**Mary Cartwright**'s father was William Degby Cartwright (born in Tilney Street, London about 1865), and at the time of Mary's birth he was the Vicar at Aynho. Her mother was Lucy Harriette Maud Cartwright (born in Paddington, London about 1869). Mary had four siblings: John (born about 1896), Nigel (born about 1898), Jane (born about 1905) and William (born about 1907).

When she was eleven years old, Mary Cartwright was sent away to school, first attending Leamington High School, then later attending the Godolphin School in Salisbury. Her best subject at school was history but it had the disadvantage of requiring much effort in learning endless lists of facts. When she was encouraged in her studies of mathematics in her final year at school, Mary realised that it was a topic where one could succeed without the long hours of learning facts. It became the topic that she wanted to study at university.

In October 1919 Cartwright entered St Hugh's College in Oxford to study mathematics. At that time she was one of only five women in the whole university who were studying mathematics. This was a difficult time to enter university since, World War I having just ended, there were large numbers of men returning from the army who were either restarting the university studies they had begun before the war or were taking up their studies for the first time. The lecture halls were crowded and often Cartwright had to copy up notes of lectures which she could not get into because of the crowds.

After two years of study she took her Mathematical Moderations examinations and was awarded second class. It was not only Cartwright who had found the crowded conditions hard, for there were very few first class awards that year. This did nothing, however, to stop a deep sense of disappointment at failing to get the first class that she had aimed for, and Cartwright seriously considered giving up mathematics altogether and returning to her first love of history. It was a painful decision, over which she agonised for some time. However, she was enjoying mathematics so much and she still remembered the long hours of learning facts when studying history at school. She decided to stick with her mathematics course but [4]:-

Her decision to remain in mathematics did not diminish her interest in history. Many of her mathematical papers include historical perspectives that add an interesting dimension to her work. She wrote several biographical memoirs that portray her exceptional sense of history.

Having made her decision to complete the mathematics honours course, Cartwright was fortunate to meet a fellow student V C Morton. Morton was a fine mathematician - he later became Professor of Mathematics at Aberystwyth - and he gave her very sensible advice. He told her to read Whittaker and Watson's *Modern analysis* and to attend Hardy's evening sessions. These sessions took place after dinner on Monday and consisted of a talk and then mathematical discussions until later in the evenings. Having received permission to attend these inspiring sessions which ([5] or [6]):-

... set the course of her career ...

Cartwright went on to be awarded a first class degree in Final Honours, and graduated from Oxford in 1923.

Cartwright then taught in schools for four years before returning to Oxford to read for her D.Phil. The reason for not continuing to her doctorate in 1923 seems to have been a wish not to impose further strains on her family's finances. She taught first at Alice Ottley School in Worcester, and then at Wycombe Abbey School in Buckinghamshire. This second post also carried with it a position of assistant mistress and Cartwright soon found that she was being diverted from teaching by the administration. Also [3]:-

... teaching and method content were strictly dictated at the school. Having no room to experiment led Cartwright to feel discontent with her career.

Back to Oxford in 1928, she was supervised by Hardy in her doctoral studies. During the academic year 1928-29 Hardy was at Princeton, and it was Titchmarsh who took over the duties as a supervisor. Her thesis on zeros of integral functions was examined by J E Littlewood who she met for the first time as an external examiner in her oral examination for the D.Phil. She could never have guessed on that stressful occasion that she would become a major collaborator with Littlewood over many years.

In 1930 Cartwright was awarded a Yarrow Research Fellowship and she went to Girton College, Cambridge, to continue working on the topic of her doctoral thesis. Attending Littlewood's lectures, she solved one of the open problems which he posed. Her theorem, now known as Cartwright's Theorem, gave an estimate for the maximum modulus of an analytic function which takes the same value no more than *p* times in the unit disc. To prove the theorem she used a new approach, applying a technique introduced by Ahlfors for conformal mappings. From this time her research flourished and ([5] or [6]):-

... in a long series of papers she continued to explore the theory of complex(especially entire)functions; particularly their strange behaviour where they "blow up" ... Some of the complexity has been captured in modern pictures of fractals, many of which are created by iterating functions of this kind. Cartwright's work describes, among other things, deep and delicate phenomena which can appear near fractal boundaries, and has found new applications in this field.

Cartwright was appointed, on the recommendation of both Hardy and Littlewood, to an assistant lectureship in mathematics in Cambridge in 1934, and she was appointed a part-time lecturer in mathematics the following year. In 1936 she became director of studies in mathematics at Girton College, and in 1938 she began work on a new project which had a major impact on the direction of her research. The Radio Research Board of the Department of Scientific and Industrial Research produced a memorandum regarding certain differential equations which came out of modelling radio and radar work. They asked the London Mathematical Society if they could help find a mathematician who could work on these problems and Cartwright became interested in their memorandum.

The dynamics which lay behind the problems was unfamiliar to Cartwright and so she approached Littlewood for help with this aspect. They began to collaborate studying the equations. Littlewood wrote:-

For something to do we went on and on at the thing with no earthly prospect of "results"; suddenly the whole vista of the dramatic fine structure of solutions stared us in the face.

The fine structure which Littlewood describes here is today seen to be a typical instance of the "butterfly effect". The collaboration led to important results, and these have greatly influenced the direction that the modern theory of dynamical systems has taken. In 1947, largely on the basis of her remarkable contributions in the collaboration with Littlewood, she was elected a Fellow of the Royal Society and, although she was not the first woman to be elected to that Society, she was the first woman mathematician.

Cartwright was appointed Mistress of Girton in 1948 then, in addition, a Reader in the Theory of Functions in Cambridge in 1959, holding this appointment until 1968. As Mistress of Girton [5]:-

... without imposing her views, but carrying her responsibilities to the full, she guided the College with wise and clear headed decisions.

Although the administration involved in her role at Girton was substantial she found time for research, particularly her work on cluster sets in the 1950s. After retiring she found more time for the travelling which she so enjoyed. She spent extended periods at various institutions in the United States and Europe; in particular she spent the academic year 1968-69 at Brown University then Claremont Graduate College, with the University of Wales and Poland being visited in 1969-70.

She received many other honours including the Sylvester Medal of the Royal Society in 1964:-

... in recognition of her distinguished contributions to analysis and the theory of functions of a real and complex variable.

She was the first woman to receive the Sylvester Medal and, the first woman to serve on the Council of the Royal Society. Cartwright was President of the London Mathematical Society in 1961-62 becoming the first woman president, and until now the only woman president. She also received the De Morgan Medal of the Society in 1968. In 1969 she received the distinction of being honoured by the Queen, becoming Dame Mary Cartwright, Commander of the Order of the British Empire.

A remarkable person in many different ways, Cartwright is described in [3] as:-

... a person who had a gift for going to the heart of a matter and for seeing the important point, both in mathematics and in human affairs.

Her sense of humour is described in [3], [5], and [6] as "wry" and Caroline Series writes in [6]:-

Even at the age of96, the TV documentary "Our brilliant careers" captured the sharp sparkle of her wit.

I [EFR] watched the TV documentary and fully agree with Caroline Series' comment. It was a wonderful experience to see the sparkle in Cartwright's eyes.

Her other interests are mentioned in [1]:-

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.

**Article by:** *J J O'Connor* and *E F Robertson*

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