In 1945 she simplified Hermite's elementary proof of the irrationality of π.
The following was set as an example in the Mathematics Preliminary Examination at Cambridge in 1945 by Dame Mary Cartwright, but she has not traced its origin.
1930s: British mathematician Mary Cartwright proved her theorem, now known as Cartwright's theorem, which 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.
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1968: Mary Cartwright became the first woman to win the De Morgan Medal, the London Mathematical Society's premier award.
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1964: Mary Cartwright became the first woman to win the Sylvester Medal of the Royal Society of London, which is given every three years since 1901 for the encouragement of mathematical research, without regard to nationality.
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