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Angles of Reflection: Logic and Mother's Love

Joan Richards
W. H. Freeman and Company
Publication Date: 
Number of Pages: 
[Reviewed by
Libby Krussel
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I really enjoyed this book — I couldn't wait to get to the end and find out how everything unfolded. It is a well written, compelling story that would strike a chord with anyone who has ever struggled to find a balance between their professional and personal lives. The author experienced such a conflict at first hand and in a particularly acute form.

Joan Richards is a historian of mathematics at Brown University who was at work on a biography of Augustus De Morgan, a 19th century British mathematician, when her nine-year old son suddenly collapsed at school one day and began having seizures. Several weeks and doctors later, Ned was diagnosed with a brain tumor. Joan and her family had been eagerly anticipating her sabbatical year at the Wissenschaftskolleg in Berlin. This would give her the opportunity to immerse herself in her work, in the research atmosphere of the institution, and luxuriate in the long stretches of time afforded her to write her book. But the looming specter of brain surgery for her son threatened to disrupt this idyllic environment. The family ultimately decided to keep the plans to travel to Germany and went there shortly after her son's surgery. Once there, they encountered further complications — but I don't want to give it all away! You'll just have to read the book.

It was heart-wrenching to read of Joan's desire to work, her inability to concentrate on it, and her guilt at not being able to disassociate herself from her family's troubles and buckle down to work, as De Morgan had done while his daughter was dying. In the story, Joan draws contrasts between the black-and-whiteness of De Morgan's logic and probability theory, the ability he had to leave the problems of his children's health to his wife, and the grayness of her choice to remain involved in the process of her son's illness and recovery. She struggled to advocate for her son and his rehabilitation in a country where she was unfamiliar with the language, the medical system, the hospitals, the nurses, and the doctors. At the same time, she continued to try to focus on her work. She describes one of her attempts at work at the Wissenschaftskolleg:

"In my office I had begun again to work. The issue that was bothering me was the one that had arisen as I had tried to apply De Morgan's ideas to the Ned [her son] situation in the spring. It was clear to me that probabilistic thinking was simply silly as a model for the way we think in particular situations and that De Morgan knew it... The answer I found had to do with De Morgan's views of how we know things. In a typically Victorian fashion, De Morgan saw Newtonian physics as the quintessential example of something successfully known... Sometimes we know things necessarily, absolutely, certainly... Most things, however, we know only contingently."

Joan's life was inexorably changed by her experiences. "My sabbatical time as Ned's mother had left its mark. I was there [in De Morgan's London neighborhood, Bloomsbury, studying his papers] under false pretenses, an impostor, an intruder. I constantly felt De Morgan's judgment of me as a woman working in a man's world, and as I read his letters I found myself judging him in return." In final realization of how changed she was by her experience, she writes: "Their mathematical work was magnificent, but they had only been able to sustain it by disparaging the relative and consigning it to their servants and their wives. Wives are, after all, merely relative. So, I realized, are mothers." I found myself understanding why Joan Richards felt betrayed by this discipline that now seemed cold, and pure, precise but unfeeling in the arena of the personal and the family — the very qualities that had attracted her to it in the first place: its certainty, its truth, its comforting peace.

I found this to be a fascinating, engaging, thought-provoking book.












Libby Krussel ( is associate professor of mathematics education in the Department of Mathematical Sciences at The University of Montana, Missoula, MT. She is interested in the preparation and professional development of mathematics teachers and teaches classes for them such as geometry, history of mathematics, algebra, modeling. She has a long-standing interest in the history of mathematics and in particular the place of women in that history. She also conducts research in undergraduate mathematics education, and is currently working on a project involving the learning of geometry at the college level.

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