AWM Book Review

WHAT I READ ON MY SUMMER VACATION

Angles of Reflection: Logic and a Mother's Love

Joan L. Richards, W. H. Freeman, New York, 2000. 282pp. ISBN 0-7167-3831-7 (cloth), $23.95.

From: AWM Newsletter, September/October 2000.

Reviewed by: Marge Murray, Book Review Editor, Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123; email: murray@calvin.math.vt.edu.

Joan L. Richards is an historian of mathematics at Brown University whose research specialty is the mathematics of Victorian England. She is also married and the mother of two sons. Her remarkable book, Angles of Reflection , is an account of two particularly difficult years in her personal and professional life, during which the claims of love and the responsibilities of motherhood came into direct conflict with her academic and scholarly aspirations. This book stands as a testament to those years, and as her (not entirely successful) attempt to reconcile the conflict.

In the fall of 1994, Joan Richards embarked upon what promised to be an exciting two-year sabbatical from her teaching responsibilities at Brown University, spending one year as a fellow at the Dibner Institute at Harvard, and a second year at the Wissenschaftskolleg in Berlin. During these fellowship years, her goal was to write a book about the life and work of Augustus DeMorgan, the Victorian mathematician whose lasting contributions to logic and probability would shape the thinking of generations of mathematicians and scientists to come.

The fellowships came at an auspicious moment. As the mother of two sons, Richards was long accustomed to juggling the responsibilities of work and family. She writes:

Somehow I had managed to teach and finish my dissertation after Brady, my first child, was born. I finished my first book when Ned, my second child, was still in diapers. But my second book had not followed as expected. Raising two children had proved itself to be just too distracting to allow me to think through a whole new project. Though I scheduled a full workload around them . . . I could not muster the kind of total concentration required to write. Six years into my tenure, my department turned down my promotion. I could not refute their objection that I had not written a second book. Would I could do was recognize that at nine and fourteen the boys were no longer as demanding as they had been before, and it was high time to concentrate on my research and writing. (p. 3)

Thus Richards embarked upon her sabbatical with every expectation that it would offer her the precious time and space she needed to explore the life and thought of DeMorgan, to get a new book project well underway, and in so doing to revitalize her relationship to research.

As John Lennon once said, "Life is what happens while you're making other plans," and this seems to be the dominant motif of Richards' entire book. In the fall of 1994, Richards established a comfortable routine, at home with the family in Providence, Rhode Island by night, and at work in Cambridge, Massachusetts by day. She had just begun to settle in to her work on DeMorgan when her younger son, Ned, suffered a grand mal seizure in the middle of an otherwise normal day at school. In the aftermath of her son's seizure, Richards and her family endured an anxious period of vigilance and worry, with endless trips to doctors and clinics, which finally culminated in successful neurosurgery to remove a tumor from Ned's brain the following spring. During these difficult months, Richards maintained a tenuous connection to her professional life in Cambridge, but ultimately realized that her concentration had been broken and her heart and mind belonged with her son and her family in Providence.

As Richards reflects upon these early months of her son's illness, she finds curious parallels between her own life and that of Augustus DeMorgan and his wife, Sophia. The DeMorgans had seven children, and as one might expect in nineteenth-century England, responsibility for the care and nurturance of the children fell almost entirely to Sophia DeMorgan. As Richards became more deeply involved in the medical crisis of her own son, she found that her sympathies lay much more with Sophia than with Augustus, whose life and work were almost totally insulated from the day-to-day lives of his wife and children.

In the early pages of her book, Richards also reflects upon the factors which first attracted her to the study of mathematics and its history. As a young woman, Richards found refuge from the vicissitudes of adolescence by studying mathematics:

Throughout junior high school, as I struggled to fit the loud, clumsy, fast- growing Joan that I was into the social spaces allotted to young women, mathematics sustained me. In the midst of efforts to maintain my dignity through school dances, clothes shopping, and hair dressing, mathematics provided peace. It was like a daily miracle to hear my classmates read out their answers to problems and find that we had come to the same conclusion. When the rest of life seemed an unending struggle to find the right thing to say, the right place to be, mathematics class was a safe haven. (p. 36)

Mathematics and physics --- particularly the work of Isaac Newton --- offered Richards the kind of purity of thought and experience that many people seek through religion. The attraction of mathematics, for Richards as for many others of us who enter the profession, was its clarity, its certainty, its purity, and its peace.

Yet, faced with her son Ned's health crisis, Richards found herself chafing against the very purity and insularity that first attracted her to mathematics. She came to realize, through reflection upon the lives of Newton (who never married and had no children) and the DeMorgans, that academic life in general, and mathematics in particular, have long been uncomfortably insulated from the messiness, uncertainty, and passion of "real life." In the aftermath of her son's successful surgery, Richards' faith in the purity and safety of mathematics and academia were clearly shaken. But with the crisis past, she once again looked to her academic future, and in particular, to the coming year 1995-96, which she would spend with her sons in Berlin.

Richards began her year in Berlin with high hopes and a sense of adventure. Her plan was to spend the year in Germany with her two sons; her husband, Rick, would spend the first month with them in Germany, and would return for a series of extended visits during the year. Indeed, the first month went very smoothly, as her sons settled into a sense of routine in this strange and fascinating city, and Richards began to settle into a comfortable niche at the Wissenschaftskolleg. Once again, she began to contemplate the work of Newton and Leibniz, the logic and probability of DeMorgan. Once again, her concentration was shattered by a crisis involving her son, Ned.

During her first month in Berlin, even before Rick's departure for the States, Ned suffered a playground fall at his school and broke his left arm. At first, especially when compared to the neurosurgery of the previous year, Ned's injury seemed like a minor annoyance. But as the break began to heal, Ned suffered severe pain and failed to regain normal mobility in his arm. By this time her husband had gone back home, leaving Richards to negotiate the frustrating German health care system on her own. Thus began a months-long, harrowing encounter with hospitals, clinics, physicians, surgeons, nurses, and physical therapists, during which Richards lobbied relentlessly for the health and welfare of her son, struggling to make herself understood in a language (German) whose nuances she could not fully understand. In the end, Ned required three surgical operations and intensive physical therapy before he began to regain normal use of his arm. As Richards devoted herself ever more fully to her son's care and healing, she once again found herself alienated from the insular world of academia and unable to reconcile the competing demands of the two.

By the end of her fellowship year in Berlin, Richards found herself increasingly alienated from the purity and insularity of academic and mathematical life. Reflecting on the work of Augustus DeMorgan and his colleagues toward the end of her fellowship year, she writes:

I saw them engaged in a powerful purifying project, trying always to separate the necessary and absolutely true from the contingent and the relative. I had long been intrigued by their effort, but my years with Ned had shown me the dark side of their drive toward purity. 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. (p. 237)

Attending seminars during her final months at the Wissenschaftskolleg in Berlin, Richards felt an increasing restlessness. Listening to clean, precise academic discussions of science and mathematics, she found herself asking, "What does this have to do with anything?" (p. 224)

In the closing chapters of the book, Richards recounts her final days in Berlin, her return to the States, the resumption of "normal" life, and her son's gradual return to the typical pursuits of a growing preadolescent boy. It is clear that the years of her fellowship and of Ned's illness and injury have left an indelible mark on her approach to academic and scholarly work. Through this book, Richards has begun to make her scholarly work more personal, to bring to her academic work a sense of the richness, complexity, and complication of life.

Reading this book, I am also profoundly aware of just how clearly it is a woman's story. Indeed, at times while reading it, I found myself feeling angry at Rick for his absence from Berlin, angry that Joan had to face the intimidating German health care system alone, angry at an academic system which presumes that children should be neither seen nor heard, angry that mathematics so often comes across as a discipline lacking in both heart and soul. I salute Joan Richards' courage in writing about her experience, and look forward to reading her next book. Her sabbatical has clearly transformed her approach to scholarship, and I am eager to see what happens at the next stage in her personal transformation.