Snapshots of a Lively Character: Mary Lucy Cartwright, 1900-1998

July 15, 1998

Mary Lucy Cartwright. (Photograph courtesy of The Mistress and Fellows, Girton College, Cambridge.)

Philip J. Davis

I first saw Mary Cartwright in 1950, at the International Congress of Mathematicians at Harvard. At a session in what was then called "The New Lecture Hall," I asked a friend, "Who is that lady sitting next to Norbert Wiener?" His answer was immediate: "Oh, that is Mary Cartwright."

If I now had the guts to turn this true story into a version of the classic joke, I would have written "Who is that man sitting next to Mary Cartwright?"

I was familiar with the name because I had read some of her papers on integral (i.e., entire) functions, the area of my own thesis, and within a few years, I made use of one of her results from 1936. Within a few years also, there would appear two books on entire functions-one by my thesis adviser, Ralph Boas (1954), which contained substantial references to Cartwright's work, and then one by Cartwright herself (1956), both of which I studied carefully.

But my intention here is not to provide a description of her mathematical work in complex variables and nonlinear differential equations; that has been done far better by more qualified people. (See, for example, the article by Shawnee L. McMurran and James J. Tattersall on the long mathematical collaboration between Mary Cartwright and J.E. Littlewood in The American Mathematical Monthly, Vol. 103, December 1996, pages 833-845.) My intention is to provide a description of her personality as I experienced it.

I first met Mary Cartwright socially in the fall of 1968, when she was visiting the Dynamical Systems Group (later named the Lefschetz Center) of the Division of Applied Mathematics at Brown University. Tall, slender, and grey-haired, she reminded me (in appearance) of those devoted, spinsterish, mousy grammar school teachers who had provided me with an elementary education. Mousy? On further acquaintance, anything but-not on your tintype, as they say.

At Brown, as at many other American colleges, 1968 was a year of turmoil. Among other things, the curriculum was under attack. Brown was "rescued" from serious disturbances by the curricular proposals of an undergraduate by the name of Ira Magaziner (later intimately connected with the universal medical plan pushed by Hillary Rodham Clinton during her husband's first term as president.)
Mary Cartwright came occasionally to our departmental meetings, and in the course of one of them, she remarked that when she was a student, all mathematics majors were required to know a proof of the nine-point-circle theorem. Since the nine-point circle had to that audience the distinct flavor of being beautiful but irrelevant, I concluded that Professor Cartwright was telling us that we should not be too dogmatic as to what constitutes a proper mathematics curriculum. Fashion is spinach even in mathematics, and time often works to "nine-point-circle-ize" many of the seemingly most relevant and sophisticated topics that we currently insist on.

At a recent meeting, James Tattersall pointed out to me that in the early 19th century, the following question appeared on a Cambridge (England) mathematics exam: "Give two proofs of the existence of God. Do not use arguments from Revelation." I like to conjecture that given Mary Cartwright's clerical background, she would probably have done well on that one.

As the weeks went on, I got to know Mary better and we dropped the formalities of title. I could see that I was dealing not only with a very sharp mathematical mind (which I already knew, of course), but with a mind and a tongue sharpened over the years by the repartee of Oxbridge high table wits. This pleased me greatly for I can hold my own in the game of academic wisecracks. And so we got on quite splendidly. In the years that my wife and I knew Mary, I did not engage with her mathematically, although when I came to write the beginning of The Schwarz Function, I inserted in her honor the nine-point circle as an example of the use of conjugate coordinates.

During her stay in Providence, there was a mathematics meeting in Cincinnati that we both---each unknown to the other---planned to attend. We made separate air and hotel bookings. Surprise: We met getting off the plane and found out that we were booked into the same hotel. We taxied to the hotel together, I helping her with her bags. Further surprise: The room clerk booked us into adjacent rooms.
Depositing her bags in her room, which was very large and had two queen-sized beds, I decided to tease her.

"Mary, you know if I moved into your room with you, and we split the cost, we would both save a bit of money!"

She was silent for a moment; she considered the possibility, and then she looked at me sternly and said slowly, "I don't think that would do."

At this point, let me interpolate a few facts of the Who's Who variety. Mary was born to a Northhamptonshire family; her father was rector in the small village of Aynho. She told us early on that she had lost two brothers in World War I. (I always thought that from time to time a certain sadness would come out from beneath the fun.) She went up to St. Hugh's College, Oxford, taking a First in 1923. In 1927, after a few years of prep school teaching, she went back to Oxford, where she earned a doctorate under G.H. Hardy in the theory of integral functions.

When Hardy moved to Cambridge in 1930, he managed to get Cartwright a position there. She was Fellow of Girton College, Cambridge, from 1930 to 1949, and she was its Mistress from 1949 to 1960. She was a lecturer in mathematics at Cambridge University from 1935 to 1959 and a reader in the theory of functions from 1959 until she retired in 1968. Among her many honors and awards, she was elected Fellow of the Royal Society in 1947 and was named Dame of the British Empire in 1969.

To return to my story. Her sense of fun was strong (certainly math was fun); her dry humor flowed like a stream-to mix metaphors. The announcement of her being named D.B.E. came while she was at Brown. Eleanor Addison, then administrative assistant of the division and a woman who takes no guff from either man or beast, told me that when she heard the news, she approached Mary and said to her "Well, Mary, now that you've been knighted, I suppose I'll have to bow down three times."

And Mary answered, "No. Twice will do."

After Mary left us at Brown to take up visiting positions at Case Western and Claremont Graduate School, and ultimately to return to Cambridge, there was a gap of a number of years in our friendship. In the mid-eighties, though, for a week or so in the summer, my wife and I would take ourselves to Cambridge, where we had developed a number of friendships. Mary was now well into retirement, and in the minds of our Cambridge mathematical friends, she was a local legend and an icon but not an active presence. Our relationship was readily reestablished, and we found that in addition to her iconic character (which she enjoyed), she was also quite a social being. And not only a social being, but more than a bit of a gossip.

She had been everywhere worth going, mathematically speaking. She know everyone "worth knowing" in the mathematical world and she ranked them-even as Hardy had done, using the rankings of cricketers. In the larger world also she was a bit of a snob, an attitude learned early, I suspect, for as she talked about her childhood in one of her interviews, "The country gentry did not mix socially with the farmers. . . . The children of the gentry could not possibly be sent to the village school. . . . Parents who lived in the great country houses usually preferred to have a resident governess (for their daughters) which was expensive."

And she loved to talk and tell stories. The Cambridge University arena was not forbidden territory for her stories, nor were human peccadillos, whatever they were or wherever they may have occurred.

When we first vacationed in Cambridge, Mary would bicycle down from her garden apartment in Sherlock Close, which was up Castle Hill, just past Fitzwilliam College. She introduced us to tea in the Graduate Center, where for a few pence one could have tea and biscuits and look out the picture windows and see the cows in the fields opposite and the punters on the River Cam.

As the years rolled on, she was less inclined to come into town, and we would visit her in her apartment. There, her photo albums would come out, stories, scandalous and tame, would be told and retold, and occasionally she would find an old mathematical reprint and explain the gist of it to me. She remembered old friends at Brown and asked me to tell her of their subsequent careers.

All in all, she was a mathematician of world class. And this was a particularly remarkable achievement in a generation when few women entered the field.
I close these few reminiscences with the hope that it will not be long before there is a full-length biography of Mary Cartwright.

Philip J. Davis, professor emeritus of applied mathematics at Brown University, is an independent writer, scholar, and lecturer. He lives in Providence, Rhode Island.

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