marry cartwright
... universities of Edinburgh, Leeds, Hull, Wales, and Oxford. In 1969 Queen Elizabeth II elevated her to Dame Commander of the British Empire. Lectures were difficult to get into due to the flood of men recently released from the army. Cartwright went to the lectures she could and obtained notes from the others. After two years she received a second class on the Mathematical Moderations Examination. Although very few firsts were given that year, Cartwright was disappointed and seriously considered changing her focus to history. After considerable deliberation she concluded that she was hooked on the theory of residues. She joked that history would entail longer hours of work anyway. Her decision to remain in mathematics did not diminish her interest in history. Many of her mathematical papers include historical perspectives that add an interesting dimension to her work. She also wrote several biographical memoirs that portray her exceptional sense of history. Near the end of Cartwright’s third year at Oxford, an important event in her mathematical career occurred at a well-chaperoned party. She was introduced to V. C. Morton, who told her that if she was really serious about mathematics she should read Whittaker and Watson’s Modern Analysis and attend the evening classes of G. H. Hardy, then Savilian Professor of Geometry. Taking Morton’s advice, she read Modern Analysis that summer and received special permission to attend Hardy’s class. She found Hardy’s lectures inspiring. With Hardy serving as an examiner, she received a first class on the Final Honors School Examination in Mathematics, obtaining her degree from Oxford in 1923. During the next four years, Cartwright taught mathematics, first at the Alice Ottley School in Worcester and then at the Wycombe Abbey School in Buckinghamshire, where she also served as assistant mistress. Cartwright began to feel sidetracked by her mounting administrative duties. In addition, teaching and method content were strictly dictated at the school. Having no room to experiment led Cartwright to feel discontent with her career. She felt she had to return to mathematics research, and in January 1928 she arranged to join Hardy’s group of research students at Oxford. Hardy’s class consisted of an hour lecture followed by tea, biscuits, and talk about mathematics and mathematicians. Cartwright’s mathematical talent blossomed in the seminar. One evening Hardy gave a list of problems in his seminar, one of which referred to an application of Abel’s method of summation to Dirichlet series. Hardy was amazed when Cartwright completely solved the problem by contour integration. Her work on generalized Abel summability with applications to Fourier series was published that year and also appears in the index of Hardy’s book on divergent series. E. C. Titchmarsh, who succeeded Hardy as Savilian Professor at Oxford, became Cartwright’s supervisor while Hardy was at Princeton during the 1928–29 academic year. During an interview in 1990, Cartwright recalled that Titchmarsh was a good supervisor and his suggestions suited her well. Both Hardy and Titchmarsh inspired Cartwright’s interest in the theory of functions of complex variables. Cartwright completed her D.Phil. when Hardy returned to Oxford. Fortuitously, J. E. Littlewood served as an external examiner. Littlewood recalled that the first question by the other examiner was so silly and unreal as to make her blush, but he thought he helped to restore her nerve with a wink. Her thesis on the zeros of integral functions generated a series of papers and eventually led to her book on integral functions. In October of 1930, financed by a Yarrow Research Fellowship, Cartwright continued her work in the theory of functions at Girton College, Cambridge. During this time she attended several of Littlewood’s courses and seminars. She drew Littlewood’s attention when she obtained the right order of magnitude for the maximum modulus of multivalent functions, a problem that Littlewood had presented in his theory of functions class. Her result is: Cartwright’s Theorem. Cartwright was the first to obtain significant results for p valent functions, and she did so using some rather unconventional methods. She used the conformal mapping technique pioneered by Ahlfors to prove the theorem and show that an entire function of order has at most 2 asymptotic values. She had learned about the technique in her lectures from E. F. Collingwood. W. K. Hayman of Cartwright’s ninetieth birthday. According to Hayman, Ahlfors mapped a strip-like domain plane. If S meets the line in one or more corresponds to the equation, then Ahlfors showed that the map grows at least as fast as in the case when S is itself a strip. Those who have had dealings with the zeta func...