He rapidly became, and until his death remained, one of the central figures in the history of the institution which became, in 1918, the University of Cape Town. It is to a great extent due to the unstinted and unselfish labours of a very few far-sighted men, of whom Crawford was one, that the small South African College grew into the present University, with a present student body of something like twenty times the size it was at the turn of the century.
A man of unbounded energy, Crawford found time to take part in almost every branch of University activity. For many years he gave up to twenty lectures a week, was on more committees than any man could reasonably be expected to be, was for ten years head of a University residence, and was for long an Examiner of the Joint Matriculation Board. In addition he was for some time Secretary to the Senate, with duties which belonged more properly to a Registrar, and held office as Treasurer of the Royal Society of South Africa from its foundation in 1909 until 1935. It is a matter for lasting wonder that in all his multifarious duties he was well informed and well prepared down to the last detail. He was never late, never absent, and always gave the impression that the particular problem of the moment was the one, to the exclusion of all others, to which he had previously been giving his attention.
Mathematically Crawford was an analyst, with a specialised knowledge of elliptic, Lamé, and Mathieu functions, his best work being probably a new proof of Klein's Theorem in connection with Lamé's functions. In his later years, however, he showed a keen interest in the progress of Geometry, and in the theory of numbers, notably Waring's problem.
In 1916 he was elected President of the South African Association for the Advancement of Science, and, in 1936, President of the Royal Society of South Africa, an office he held until 1941.
He retired from his Chair in 1938, but his connection with the University was not entirely severed, as he remained a Member of the University Council until his death, more than once acting temporarily as Chairman.
Always interested in public affairs, he became a City Councillor in 1944, and held office for the remaining six years of his life. His remarkable physical and mental vigour remained with him to the end, and he died suddenly after returning from a public meeting.
He leaves a widow, three sons and two daughters.
He was elected a Fellow of the Society in 1903.