# Christine Mary Hamill

### Quick Info

Born
24 July 1923
London, England
Died
24 March 1956

Summary
Christine Hamill was an English mathematician who specialised in group theory and finite geometry.

### Biography

Christine Hamill's father was Philip Hamill (1883-1959) who was born in Wolverhampton, West Midlands, to Irish parents, namely the customs officer Philip Hamill (Sr) and his wife Annie. Philip (Jr) became a medical doctor and a Fellow of the Royal College of Physicians. He married Louisa Maude Zehetmayr (1891-1963) in Isleworth, London in 1918. Louisa was the daughter of the merchant Ferdinand Zehetmayr, born in Germany, and his wife Beatrice, born in Twickenham. London. Philip and Louisa Hamill had four children: Bernard John Hamill (1920-1996), who became a management consultant; Olivia Ann Hamill (1921-2006), who became a teacher; Christine Mary Hamill, the subject of this biography, and one younger boy.

Christine studied first at St Paul's Girls' School where she won a foundation scholarship. This independent school in Hammersmith, West London, had been founded in 1904. When Hamill studied there the head teacher was the classics scholar Ethel Strudwick (1880-1954). Hamill moved to Perse School for Girls in Cambridge, a school which had been founded in 1881 to provide quality education for women. She was awarded a Caroline Turle scholarship to study at Newnham College, Cambridge in 1942.

At Cambridge, Hamill was very successful in the mathematical tripos, becoming a Wrangler in 1945 and achieving a distinction in Part III the following year. She had a special flair for Algebraic Geometry and, as soon as she had obtained her degree, began research in this subject at Cambridge working for her doctorate. In 1948 she was awarded a Newnham research fellowship and, after submitting her thesis in 1950, she was awarded her doctorate in 1951 for her thesis The Finite Primitive Collineation Groups which contain Homologies of Period Two.

J A Todd supervised her research work at Cambridge and in [11] 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; On a finite group of order 576 in 1948; On a finite group of order 6,531,840 in 1951; and A collineation group of order $2^{13}.3^{5}.5^{2}.7$ in 1953. These papers describe groups of order 576, 6531840 and 348364800 respectively, see the references [6], [7] and [8]. Jack Semple, in the review [10] of the 1951 paper, writes:-
This paper, submitted for publication in June 1948 and only now appearing in print, contains the large body of fundamental results on which four other papers, already published before its appearance, were based ... The group G with which all these papers are concerned is a collineation group of $S_{5}$, of order 6,531,840 ... The main results of the paper are (i) a complete and concise description of the configuration formed by the 126 vertices; (ii) an analysis, remarkable for its simplicity and elegance, of the operations of the group, their classification into 31 types and 34 conjugate sets; and (iii) a similar analysis of the simple subgroup G' of G, of index 2, of which the operations are generated by products of an even number of the 126 projections.
In the 1953 paper, Hamill gives the following acknowledgement:-
My thanks are due to Dr Todd who supervised my researches and who gave me much valuable advice, and to the referee who made many very helpful suggestions.
Todd [11] 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.
W L Edge in [3] refers to the papers as "Miss Hamill's spectacular success." I [EFR] knew Edge quite well, and I can assure the reader that he did not give praise lightly - this is high praise indeed!

In 1950, the year before she received her doctorate, Hamill was offered an Assistant Lectureship in Mathematics 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. Douglas Northcott, who was appointed to the Town Trust Chair of Pure Mathematics at Sheffield in 1952, writes [9]:-
In 1950, Miss Hamill left Cambridge to become an assistant lecturer at Sheffield University and two years later she was promoted to a full lectureship. Her charm and friendliness soon made her on the best of terms with everyone. In her teaching, she combined lucidity of expression with a sympathetic understanding of the difficulties of the less able students. She held definite views on most matters and was not afraid to state her opinions but, even when she was being critical, she always had something constructive to offer. No head of a mathematics department could wish for a more loyal and helpful colleague.
While an assistant lecturer at Sheffield, Hamill attended the Edinburgh Mathematical Society's St Andrews Colloquium held in St Andrews from 18 to 28 July 1951. This was the first St Andrews Colloquium after a gap of thirteen years caused by World War II. The series of lectures given by Donald Coxeter was of particular interest to her. In 1952 she joined the Mathematical Association. While at Sheffield, Hamill undertook research with Herbert D Deas, who was also a lecturer in mathematics at the University of Sheffield. They wrote the joint paper A note on the geometry of lattice planes which has the following Abstract:-
This note is an attempt to give a careful restatement of a well-known result in lattice geometry, the proof of the converse part of which does not appear to be so well known.
In fact the paper did not appear in print until 1957, the year after Hamill died. It had been submitted to Acta Crystallographica on 2 August 1955 but it was revised by Herbert Deas on 8 March 1957, almost exactly a year after Hamill's death.

In 1954 Hamill accepted a post as lecturer in the University of Ibadan in Nigeria. She sailed on the Aukeon from Liverpool to Lagos, departing on 14 December 1954. 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. Douglas Northcott writes [9]:-
Miss Hamill left Sheffield in 1954 to join the staff of University College, Ibadan, as a lecturer. The pioneering spirit had caught her imagination and the work to be done in developing an educational system at University level in West Africa offered a challenge which she felt she had to accept.
W L Edge writes [3]:-
During the long vacation of 1955 she was home in Britain and attended, in addition to the St Andrews colloquium in July, the British Mathematical Colloquium at Exeter in September.
Two of the lecture courses at the St Andrews Colloquium were of particular interest to Hamill, namely Philip Hall's course on Symmetric Functions in the Theory of Groups and Michael Atiyah's course on Topological Methods in Algebraic Geometry.

Outside mathematics [1]:-
... she had wide interests, was a keen dinghy sailor and took an active part in youth welfare.
After four terms in Ibadan, Hamill contracted poliomyelitis and her death was rapid occurring only two days after she became ill. Northcott writes [9]:-
... while on a short holiday on the Gold Coast she contracted polio and, in spite of the good medical facilities available, died within forty-eight hours. [it was] was a tragedy which found her many friends quite unprepared. She always had such abundant energy that the idea of a severe illness, let alone a fatal one, was almost unbelievable. ... She will always be remembered and missed by those who knew her.
Todd remarks [11]:-
... 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 in July on which she was to have been married. She had planned to return to Britain in the summer of 1956 for her marriage.

### References (show)

1. Obituary in The Times
2. H D Deas and C M Hamill, A note on the geometry of lattice planes, Acta Cryst. 10 (1957), 541-542.
3. W L Edge, Obituary: Miss C M Hamill, Edinburgh Math. Notes 40 (1956), 22-25.
4. J S Frame, Review: A collineation group of order $2^{13}.3^{5}.5^{2}.7$, by Christine M Hamill, Mathematical Reviews MR0055348 (14,1060g).
5. J S Frame, Review: On a finite group of order 576, by Christine M Hamill, Mathematical Reviews MR0022847 (9,268a).
6. C M Hamill, On a finite group of order 576, Proc. Cambridge Philos. Soc. 44 (1948), 26-36.
7. C M Hamill, On a finite group of order 6,531,840, Proc. London Math. Soc. (2) 52 (1951), 401-454.
8. C M Hamill, A collineation group of order $2^{13}.3^{5}.5^{2}.7$, Proc. London Math. Soc. (3) 3 (1953), 54-79.
9. D G Northcott, Christine Mary Hamill, Universities Review 29-30 (1956), 37-38.
10. J G Semple, Review: On a finite group of order 6,531,840, by Christine M Hamill, Mathematical Reviews MR0042403 (13,104a).
11. J A Todd, Christine Mary Hamill, J. London Math. Soc. 32 (3) (1957), 384.