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# Mary Cartwright

Dame Mary Lucy Cartwright DBE (17 December 1900 – 3 April 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. Through her Grandmother Jane Holbech she was descended from the poet John Donne and William Mompesson the Vicar of Eyam.

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 1928–9 Hardy was at Princeton, so it was E. C. Titchmarsh who took over the duties as a supervisor. Her thesis on zeros of entire functions was examined by J. E. Littlewood whom 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 that 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.

She anticipated Ivan Niven's elementary proof of the irrationality of π. Her version of the proof was published in an appendix to Sir Harold Jeffreys' book Scientific Inference.

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 modeling 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 female 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:

* to receive the Sylvester Medal

* to serve on the Council of the Royal Society

* to be President of the London Mathematical Society (in 1961–62)

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, Dame Commander of the Order of the British Empire.

References

* Freeman J. Dyson, Mary Lucy Cartwright [1900-1998]: Chaos theory, pp. 169-177, in Out of the Shadows: Contributions of Twentieth-Century Women to Physics, edited by Nina Byers and Gary Williams, 498 p. (Cambridge University Press, 2006). ISBN 0521821975

External links

* CWP

* Mary Cartwright at the Mathematics Genealogy Project

* "Mary Lucy Cartwright", Biographies of Women Mathematicians, Agnes Scott College

* O'Connor, John J.; Robertson, Edmund F., "Mary Cartwright", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Cartwright.html .

* Times Obituary

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