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Celebratio Mathematica

Mary Lucy Cartwright

Theory of functions

Dame Mary Lucy Cartwright

by Emmy E. Pierce and Linda Kirby

Mary Lucy Cartwright was born on Decem­ber 17, 1900. Her fath­er was the vicar of Aynho, Northamp­ton­shire. She was edu­cated at home in Aynho un­til the age of 11, when she was sent to Leam­ing­ton High School. It was later, in her last year at the Godol­phin School in Salis­bury, that Cartwright was en­cour­aged to study math­em­at­ics.

In 1919, Cartwright be­came one of five wo­men study­ing math­em­at­ics at Ox­ford Uni­versity. She suffered a dis­ap­point­ment in her second-year Math­em­at­ic­al Mod­er­a­tions, when she re­ceived second-class hon­ors in­stead of the first-class award for which she had been aim­ing. For a time Cartwright ser­i­ously con­sidered giv­ing up math­em­at­ics al­to­geth­er and re­turn­ing to his­tory, which had been her first love and her best sub­ject as a child. Ul­ti­mately, however, she de­cided to stay in the dis­cip­line, and in 1923 she gradu­ated from Ox­ford with a first-class de­gree from her Fi­nal Hon­ors. It was the second year in which Ox­ford al­lowed wo­men al­lowed to take Fi­nal De­grees.

Cartwright taught math­em­at­ics in Worcester and Buck­ing­ham­shire for the next four years be­fore re­turn­ing to Ox­ford for her D.Phil. in 1928. Her stud­ies were su­per­vised by G. H. Hardy, whose even­ing ses­sions she had at­ten­ded as an un­der­gradu­ate, and E. C. Titch­marsh. In 1930 she was awar­ded her D.Phil and her thes­is, “The zer­os of in­teg­ral func­tions of spe­cial types,” was pub­lished in two parts in the Quarterly Journ­al of Math­em­at­ics, vol. 1 (1930) and vol. 2 (1931).

The end of Cartwright’s edu­ca­tion at Ox­ford began a trans­ition to many years of re­search and teach­ing. After fin­ish­ing her doc­tor­al thes­is, Cartwright was awar­ded a re­search fel­low­ship at Gir­ton Col­lege, Cam­bridge Uni­versity, to con­tin­ue her study of the the­ory of func­tions. By 1935, she had been ap­poin­ted a Lec­turer in Math­em­at­ics at Cam­bridge. She would hold this post un­til 1959, when she would be­come a Read­er in the The­ory of Func­tions, the po­s­i­tion she would re­tain un­til her re­tire­ment. Dur­ing this time she also served as Dir­ect­or of Stud­ies in Math­em­at­ics, and as Mis­tress of Gir­ton Col­lege from 1949 to 1989. Al­though she took on fairly few re­search stu­dents (in an ef­fort to avoid be­com­ing over­burdened with both ad­min­is­trat­ive and teach­ing du­ties), she was known as an ex­cel­lent and me­tic­u­lous su­per­visor of those stu­dents she did ac­cept.

Dur­ing her ca­reer, Cartwright pub­lished over 100 pa­pers in clas­sic­al ana­lys­is, dif­fer­en­tial equa­tions, and re­lated to­po­lo­gic­al prob­lems. She made ground-break­ing con­tri­bu­tions to chaos the­ory, after be­com­ing in­trigued by a memor­andum put out by the Ra­dio Re­search Board of the De­part­ment of Sci­entif­ic and In­dus­tri­al Re­search. The Board in­ten­ded “to bring to the no­tice of math­em­aticians cer­tain types of non-lin­ear dif­fer­en­tial equa­tions in­volved in the tech­nique of ra­dio en­gin­eer­ing.” As a res­ult of this memor­andum, Cartwright col­lab­or­ated for many years with John E. Lit­tle­wood (who had first met Cartwright when he ex­amined her doc­tor­al thes­is) on the solu­tions to the Van der Pol equa­tion. Be­sides the aca­dem­ic value of the team’s dis­cov­er­ies, the work also en­abled sig­ni­fic­ant prac­tic­al im­prove­ments to the ra­dio amp­li­fi­ers used for com­mu­nic­a­tion dur­ing World War II.

Cartwright re­tired from Gir­ton in 1969, but con­tin­ued to teach as a vis­it­ing pro­fess­or in Eng­land, Amer­ica and Po­land. By this time she had been elec­ted a Fel­low of the Roy­al So­ci­ety (the first wo­man math­em­atician to be so honored, and the only wo­man math­em­atician un­til 1995); re­ceived hon­or­ary doc­tor­ates from the Uni­versit­ies of Ed­in­burgh, Leeds, Hull, Wales, and Ox­ford; and been awar­ded both the Sylvester Medal of the Roy­al So­ci­ety and the de Mor­gan medal by the Lon­don Math­em­at­ic­al So­ci­ety (where she had served as pres­id­ent from 1961 to 1963). She was ap­poin­ted Dame of the Brit­ish Em­pire the year after she left Gir­ton Col­lege.

After years of teach­ing abroad, Cartwright re­turned to Cam­bridge, where she was one of the ed­it­ors of The Col­lec­ted Pa­pers of G. H. Hardy. She died there in 1998.