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Crispin's mother, together with his younger brother Piers, moved to Swaffham in Kent when she was appointed as a classics teacher at the local grammar school. The family now had no real home since Crispin's mother and younger brother lived at the home of the head of the grammar school during term time and rented a flat in Reading for the school holidays. Later she moved to London, teaching at a girl's grammar school there and renting a flat in Chelsea. The war was coming to an end in 1945 when Nash-Williams left Christ Church Cathedral School in Oxford and entered Rugby School. There his interest in mathematics was greatly encouraged by the mathematics teacher and after completing his School Certificate in 1946 he concentrated entirely on that subject. Hilton writes in that at Rugby:
His father returned to his work in Cardiff after his war service but the family could not reunite since paying school fees for their two children meant that both parents needed to work. However :
In the summer between leaving school and entering Trinity Hall, Cambridge, he lived with a family in Grenoble for three months while he studied French. During his first year at Cambridge Nash-Williams spent a considerable amount of time with the boat club and was cox of a Trinity Hall boat. However from his second year onwards he gave up his other interests to concentrate completely on his studies of mathematics. In this he was outstandingly successful and graduated as Senior Wrangler in 1953. After graduating, Nash-Williams remained at Cambridge where he undertook research under Shaun Wylie and Davis Rees. He was supported by a scholarship and he was then awarded a Visiting Fellowship to Princeton where he studied during 1956-57. Norman Steenrod was a considerable influence on Nash-Williams during this year. When he returned to the UK, Nash-Williams was appointed as Assistant Lecturer in Mathematics at the University of Aberdeen in October 1957. He was still working on his doctoral thesis, but the first two papers which he submitted were not part of this thesis. He submitted Abelian groups, graphs and generalized knights and Random walk and electric currents in networks to the Proceeding of the Cambridge Philosophical Society on the same day. Both were published in 1959. In the first of these papers Nash-Williams considered an infinite chessboard in a-dimensional space for some cardinal number a. It has the property that every square has only finitely many non-zero coordinates. In the paper necessary and sufficient conditions are given so that a knight can visit each square exactly once in a single infinite sequence of moves. The problem is solve by reformulating it as a question about infinite abelian groups. In the second of these two papers Nash-Williams considers a recurrent graph, namely one in which if you start at any vertex and move at random to an adjacent vertex then you will return eventually to the starting vertex with probability 1. In the paper Nash-Williams characterises infinite recurrent graphs. D G Kendall writes in a review of the paper that graphs satisfying Nash-Williams' conditions:
Nash-Williams' doctoral thesis Decomposition of graphs into infinite chains was submitted to Cambridge University in 1958 and the degree was awarded in the following year. Not only was it a remarkable piece of mathematical work but the thesis was also remarkable for its length being over 500 pages. A number of papers came out of the work of the thesis, the first being Decomposition of graphs into closed and endless chains published in the Proceedings of the London Mathematical Society in 1960. Hilton, in , summarises Nash-Williams' mathematical interests:
In fact Nash-Williams had a particular liking for infinite graphs as he expressed in the Introduction to the Proceedings of the conference on Directions in Infinite Graph Theory and Combinatorics:
At Aberdeen Nash-Williams was promoted to Senior Lecturer in Mathematics in 1964 then visited the University of Waterloo in Canada as a Visiting Professor in the following year. The Department of Combinatorics was established at Waterloo in 1967 and Nash-Williams left Aberdeen to become one of the founding professors. After five years, during which he helped build a strong group of research students in the department, he returned to Scotland to become Professor of Pure Mathematics at Aberdeen. He attended the third British Combinatorial Conference which was held in Oxford in 1972 and became part of a committee set up at that conference to make such conferences regular events. The Fifth British Combinatorial Conference was held in Aberdeen in 1975 and Nash-Williams wrote in the Preface of the Proceedings of the Conference:
Shortly after the 1975 conference Nash-Williams moved to Reading where he was appointed to the chair of mathematics following Richard Rado retirement. Hilton writes :
Such care, of course, meant that his lectures were a joy at attend as I [EFR] can indeed relate through personal experience having attended many excellent lectures by Nash-Williams at conferences. Welsh writes in :
Such attention to detail was also obvious in the surveys which he wrote. One such survey appeared as a two-part paper A glance at graph theory published in the Bulletin of the London Mathematical Society. This survey was based on lectures which Nash-Williams gave at the Edinburgh Mathematical Colloquium held in St Andrews in 1980. I [EFR] had the privilege of attending these lectures which were extremely successful in meeting Nash-Williams' aim:
Other earlier surveys included Infinite graphs - a survey (1967) which Nash-Williams describes as follows:
Also Hamiltonian circuits (1975) which he describes in the introduction as follows:
Nash-Williams did not enjoy administration and in particular being Head of department at Reading was a chore which he did for six years out of a sense of duty rather than for any other reason. In 1996 he retired, somewhat earlier than was necessary since he wanted to devote time to mathematics free from any worries of administration. A conference was held to mark his retirement and the 272 page Festschrift for C St J A Nash-Williams was produced which contains and . Sadly his retirement was short for in the summer of 2000 he fell ill with cancer and, after a major operation, he had to move into a retirement home since he was no longer able to look after himself. He went to a home in Ascot so that he could be near to his brother Piers who was Rector of Ascot. After his death the 18th British Combinatorial Conference was held in his memory at the University of Sussex, Sussex, from 1 July to 6 July 2001. Source:School of Mathematics and Statistics University of St Andrews, Scotland |