Mary Cartwright

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Dame Mary Cartwright DBE (December 17, 1900 - April 3, 1998) was a leading 20th century British mathematician. She was born in Aynho, Northamptonshire where her father was the vicar and died in Cambridge, England.

In October 1919 she entered St Hugh's College of the Oxford to study mathematics, one of only five women at that university studying the subject. She graduated from Oxford in 1923 with a first class degree in Final Honours.

She then taught at Alice Ottley School in Worcester and Wycombe Abbey School in Buckinghamshire before returning to Oxford in 1928 to read for her D.Phil.

She was supervised by G. H. Hardy in her doctoral studies. During the academic year 1928-29 Hardy was at Princeton, so it was E. C. 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 would later 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, gives 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 Lars Ahlfors for conformal mappings.

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 this memorandum. The dynamics lying behind the problems were unfamiliar to Cartwright 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 she was elected to be 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.

She was the first woman:

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 British Empire.

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