Mary Cartwright's standing in the mathematical world was such that she was elected to the fellowship of the Royal Society in 1947, shortly after it was opened to women, and she became the first woman to serve on its council. But she also took a great interest in mathematical teaching in schools and was president of the Mathematical Association in 1951-52. Although her published work is nearly all severely technical, she could also appeal to a wider public as she showed in her James Bryce Memorial Lecture, The Mathematical Mind , given at Somerville College in 1955.
In her Cambridge career she was not only Mistress of Girton, but for three years president of the Cambridge Association of University Women.
Mary Lucy Cartwright came from a Northamptonshire family with a long tradition of public service. Her two older brothers were killed in action before she went up to St Hugh's College, Oxford, in 1919, from the Godolphin School, Salisbury. After leaving Oxford with a first, she taught maths at Alice Ottley School, Worcester, and then at Wycombe Abbey School. But the urge to do further mathematical work was strong and in 1927 she returned to Oxford to work under G. H. Hardy.
She proceeded to the degree of Doctor of Philosophy in 1930 and was elected to a Yarrow Research Fellowship at Girton College, Cambridge. There followed a period of great productivity, leading to a readership and her appointment as Girton's director of studies.
In the years preceding and during the Second World War she carried out a very full programme of teaching and research. In particular, she was an excellent supervisor of research students, taking great care in reading and criticising their work, both in content and form, and giving due encouragement. From 1940 to 1944 she was also commandant of the college's Red Cross detachment.
In July 1948 she was pre-elected Mistress of Girton. She spent part of the year 1948-49 at American universities, including Princeton and Stanford, before taking up office. In 1959 she additionally became a university reader in the theory of functions.
She had become Mistress of Girton soon after women were admitted to full membership of the university, and the demands on her from many university committees was very heavy. She gave long service as chairman of the Cambridge University Women's Appointments Board and on the Education Syndicate.
Mary Cartwright's mathematical work ranged over a wide field of classical analysis. The part contained in a long series of papers on integral functions exceeded in depth and precision anything that had gone before. The essence of it is in her Cambridge Tract of 1956, which was all she chose to publish of a much larger book she had almost finished when the war began in 1939.
Up to then possibly her best known achievement was in the field of conformal mapping. In 1935 she produced a proof of a certain inequality, after attempts by others had failed. The first of her papers on cluster sets appeared in the following year, and she returned to this field later in collaboration with Sir Edward Collingwood.
In 1938 a note was circulated to mathematicians by the Radio Research Board of the Department of Scientific and Industrial Research. The object of the note was "to bring to the notice of mathematicians certain types of non-linear differential equations involved in the technique of radio engineering". Cartwright was immediately interested in this, and she persuaded Professor J. E. Littlewood to collaborate with her in what proved to be ground-breaking work making an important contribution to chaos theory.
Although she disclaimed any specialised knowledge in these fields of application, Cartwright could bring her critical faculty to bear on the non-mathematical aspects: she was always stimulated by contact with those working in these subjects.
Although fragile in appearance Mary Cartwright had a fine constitution and could carry a heavy load of different kinds of work. She attended meetings of the International Mathematical Congress from 1932 onwards. From the middle 1930s she was recognised as one of the leading analysts in this country, and her reputation continued to grow both at home and abroad.
In 1956 she was a member of the Royal Society delegation that visited the Soviet Union as guests of the Academy of Sciences. She also visited Moscow University and the Polish Academy of Sciences at Warsaw and Cracow, as well as taking part in many other mathematical conferences. She received honorary doctorates from the universities of Edinburgh, Leeds, Hull, Wales and -- in 1966 -- from Oxford. From 1961 to 1963 she was president of the London Mathematical Society, which awarded her its de Morgan medal in 1968, to add to the 1964 Sylvester medal of the Royal Society. In 1969 she was appointed DBE.
After her retirement from Girton in 1968 she worked at universities in England, America and Poland, before returning to Cambridge, where she was one of the editors of The Collected Papers of G . H . Hardy.
She was no narrow specialist, being exceptionally well informed on a wide variety of subjects, among them painting and music. Stanley Spencer's portrait of her will convey to future generations at Girton some idea of Dame Mary as scholar and administrator, but they may miss the warm sense of humour and sympathy that her friends knew. In human affairs as in mathematics she had a gift for going to the heart of a matter and for seeing the important point.
She is survived by her brother.
© The Times, 1998