Mary Lucy Cartwright

Dame Mary Lucy Cartwright (1900–1998) was one of the few twentieth century women to make significant inroads in the predominantly male world of mathematics. She contributed important advances in function theory and differential equations. Her work led to the development of the modern chaos theory. The elite Briton led a distinguished career as both a mathematician and administrator at Girton College, Cambridge University. She was respected and well–loved for her direct, clear–sighted solutions to human and mathematical problems.

Family in Public Service

Born on December 17, 1900, in Ayhno, Northamptonshire, England, Cartwright was the second youngest of four children in a well–to–do family. Her two older brothers died in action in World War I and her father worked as a curate for a church and later as rector. Educated thus far by governesses and at various local boarding schools, she was sent to her uncle's home at age eleven to attend the well–regarded Learnington High School (now the Kingsley School). As she later recalled to Brown University mathematician Philip J. Davis, "The children of the gentry could not possibly be sent to the village school." There she benefited from exposure to a talented female mathematics teacher who took Cartwright under her wing.

In 1919, Cartwright went on to St. Hugh's College at Oxford University to study mathematics, but had trouble getting into lectures she needed for her course work, as male students returning in droves from World War I were filling them up. She got as many class notes as she could from friends who got into the classes, but to her great disappointment, earned only a second degree in mathematics in 1921. Cartwright nearly changed her academic focus to her original favorite, history, but decided mathematics would be easier, she told Davis with a touch of irony. She only made up her mind to stay with mathematics after a professor suggested at a party that she drop in on some evening classes of Godfrey H. Hardy, a revered geometry professor. Hardy's teaching enthralled her, and Cartwright graduated in 1923 with a first degree in mathematics. The school had only began permitting women to take final degrees the previous year.

Cartwright began her career at the Alice Ottley School in Worcester, where she taught and served as assistant director from 1923 to 1927. She spent another year teaching and directing at the Wycombie Abbey School in Buckinghamshire, but felt the prescribed curriculum there was too restrictive. She felt compelled to return to her research at Oxford. Cartwright began doctoral work there in 1928, initially under the supervision of Hardy and later under E. C. Titchmarsh. With the innovative Hardy as her teacher, Cartwright began to blossom. In fact, some of her work on generalized Abel summability with applications to Fourier series was published later that year. Cartwright's examiner for her doctoral dissertation in 1930, the first time in Oxford's long history that a woman had ever reached doctoral status, was John E. Littlewood, with whom Cartwright would collaborate many times. Her thesis was entitled The Zeros of Integral Functions of Special Types.

After completing her doctoral work at Oxford, Cartwright received a Yarrow Research Fellowship at Girton College (Cambridge University) in 1930. She published a seminal article, "From non–linear oscillations to topological dynamics," in The Journal of the London Mathematical Society in 1931. Financed by the fellowship, she worked for five years on cluster sets in the theory of functions of one complex variable. Her results, which centered around what came to be known as Cartwright's Theorem, were deemed important in many mathematical circles, and were published in 1935 in Germany's Annals of Mathematics. In addition, Hardy and Littlewood were so impressed that they recommended Cartwright for assistant lecturer at Girton. Cartwright also served on the prestigious London Mathematical Society from 1933 to 1938. In 1934, she had been appointed to a College Lectureship in Mathematics and a staff fellowship.

Moved into Professional Academia

As a part–time assistant lecturer at Girton beginning in 1935, Cartwright continued to excel not only as a mathematician, but in smoothing out administrative difficulties, often with dry humor. She became director of studies in mathematics at Girton College in 1936. Cartwright soon became a familiar figure to Cambridge students as she bicycled to and from classes and committee meetings and her garden apartment in nearby Sherlock Close.

Added Volunteer War Duties

In 1939, the British Department of Scientific and Industrial Research's Radio Research Board asked Cartwright to help solve some nonlinear differential equations that seemed at the heart of problems scientists were having with the new radar technology. As the Allies prepared for World War II, radars were being pushed to their limits. She and Littlewood undertook the research, although her background and expertise were in complex analysis, not dynamics. They studied the Van der Pol equation, including a factor known as "sinusoidal forcing," and discovered that as power increases, the periodic solutions go through a series of increasingly higher subharmonic phases until they ultimately become aperiodic, or recurring irregularly. The mathematicians showed the radar scientists how this caused the disastrous results they were experiencing with their radars. Meanwhile, Cartwright and Littlewood had also learned that the aperiodic solutions have a fragile topological structure. Cartwright and Littlewood published their findings when the war ended, but by then people had moved on to other research interests. Only in the 1960s did mathematicians, such as Edward Lorenz, come across Cartwright's and Littlewood's findings and make them the foundation of chaos theory, which quickly became the most fashionable area of physics research.

Although she appeared frail, Cartwright was a workhorse who enjoyed maintaining a busy teaching and administrative schedule. During World War II, she volunteered and served extensively with the British Red Cross Detachment from 1940 to 1944. Cartwright managed to co–publish, with Littlewood, an article in The Journal of the London Mathematical Society titled "On non–linear differential equations of the second order." This would be remembered as one of her most important publications. In 1947, due to her contributions to mathematics, she became the first woman elected as a Fellow of the Royal Society of England. She would remain its only female member until Dusa McDuff joined her in 1994. Cartwright took a brief sabbatical from her duties at Girton in 1948 to serve as a visiting professor in the United States, spending a few weeks at a time lecturing advanced mathematical students at Stanford and Princeton universities, and the University of California, Los Angeles.

Career Changed to Administration

Cartwright became Girton's head of school in 1949. Fully incorporated into Cambridge University just the year before, Girton had been founded in 1869 as the university's first residential college for women. She began to spend the bulk of her time interviewing prospective students and meeting with other members of the school staff. Her duties also included serving as chairperson of the Cambridge University Women's Appointment Board, a member of the Education Syndicate, and board member of the Council of the Cambridge University Senate. Cartwright was known for her gentle, encouraging corrections of students; her dedication to precise English usage; and devotion to her students' work. Despite her administrative mandates, she remained a respected fixture of British and international mathematics circles and served as president of the British Mathematical Association from 1951 to 1952. Cartwright often traveled to the United States and Europe for conferences and continued writing about her research, publishing Integral Functions in 1956. The book was lauded for offering unprecedented depth and precision on its subject.

In 1959, Cartwright was promoted to Reader in the Theory of Functions at Girton. From 1961 to 1963 she was president of the London Mathematical Society, and in 1964 she received the coveted Sylvester Medal of the Royal Society of Mathematics. In 1968, the year she received the London Mathematical Society's DeMorgan Medal, she retired from Girton. This freed her to devote more time to universities and professional associations. Cartwright, well in demand, spent the 1968–1969 academic year as a resident fellow at Brown University in Providence, Rhode Island, and from 1969 to 1970 as a visiting professor in Poland and Wales. Meanwhile, in 1969, she was ordained Dame Commander of the British Empire by Queen Elizabeth II, making her the female equivalent of a knight. (Dame Cartwright became her formal name).

Though she broke her hip in a bicycling accident, Cartwright remained busy, serving in 1971 as a visiting professor at Case Western Reserve University in Cleveland, Ohio, and then returning to Great Britain to begin a productive, decade–long collaboration with H. P. F. Swinnterton–Dyer. The two produced three highly regarded papers on boundedness theorems for second–order differential equations. The time she had spent in the United States during the Vietnam War years of the 1970s made a deep impression on Cartwright, and in her later years she wrote extensively in her memoirs about the many protests and conflicts she had witnessed within the American university system, including the 1970 killing of four student protesters at Kent State University in Ohio.

She continued to write papers on mathematical research subjects into the late 1980s. Her concern for the education of females remained an important topic for her, and in 1989 she published the article "Moments in a Girl's Life" in the Bulletin of the Institute of Mathematics and Its Applications. Cartwright, however, spent most of her later years editing Hardy's and Littleton's manuscripts, as well as indulging in painting and music, her other favorite pursuits. She said she had never been appointed to a full professorship because of her reluctance to take on more than a very few "special" graduate students and because she was already head of a college. Cartwright squelched many biographers' notions that sexism had held her back, often believing she was preferred over her male counterparts in professional contexts.

Cartwright died at age 97 in Cambridge on April 3, 1998. Her other publications included Religion and the Scientist, The Mathematical Mind, and Specialization in Education.

Periodicals

Notices of the American Mathematical Society, February 1999.

Society for Industrialand Applied Mathematics, July/August 1998.

Times (London), April 7, 1998.

Online

"Contributions of 20th Century Women to Physics," University of California, Los Angeles,http://cwp.library.ucla.edu (November 29, 2004).

"Dame Mary Lucy Cartwright," Biographies of Women Mathematicians—Agnes Scott College,http://www.agnesscott.edu/lriddle/women/cartwght.htm (November 29, 2004).