# Mary Cartwright

**Dame Mary Lucy Cartwright**, DBE, FRS, FRSE (17 December 1900 – 3 April 1998)[1] was a British mathematician.

Dame Mary Cartwright | |
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Born | Aynho, Northamptonshire, England, UK | 17 December 1900

Died | 3 April 1998 97) Cambridge, England, UK | (aged

Residence | Cambridge, England, UK |

Alma mater | St Hugh's College, Oxford |

Known for | Cartwright's theorem |

Awards | FRS DBE De Morgan Medal (1968) Honorary Fellow, Royal Society of Edinburgh (HonFRSE) 1968 Sylvester Medal (1964) |

Scientific career | |

Doctoral advisor | G. H. Hardy |

Doctoral students | |

Other notable students | Sheila Scott Macintyre |

Influences | J. E. Littlewood |

With J. E. Littlewood Cartwright was one of the first mathematicians to study what would later become known as chaos theory.[2] She saw many solutions to a problem she was studying and this would later be seen as an example of the butterfly effect.

## Early life and education

Cartwright was born in Aynho, Northamptonshire, where her father, William Digby Cartwright, was vicar. Through her grandmother Jane Holbech she was descended from the poet John Donne and William Mompesson, the Vicar of Eyam.[3][4] She had four siblings, two older and two younger: John (born 1896), Nigel (born 1898), Jane (born 1905), and William (born 1907).[5]

Cartwright's early education was at Leamington High School (1912–1915) then Gravely Manor School in Boscombe (1915–1916) before completion in Godolphin School in Salisbury (1916–1919).[6]

Cartwright studied mathematics at St Hugh's College, Oxford, graduating in 1923 with a first class degree. She was the first woman to attain the final degree lectures and to obtain a first. 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.[4]

Cartwright 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 "The Zeros of Integral Functions of Special Types" was examined by J. E. Littlewood whom she met for the first time as an external examiner in her oral examination for this 1930 D.Phil. She would later establish an enduring collaboration with Littlewood.[4]

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 mathematical 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.[7]

## Career

In 1936, Cartwright 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.[8] 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.[9][10]

In 1945, Cartwright simplified Hermite's elementary proof of the irrationality of π. She set her version of the proof as a Tripos question, later published in an appendix to Sir Harold Jeffreys' book *Scientific Inference*. In 1947, she was elected to be a Fellow of the Royal Society and,[11] although she was not the first woman to be elected to that Society, she was the first female mathematician.[9][10]

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.[4] From 1957 to 1960 she was president of the Cambridge Association of University Women.[12]

After retiring from Girton, Cartwright was a visiting professor at Brown University from 1968 to 1969 and at Claremont Graduate School from 1969 to 1970.[12]

## Recognition

Cartwright was the first woman:

- to receive the Sylvester Medal[5]
- to serve on the Council of the Royal Society[11]
- to be President of the Mathematical Association (in 1951)[13]
- to be President of the London Mathematical Society (in 1961–62)[5]

Cartwright also received the De Morgan Medal of the Society in 1968,[14] and that same year she was elected an Honorary Fellow of The Royal Society of Edinburgh (HonFRSE).[15] 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.

## Publications

- 1945: (with J. E. Littlewood) "On Non-linear Differential Equations of the Second Order",
*Journal of the London Mathematical Society*20: 180 doi:10.1112/jlms/s1-20.3.180 - 1956:
*Integral Functions*, Cambridge Tracts in Mathematics and Mathematical Physics No. 44 - 1964: "From non-linear oscillations to topological dynamics,"
*Journal of the London Mathematical Society*39: 1931[16]

## References

- "Obituary: Mary Cartwright".
*The Times*. 1998. - 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 0-521-82197-5 - Mary Cartwright at the Mathematics Genealogy Project
- O'Connor, John J.; Robertson, Edmund F., "Mary Cartwright",
*MacTutor History of Mathematics archive*, University of St Andrews. - O'Connor, J. J.; Robertson, E. F. "Dame Mary Lucy Cartwright". School of Mathematics and Statistics, University of St Andrews. Retrieved 3 April 2019.
- "Former Fellows of the Royal Society of Edinburgh 1783–2002" (PDF). Royalsoced.org.uk. Retrieved 20 December 2015.
- DeFuria, Jack (22 October 2014). "Mary Lucy Cartwright". Prezi. Retrieved 8 March 2017.
- "A Point of View: Mary, queen of maths".
*BBC News Magazine*. 8 March 2013. - "Mistress of Girton whose mathematical work formed the basis of chaos theory".
*Obituaries Electronic Telegraph*. 11 April 1998. Retrieved 8 March 2017. - Walter Hayman (1 November 2000). "Dame Mary (Lucy) Cartwright, D.B.E. 17 December 1900 – 3 April 1998".
*Biographical Memoirs of Fellows of the Royal Society*.**46**: 19–35. doi:10.1098/rsbm.1999.0070. Retrieved 8 March 2017. - Hayman, Walter K. (2000). "Dame Mary (Lucy) Cartwright, D.B.E. 17 December 1900 – 3 April 1998: Elected F.R.S. 1947".
*Biographical Memoirs of Fellows of the Royal Society*.**46**: 19. doi:10.1098/rsbm.1999.0070. -
*Cartwright, Dame Mary Lucy (1900–1998), mathematician | Oxford Dictionary of National Biography*. 2004. doi:10.1093/ref:odnb/69671. - Williams, Mrs. E. M. (October 1966), "Presidential Address: The Changing Role of Mathematics in Education",
*The Mathematical Gazette*,**50**(373): 243–254, doi:10.2307/3614669, JSTOR 3614669 - List of LMS prize winners, LMS website, accessed July 2011
- "Dame Mary Lucy Cartwright Hon FRSE".
*The Royal Society of Edinburgh*. 28 October 2016. Retrieved 23 March 2019. - "CWP Profile". UCLA. 2001. Archived from the original on 17 October 2016. Retrieved 8 March 2017.

## External links

- Mary Cartwright at the Mathematics Genealogy Project
- Dame Mary Lucy Cartwright at Biographies of Women Mathematicians, Agnes Scott College
Media related to Mary Cartwright (mathematician) at Wikimedia Commons

Academic offices | ||
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Preceded by Kathleen Teresa Blake Butler |
Mistress of Girton College, Cambridge1949–1968 |
Succeeded by Muriel Clara Bradbrook |