The mathematician and the philosopher: A tale of two siblings

Anyone who has an overachieving sibling will be able to relate to Simone Weil, the French writer and mystic whose brother André was one of the most influential mathematicians of the 20th century.

Clever as Simone was, she had no hope of competing with her precociously brainy older sibling. As he waded deeper into the world of complex number theory, she looked on with a mixture of bewilderment and awe – as letters between the two reveal.

Karen Olsson has documented their complex relationship in The Weil Conjectures, a book which serves as both a joint biography of two extraordinary individuals and an insightful study of sibling dynamics.

A science writer with a background in maths, Olsson had set about writing a book about André Weil and his groundbreaking research in algebraic geometry but his sister – who would gain fame for her philosophical writings and self-sacrificing works – kept pushing into the narrative. Simone’s death in 1943 aged just 34 gave her the status of a martyr, her transition to Catholicism helping to create the aura of a soul too good for this world.

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As this week’s Unthinkable guest, Olsson discusses the challenge of fact-checking a sainted life while also addressing the limits of public understanding of science and the lack of gender balance in mathematics.

Simone Weil seemed to imitate her brother by trying to build a moral scheme – rather than a mathematical scheme – from first principles. Does her example prove the futility of that exercise?

Karen Olsson: Rather than say that she was imitating her brother, I would say that Simone was her brother’s sister. In other words, one way in which the Weil siblings resemble each other is in their mental dispositions. They were brilliant arguers in different arenas, he in mathematics and she in philosophy and later mystical thinking.

As for the worth of her efforts, I’m not deeply versed in philosophy but it seems to me that often the value in moral reasoning lies more in the process, the argument, the clarifying of one’s assumptions and ideas than in the end, if by “end” we’re talking about constructing a watertight scheme or system.

In Simone’s case, I’m not even sure she was trying to build out a scheme; much of the writing she left behind is in the form of fragments, diary entries, aphorisms. Her thinking seems to me more directed to achieving a rigorous and honest relationship with the world – and later in her life, with God – which I wouldn’t call futile, even if it’s not fully realisable.

You are more sympathetic in the book to André than Simone. Why was that? Was it a reaction to the way Simone Weil has been canonised in some quarters?

I was writing about Simone as André’s sibling and as a thinker influenced by math, rather than trying to capture the totality of her thought. But I think by writing about her in this way, and by highlighting her biography, which is full of strangeness, I wound up portraying her in a manner that some readers find unsympathetic or dismissive – which I regret.

I don’t at all think of her as somehow the lesser of the two; I find her fascinating. So much has already been written about her, and I was trying to avoid the traps of making her out to be a saint or making her a crazy person, which is what tends to happen when she’s portrayed. This turns out to be harder than I thought.

Your book deals with the problem of writing about complex science, and you admit the mathematical conjectures proposed by André Weil are “over your head”. Do we have to accept that some forms of knowledge can never be democratised?

In practice, none of us will ever know everything. So the question I suppose is theoretical – are some forms of knowledge unavailable to most of us, even in principle?

I like to think that the Weil conjectures are theoretically something I could learn, but it would take a long time – like learning a difficult piece of music on an instrument I only play a little bit. I’d have to really dedicate myself to that one goal.

Simone argued a related point with André. She asked him directly, what is the point of work like yours, work that no one but a few can understand? She preferred the geometry of the ancient Greeks and saw it as an ideal from which math had fallen. Contemporary math, the work her brother did, she saw as regrettably abstract. And yet she felt it was very important that he continue doing it.

You describe feeling – as a white, American woman – in a minority studying advanced mathematics. Did “imposter syndrome” stop you from going further in the subject?

There just weren’t that many women in my math classes at all, and meanwhile, humanities classes were full of women like me. I sometimes felt like an imposter, but I also liked going against the grain.

I wouldn’t say that this stopped me from going further. By college, I’d already formed an idea of myself as a writer. I also had always been interested in a lot of different things, and graduate school works better for people who want to concentrate on one thing.

I will say that one reason I’d developed that idea of myself as a writer is that my grade-school teachers told me I was a writer. I was also good at math, but my teachers didn’t respond in the same way, and I’ve since read that this is often how it works – in the US, that is. Girls who are talented in math are often also talented in humanities, and nudged in the humanistic direction. Meanwhile, mathematically inclined boys are often encouraged to continue in math.

Ask a sage

Question: Only fools fall in love: true or false?

Simone Weil replies: "Nothing which exists is absolutely worthy of love. We must therefore love that which does not exist."