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Book review: Cromwell, Eleanor Catharine (ed. Hopkins and Puckle-White), Accounting for Her (Penguin, 1982). A rigorous and thoughtful discussion of the lives of the mathematicians Maria Gaetana Agnesi, Mary Somerville, Charlotte Scott, Mary Everest Boole, and Philippa Fawcett.

 

Born in 1915 in Stoke, Cromwell earned a First in mathematics from Shrewsbury College in 1937 and an MA two years thereafter. Her long career as a teacher of maths for girls began in 1943 and continued until her retirement in 1972; during the early part of the war she is thought to have assisted with codebreaking work at Bletchley Park (this was covered by the Official Secrets Act for most of her life, and she left no diaries or other indications). The Kingscote School for Girls, her longtime employer, now awards a Cromwell Prize yearly for outstanding work in mathematics.

Accounting for Her was apparently a labor of love on the part of its author; drafts in various forms were found among her papers after her death, dating back to her undergraduate years. As the shape of the book gradually developed, she seems to have worked on it a little at a time during school holidays, often returning to Oxford to make use of the Bodleian, and occasionally traveling abroad. Her research in Italy on Agnesi was assisted by Emily Latimer, a colleague at Kingscote who, as a Latin teacher, was able to offer Italian support.

Reflecting her background in the field, Cromwell goes into considerable detail on the mathematical work of each of her subjects; perhaps as a legacy of her years of teaching, this material is remarkably accessible even to the lay reader, and it is notable in particular that we are able to understand both intellectually and emotionally why the work of each woman was particularly significant in each time, from the Witch of Agnesi to Mary Everest Boole’s philosophies of education and Charlotte Scott’s rigor in principle and proof. Her subjects seem to have been chosen with a particular eye to their work in mathematics education, and Cromwell effectively elucidates their context.

 

Emily H. Latimer, for many years a teacher of Classics at Kingscote School, now living in retirement in Cornwall, recalls their long friendship. “I was familiar with Eleanor’s hobby of research, of course, and even suggested to her once or twice that she should take a leave of absence and get the book ready for publication. She might have done, but she really did love teaching—I think at any given time there were a handful of students whose work and whose personalities she found too interesting to abandon, although many of the others she would cheerfully have walked away from without a second thought. And she seemed to enjoy the process of research and writing more than the idea of publication itself.

“I enjoyed the opportunity to travel around Europe with her to certain foreign libraries. In Italy I was able to be rather useful, given my Latin. During one long vacation, courtesy of a flu epidemic at the school which we both managed to escape, we traveled to America and visited Charlotte Scott’s old haunts at Bryn Mawr. Eleanor was, in fact, offered an opportunity to go on for her doctorate there, and I believe she was tempted, but there were pupils at Kingscote at the time whom she was most reluctant to abandon midway. I recall that during the term immediately following that, she was exceptionally inclined to follow her own judgment rather than the conventions of the school.”

(Were you familiar with Cromwell’s work at Bletchley Park?) “Only indirectly. I remember she was very, very angry—it was just after she retired, I believe. I was in my own last year of teaching, and I had gone down to spend a holiday with her, and found her absolutely incandescent with rage, one might say. This man—Winterbottom? had published a book about Bletchley Park. It was far outside my own interests and I never read it then or thereafter, but Eleanor was extremely angry that he had breached the code of silence which had been maintained for so long. She found it entirely irrelevant that the war had been over for nearly thirty years. No, I didn’t ask her about anything she might have done; I knew she was not prepared to tell me, but it was quite clear that she was taking the issue very personally indeed. I understand that she wrote Winterbottom, or whatever his name may have been, a particularly scathing letter.”

(Do you think this unusual experience at Bletchley shaped her interest in mathematics thereafter?) “Again, not in any direct sense; we first encountered one another as freshers at Shrewsbury, and I remember that she was always very passionate about the study of maths. I’m sure she was given the chance to work at Bletchley Park, assuming of course that that is what she did, because she was a mathematician, not the other way around. If it affected her at all, it might have been in her tendency to disregard hierarchies, and to view much of life as problems to be solved. In the most complex sense thereof. She was considered probably the strictest disciplinarian of us all by the girls, but her rewards and punishments were always original and well thought out, not to speak of informed by her sense of humour.”

 

The editors of the volume, E. A. Puckle-White (Lecturer in Statistics, Durham) and M. K. Hopkins (Fellow of Gladstone College, UCL), are both former students of Cromwell at Kingscote School. “Reading over the drafts, we were able to hear Miss Cromwell as if she were there lecturing to us,” Puckle-White says. “She had a very distinctive voice in every sense, and one always paid attention in her classes because it was simply impossible not to.” Hopkins adds, “Her work in the book reflects her exceptionally broad general knowledge and interests. There were times in maths class when a question or something in the news would set her going on a topic she felt we should know more than we did about—I recall one discussion about religious beliefs at the time of Jesus’ birth, and another about the Berlin airlift. At the time I was particularly anxious to do well in maths and resented the time taken away from classwork, but later on I came to respect the ideals of a good education, including but not limited to mathematics, which she held for us.”

(Do you feel she would have preferred to live on a wider stage than that of mathematics instructress at a girls’ seminary?) “Well, that’s a rather reductive way to put it in itself. As you know I teach at a women’s college, and hold very strong views on women’s education, especially in the single-sex context. I feel that Miss Cromwell and a few of her colleagues were exceptionally influential for me in this way. In her classes the fact that we were girls, women, was entirely irrelevant; we never thought of it, we experienced ourselves entirely in relation to one another and to our teachers, women themselves. We were held to very high standards; it was in no sense a “finishing school”, and we were expected to do well in classes and on public exams. A surprising number of our classmates have gone on to do well in various fields, and I feel that the presence of Miss Cromwell and her ilk had a great deal to do with this.” (Hopkins)

“Meg and I don’t entirely agree on this point. I do go along with her feeling that Miss Cromwell’s work as a maths teacher at a girls’ school was important, that the academic rigor she imposed on us opened doors for us and set patterns for us later in life; that’s undeniable. Going back to your original question, though, I do imagine she might have liked at times to lead a different sort of life. She was not a self-immolator, I believe, not someone who fretted not at the convent’s narrow cell, if you will. As an older teenager, and especially looking back thereafter, I came to see that she found the format of boarding-school life frustrating in some ways. She was famous for her caustic tongue with regard to the prefects, willing to scold them in front of the younger girls, as other mistresses generally would not. I can remember cringing more than once. I think now she was probably impatient with the artificial structure which set seventeen-year-olds in authority over fourteen-year-olds, when we all looked very much the same from her perspective. She was very concerned with perspective in all its senses.” (Puckle-White)

In the epigraph to her book, Cromwell quotes Mary Somerville: “In writing this book I made a great mistake, and repent it—Mathematics are the natural bent of my mind. If I had devoted myself exclusively to that study, I might probably have written something useful.”

Hopkins and Puckle-White are in agreement that Cromwell is indulging in a degree of self-mockery thus, referring ironically both to the time spent on her study of women mathematicians and to her career as a teacher rather than a pure researcher. “It would be like her to turn the same rigorous eye on her own career that she did on her students’ work. Even for the particularly mathematically gifted, an ‘alpha’ marking in her class was something of an event, and we feel that she expected as much of her own work, her own life in general, as she did elsewhere.” (Hopkins)

While confining themselves largely to a brief account of Eleanor Cromwell’s life, Puckle-White and Hopkins close the short Editors’ Afterword with a quotation from a student of Philippa Fawcett: “She was ruthless towards mistakes and carelessness…My deepest debt to her is a sense of the unity of all truth, from the smallest detail to the highest that we know.”