At Cambridge Hamill was very successful, becoming a Wrangler (an honors recognition) in 1945 and achieving a distinction in Part III the following year. She continued to study at Cambridge working for her doctorate. In 1948 she was awarded a Newnham research fellowship and she was awarded her doctorate in 1950.
The year she received her doctorate, Hamill was offered an assistant lectureship at the University of Sheffield which she accepted. She was to spend four years at Sheffield being promoted to a Lecturer in Mathematics in 1952.
J. A. Todd supervised her research work at Cambridge and he describes the work of her doctoral dissertation:-
This work contains a detailed study of the finite primitive collineation groups which contain homologies of period two. Starting with an analysis of the geometrical configuration formed by the centres and the invariant primes of the homologies, she was able, by a very thorough and careful investigation, to obtain, for each of the groups, the distribution of the operations in conjugate sets, and to make the nature of these operations clear.Hamill published three papers based on her dissertation in 1948, 1951 and 1953. These papers describe groups of order 576, 6531840 and 348364800 respectively.
Todd assesses the importance of these papers:-
The groups concerned are of interest from various points of view, and the detailed results contained in her papers contain something of permanent value.In 1954 Hamill accepted a post as lecturer in the University of Ibadan in Nigeria. She had already earned a high reputation as a teacher both at Cambridge and at Sheffield and was said to have great talent at getting the best from weaker students. In Ibadan she quickly began to show the same lecturing talents giving lectures of great clarity.
After four terms in Ibadan, Hamill contracted poliomyelitis and her death was rapid occurring only two days after she became ill. Todd remarks:-
... she will be remembered for her natural and innate friendliness, for her complete sincerity, and for her strength of character, fortified by a firm Christian faith, and a sincere acceptance of all that that implied.She died a few months before the day on which she was to have been married.