Mary Cartwright

Mary Cartwright (born December 17, 1900, Aynho, Northamptonshire, England—died April 3, 1998, Cambridge, England) was a British mathematician known for contributing to the development of chaos theory—specifically what later came to be called the “butterfly effect.” Cartwright was honored as the first female mathematician elected as a Fellow of the Royal Society.

Early life and Oxford

Cartwright was one of five children born to William Digby Cartwright, the rector of St. Michael’s parish, Aynho, Northamptonshire, and Lucy Harriette Maud Cartwright (née Bury). She was homeschooled by governesses until the age of 11, when her parents sent her away to continue her education at a series of boarding schools—first Leamington High School (later the Kingsley School) in Leamington Spa from 1912 to 1915, then Gravely Manor School in Boscombe from 1915 to 1916, and finally Godolphin School in Salisbury from 1916 to 1919. It was during her final year at Godolphin that she developed a particular interest in mathematics, mainly through the lessons of her teacher Miss Hancock, who encouraged Cartwright to further her mathematical studies at the University of Oxford.

In October 1919 Cartwright began attending St. Hugh’s College, Oxford. At the time, she was one of just three women entering the college to study mathematics and one of only five women studying the subject at Oxford. Moreover, the campus was particularly crowded that year: in addition to the usual contingent of first-year students, students whose education had been interrupted by World War I (a war that had claimed her two elder brothers’ lives) were then returning to class. Sometimes Cartwright struggled to find space in her professors’ lectures and relied on copying the notes of a more fortunate peer.

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After two years of study, Cartwright ranked second class in her mathematical moderations exams in June 1921. This was no mean accomplishment—only four men ranked first class—but it caused Cartwright to experience a crisis of confidence, wherein she seriously considered studying history instead. However, Cartwright continued studying mathematics and, on the advice of fellow student V.C. Morton, supplemented her studies by reading E.T. Whittaker and G.N. Watson’s A Course of Modern Analysis (1902) and attending evening classes taught by G.H. Hardy. The extra effort paid off: in 1923 Cartwright graduated with a first-class degree.

Higher education and teaching career

According to some sources, Cartwright wished to continue her education immediately by pursuing a Ph.D., but, out of concern for her family’s ability to support her financially, she instead left Oxford to teach. Cartwright taught at the Alice Ottley School in Worcester and at Wycombe Abbey in Buckinghamshire. In 1927, however, she returned to Oxford and began work on her Ph.D. under Hardy, the same professor whose evening classes had helped her previously. During the 1928–29 academic year E.C. Titchmarsh took over as her supervisor.

In 1930 Cartwright successfully defended her doctoral thesis, “The Zeros of Integral Functions of Special Types,” before mathematicians W.L. Ferrar and J.E. Littlewood. Meeting Littlewood would prove significant, as he and Cartwright would later become collaborators. After her defense, Cartwright began working at Girton College, Cambridge, as a Yarrow research fellow to continue working on the topic of her thesis. There she further impressed Littlewood, who taught at Girton, by solving one of the open problems he had described in his lectures. She explained her answer, now known as Cartwright’s theorem, in “From Nonlinear Oscillations to Topological Dynamics” (1931).

On Hardy’s and Littlewood’s recommendation, Girton hired Cartwright as an assistant lecturer in mathematics in 1934. She began lecturing the next year and taught part-time initially and then full-time until 1959. In 1936 she also became the college’s director of studies in mathematics, a position she would hold until 1949.

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Chaos theory and the butterfly effect

Cartwright’s research took an important turn in 1938 when a memo from the Radio Research Board of the British Department of Scientific and Industrial Research piqued her interest. The board wished to “bring to the notice of mathematicians certain types of non-linear differential equations involved in the technique of radio engineering.” Cartwright was unfamiliar with the dynamics behind the problems that the board was facing and took the equations to Littlewood. “For something to do we went on and on at the thing with no earthly prospect of ‘results,’ ” Littlewood would later recall, and “suddenly the whole vista of the dramatic fine structure of solutions stared us in the face.”

What Littlewood described is now known as a typical example of the butterfly effect. He and Cartwright had become two of the first mathematicians to investigate chaos theory. The pair continued to collaborate for years on the subject and, in doing so, not only furthered academic knowledge but also significantly improved radio amplifiers used during World War II. In 1947 Cartwright’s work with chaos theory led to her being the first female mathematician elected to the Royal Society.

Honors and awards

In 1948 Cartwright was assigned to be the mistress of Girton, a post she would hold from 1949 until 1968. Overseeing the college required a great deal of time and energy, but Cartwright nevertheless made time to continue conducting research, notably on cluster sets in the 1950s. In 1951 she served as the president of the Mathematical Association and from 1961 to 1963 as the president of the London Mathematical Society. In both cases, she was the first woman to do so. Other honors she accrued during her later career included the Royal Society’s Sylvester Medal in 1964 and the London Mathematical Society’s De Morgan Medal in 1968. In 1969 she was honored by Queen Elizabeth II, who appointed her Dame Commander of the Order of the British Empire (DBE).

After her retirement in 1969 Cartwright used her new freedom to travel as a visiting professor to various universities in the United States and continental Europe. After teaching abroad, she returned to Cambridge, where, among other activities, she coedited several volumes of the Collected Papers of G.H. Hardy (1966−79). Over the course of her life Cartwright authored more than a hundred papers.