references to her increasing turn to Roman Catholicism, but they come together to reinforce the connections that Olsson foregrounds between mathematics, writing and abstract thinking.

‘Slightly adulterous relationships’

Olsson’s writing is densely lyrical and meditative, but it is seductive because of its potent conjectures and theorisations. The lives of the siblings intertwine with biographies of mathematicians and a history of ideas to produce a social history with poignant moments. The reader is surprised by Simone’s outrageous ideas: She wanted nurses to be dropped onto the middle of a battlefield to tend to injured soldiers.

Yet, this very eccentricity is movingly subsumed into the rich folds of her personality when provided with context through her parents and brother. Simone is, after all, not a radical philosopher for her parents; she will always be the little girl who went stomping through the doorways. Learning of her sister’s death, Andre remarks that nothing about her came as a surprise to him except her death. The Weil Conjectures is thus also an ode to the bonds of family – to those way people who have seen us grow up and love us.

The less conspicuous charm of the book is Olsson’s memoiristic interventions about her own life. She mulls over her fascination with mathematics which has culminated in her writing about it without pride or affectation. The Weil Conjectures is ultimately a Künstlerroman about Olsson’s coming-of-age as a writer. We see her watching YouTube videos on maths and pondering over her son’s questions on the subject, but this personal narrative doesn’t underwhelm next to the lives of her luminaries. Instead, as Olsson shows, the sheer mundaneness of contemporary life is bolstered by analogy with the great masters.

This interweaving between individuality and inheritance adroitly avoids the celebration of ordinary life and banality à la Knausgård’s novels, thereby avoiding the charge of a self-absorbed egoism. The author borrows Weil’s definition of analogy as “slightly adulterous relationships” to discuss their role in mathematics. Analogies permeate the book, drawing together disparate lives. This style allows Olsson to freely quote famous mathematicians and reflect on her own entanglement with mathematics with poise. The variety of the ways that analogies work in The Weil Conjectures offer startling perspectives and an extravagant layering.

It is along such routes that she puts forward the thesis of the book. Perhaps mathematicians and writers are bewitched by alternate worlds because of the very manner in which the beauty of abstract representation works. She wonders whether putting down numbers or words on paper already takes the author away to a parallel universe. The enmeshment of lives and ideas slowly unravels the contours of the discipline itself, and what remains is the “mood of knowledge”.

The Weil Conjectures

The Weil Conjectures: On Maths and the Pursuit of the Unknown, Karen Olsson, Bloomsbury.