A friend who recently defended his dissertation in comparative literature mentioned Simone Weil’s writing on the *Iliad* in his defense. Afterwards, I told him her brother André was a famous mathematician. (In my former field of research, his name adorns the frequently-referred-to Weil-Petersson metric, but he is also a household name in other fields of math for other reasons.) My friend was unfamiliar with him. I myself had only learned of Simone a few years ago in Francis Su’s poignant lecture “Mathematics for Human Flourishing,” which repeatedly circles back to her words: “Every being cries out silently to be read differently.”

Both Weil siblings were intense and devoted to their work. They were close and loved each other, but their ways of moving through the world were starkly different. Simone was a philosopher and political activist, dedicated to the struggle of the common person. Alongside her dense philosophical writing, she was drawn to manual labor and wanted to suffer with those who were suffering. She died at age 34 in the middle of World War II, possibly as a result of her refusal to eat more than she believed children in German-occupied France had for rations after she contracted tuberculosis. André was a bold, often abrasive mathematician who traveled extensively and eventually married a woman who was the wife of a colleague when they met. He was arrested in Finland on suspicion of being a Soviet spy near the beginning of the war and held in prison before leaving to join the French army briefly and then emigrating to the U.S. after Germany occupied France. He died in 1996 at age 92.

Karen Olsson paints vivid portraits of both siblings in her forthcoming book The Weil Conjectures*. *With it, she invites the reader to sit with the Weils, to appreciate their relationship and ponder what their lives and work say to contemporary writers and mathematicians.

The book is not a biography of either Weil or a detailed look at any of André’s math, which was what I was expecting to some degree based on the title. It is more impressionistic than that, with Olsson weaving other historical vignettes and her own relationship to math and writing in with the story of the Weils. Olsson was enamored of mathematics for a few years in college and flirted with the idea of going to graduate school for math before deciding she wanted to be a writer instead. (In an amusing passage, she writes about pestering a friend “to admit that he hoped to write a novel eventually, which I believed everyone secretly did.” Eventually his insistence that he really wanted to be a mathematician and not a novelist helped her understand that her desire to write was not universal and that perhaps she should pursue writing seriously.)

But throughout the book she writes about revisiting the subject decades after her last college math course, watching abstract algebra lectures from a Harvard class as a refresher. She is not sure why she is pulled to the subject again so strongly but observes similarities between writing and mathematics. “How I would like to write something as clean and powerful as the best kind of mathematical proof,” she writes. Later: “A quality of both good literature and good mathematics is that they may lead you to a result that is wholly surprising yet seems inevitable once you’ve been shown the way, so that—aha!—you become newly aware of connections you didn’t see before.” As a mathematician-turned-writer who took a different trajectory than Olsson did, I was interested in our similarities and differences in our stories and feelings about math and writing. (I was amused by her recollection of something she felt in college: “I want to be a *real* writer. I’m not going to write about *math*.” Sick burn!)

Simone and André butted heads about mathematics, though both were interested in it. Simone thought mathematics was too abstract and irrelevant to the life of the common person, André was dismissive about explaining mathematics to non-mathematicians, describing it as “explaining a symphony to a deaf person.” But he did try to explain his work to his sister

The book feels deliberately fragmentary. Olsson will spend a few paragraphs with Simone or André, move to the other abruptly, and then switch to another piece of mathematics or history, or her own story. The quick changes can cause a little bit of whiplash and could probably have been deployed a bit more sparingly. On the other hand, some of her insights about the process of writing or mathematics are sharper for having been juxtaposed so closely with relevant parts of the Weils’ story.

After reading the book, my overwhelming thoughts (though I don’t know if it was Olsson’s intent) are of the form “what if?” What if Simone had survived the war? What if the Weils had been born at a different time, when the war would not have interrupted (or ended) their lives? What if André had been a more compassionate person? What if Yutaka Taniyama, a younger Japanese mathematician who helped formulate an important conjecture in number theory known as the Taniyama-Shimura-Weil conjecture or the modularity theorem now that it has been proved, had not died by suicide so young? (Olsson writes about him and his colleague Goro Shimura, who died earlier this year.) I think of all the paths not taken. Olsson and mathematics. Me and music. You probably have your own. We all make the choices we think are right given our circumstances, but what if things were different?