Brotherly and sisterly love

André and Simone Weil were two sides of the same coin: impatient; determined; brilliant; attracted to ancient wisdom and ideas

Mark Ronan

Nearly 40 years ago, when my wife and I were in a bookshop in Paris, she bought La Source Grecque by Simone Weil. As a mathematician, I knew nothing of the author except that she was sister to the famous mathematician André Weil at the Institute for Advanced Study, Princeton. A prodigious intellect, he and a colleague had defeated the institute’s hiring of a prominent sociologist — “the worst appointment since Caligula’s horse”. The two men read everything the sociologist had written so they could challenge any claims made to support him. No one could deny André Weil’s determination on any matter he cared about, nor indeed his sister Simone’s, and this book introduces these extraordinary siblings, who would occasionally talk to one another in ancient Greek.

Simone exhibits the madness one often associates with genius, living and dying at the extremes of mental energy, while André finds his way more securely through mathematical ideas and indeed life itself. In a remarkable tour de force switching rapidly between the two, along with short digressions on her own experiences as a mathematics student, Karen Olsson allows us to glimpse the energy and creativity behind André’s passion for mathematical abstraction, and Simone’s passion for philosophical abstraction and her sympathy for humanity and its faults. Only after her death were Simone’s notes collected and published by her parents, still alive after the war despite being Jewish. They had escaped France for America, but Simone returned to Europe wanting to help the Free French. She had a madcap scheme to parachute nurses into the front line, to help the wounded and confuse the enemy. She would naturally be one of the nurses, but could she really do it? Before the war, she had insisted on working as a farm labourer but could barely cope with the physical exertion, though she would argue philosophy all evening with the farmer. During the war she insisted on eating no more than she imagined many people in Europe were getting, fatally weakening her body.

In a sense André and Simone were two sides of the same coin: impatient; determined; brilliant; attracted to ancient wisdom and ideas. She would hang in with his mathematics, which she could not understand yet appreciated. This is an idiosyncratic, even impressionistic portrait of brother and sister, demonstrating along the way an appreciation for top-flight mathematics. In a long sequence of snapshots, some only one sentence long, she illustrates the marvel and god-like wonder of mathematics, fructified by sky-high abstraction and the determination of its exponents to suffer endless battles with confusion and ideas that refuse to work. Flying through  murky clouds, they reach heights from which one can see unrelated problems connected within a broad landscape that loses its mystery the moment you comprehend it. As André himself once wrote to Simone:

Gone are the two theories, gone their troubles and delicious reflections in one another, the furtive caresses, their inexplicable quarrels; alas we have but one theory, whose majestic beauty can no longer move us. Nothing is more fertile than these illicit liaisons; nothing gives more pleasure to the connoisseur . . . The pleasure comes from the illusion and the kindling of the senses; once the illusion disappears and knowledge is acquired, we attain indifference; in the Gita there are some lucid verses to that effect. But let’s go back to algebraic functions . . .

The Gita refers to the Bhaghavad Gita (part of the Sanskrit epic the Mahabharata). In his early years as a mathematician, André Weil spent time working in India. Princeton came much later when he was fully established and in his early 50s.

By that time Simone was long dead, after eating less and less during the war, “this febrile figure in spectacles, half covered by a sheet, barely strong enough to move her legs, her arms even, binds [the chaplain] in a long, baffling chain of logic”. He blesses her and realises that, apart from the intellectual brilliance, here is “an extraordinarily pure and generous soul”. André and Simone “both undertook to translate into language something beyond words, beyond symbols, in Simone’s case maybe a realm beyond thought itself”.

As André’s mathematical work continued, Simone sacrificed herself to the exigencies of war, writing to her parents that she had made the acquaintance of several charming young girls, omitting to mention they were nurses in the hospital. Writing to André she tells him that London is full of fruit trees and flowers. A month later he receives a telegram: YOUR SISTER DIED PEACEFULLY YESTERDAY. SHE NEVER WANTED TO LET YOU KNOW. She was 34.

“How could I describe my grief?” wrote André. “But I did not have the luxury of indulging it; it was up to me to inform my parents, and I did not feel equal to the task.”

Decades later, an interviewer asked him why he had confined his autobiography to the first 40 years of his life. “I had no story to tell about my life after that.” No story to tell? Yet he and his wife had a second child and it was only later that he came up with the Weil Conjectures, the title of this book. But as he wrote later, “We remained always close to one another so that nothing about her really came as a surprise to me — with the sole exception of her death. This I did not expect, for I confess that I thought her indestructible.” André Weil (1906–1998), Simone Weil (1909–1943) — two lives entwined in one book. A novel, if it were not in fact true.

The Weil Conjectures:
On Maths and the Pursuit of the Unknown
By Karen Olsson
Bloomsbury, 224pp, £14.99

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