Editing Mary Cartwright (section)

== Career ==
Throughout her career, Cartwright wrote over ninety articles on several different mathematical concepts. Her contributions extended to topics such as the Dirichlet series, Abel summation, directions of Borel spreads, analytic functions regular on the unit disk, the zeros of integral functions, maximum and minimum moduli, and functions of finite order in an angle.<ref name="Cartwright obituary ams.org"/> 
In 1936, Cartwright became director of studies in mathematics at Girton College. 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 (United Kingdom)|Department of Scientific and Industrial Research]] produced a memorandum regarding [[Van der Pol oscillator|certain differential equations]] which came out of modelling radio and radar work.<ref name="bbc.co.uk">{{Cite news|title=A Point of View: Mary, queen of maths|date=8 March 2013|journal=BBC News Magazine|url=https://www.bbc.co.uk/news/magazine-21713163}}</ref> They asked the [[London Mathematical Society]] if they could help find a mathematician who could work on these problems and she became interested. 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, in particular the [[Van der Pol oscillator]], which greatly surprised the two:{{blockquote|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.<ref name="Littlewood Miscellany Bollobás ">{{cite book | last=Littlewood | first=John Edensor |  editor-last=Bollobás | editor-first=Béla | title=Littlewood's Miscellany | publisher=Cambridge University Press | publication-place=Cambridge New York Port Chester [etc.] | date=1986-10-30 | isbn=0-521-33702-X | page=13}}</ref>}}
The fine structure described here is today seen to be a typical instance of the [[butterfly effect]]. The collaboration led to important results which have greatly influenced the direction that the modern theory of [[dynamical systems]] has taken.<ref name="obituary">{{cite web|url=http://cwp.library.ucla.edu/articles/ebcart11.html|title=Mistress of Girton whose mathematical work formed the basis of chaos theory|work=Obituaries Electronic Telegraph|date=11 April 1998|access-date=8 March 2017}}</ref><ref name="hayman">{{cite journal|url=http://rsbm.royalsocietypublishing.org/content/46/19|author=Walter Hayman|author-link=Walter Hayman|title=Dame Mary (Lucy) Cartwright, D.B.E. 17 December 1900 – 3 April 1998|journal=Biographical Memoirs of Fellows of the Royal Society|volume=46|pages=19–35|date=1 November 2000|access-date=8 March 2017|doi=10.1098/rsbm.1999.0070|doi-access=free}}</ref> Although the duo did not supply the answer in time, they succeeded in directing the engineers' attention away from faulty equipment towards practical ways of compensating for the electrical "noise"—or erratic fluctuations—being produced.<ref name="bbc.co.uk"/>

In 1945, Cartwright simplified [[Charles Hermite|Hermite]]'s [[Proof that π is irrational#Cartwright.27s proof|elementary proof of the irrationality of {{pi}}]]. She set her version of the proof as a [[Mathematical Tripos|Tripos]] question, later published in an appendix to Sir [[Harold Jeffreys]]' book ''Scientific Inference''.<ref name="Jeffreys Inference 1973 ">{{cite book | last=Jeffreys | first=Harold | title=Scientific Inference | publisher=Cambridge University Press | publication-place=Cambridge | date=1973-12-13 | isbn=0-521-08446-6 | page=268 | edition=3rd }}</ref> In 1947, she was elected to be a [[Fellow of the Royal Society]];<ref name="frs">{{Cite journal|last1=Hayman|first1=Walter K.|doi=10.1098/rsbm.1999.0070|title=Dame Mary (Lucy) Cartwright, D.B.E. 17 December 1900 – 3 April 1998: Elected F.R.S. 1947|journal=[[Biographical Memoirs of Fellows of the Royal Society]]|volume=46|page=19|year=2000|doi-access=free}}</ref> although she was not the first woman to be elected to that Society, she was the first female mathematician.<ref name="obituary" /><ref name="hayman" />

Cartwright was appointed Mistress of Girton in 1948 and a Reader in the Theory of Functions in Cambridge in 1959 until 1968.<ref name="mactutor" /> From 1957 to 1960, she was president of the Cambridge Association of University Women.<ref name=":0">{{Cite ODNB|title=Cartwright, Dame Mary Lucy (1900–1998), mathematician {{!}} Oxford Dictionary of National Biography|language=en|doi=10.1093/ref:odnb/69671|year = 2004}}</ref> After retiring from Girton, she was a visiting professor at [[Brown University]] from 1968 to 1969 and at [[Claremont Graduate University|Claremont Graduate School]] from 1969 to 1970.<ref name=":0" /> Cartwright died in Cambridge, on 3 April 1998 at the age of 97.<ref name="Cartwright obituary ams.org"/>