Edward Foyle Collingwood was born at Lilburn Tower, near Wooler, Northumberland, on 17 January 1900, the eldest of the four sons of Col Cuthbert George Collingwood (1848–1933), landowner, of Glanton Pyke, and his wife, Dorothy, daughter of the Revd William Fawcett of Somerford Keynes, Gloucestershire. Collingwood went to the Royal Naval College at Osborne in 1913 and Dartmouth in 1914. A year later he joined the Royal Navy as a midshipman in the Collingwood (by special arrangement). Before experiencing any action he fell down a hatchway, sustaining serious injuries before the battle of Jutland, and was invalided out of the navy. After passing twelfth for Woolwich he failed the medical examination, whereupon he went up to Trinity College, Cambridge, in 1918 to read mathematics. At Lilburn there were letters of Edward's great-grandfather Vice-Admiral Cuthbert Collingwood, showing his interest in the teaching of mathematics to the young; Collingwood was much interested in these and other papers, in the small observatory built by his grandfather, and in biology, bacteria, and photographic techniques.
At Cambridge Collingwood's director of studies, G.H. Hardy, inspired him to aim at mathematical research. He obtained a third class in part one of the mathematical tripos in 1919 and in political specials one and two in the Michaelmas term of 1920, and then took his degree the following year. This unorthodox course left him free to study those parts of mathematics which interested him at his own pace and omit large parts of the heavy course for part two of the mathematical tripos. As an undergraduate he kept somewhat aloof from his mathematical contemporaries, and had a full, but entirely separate, social life. He used his private means to entertain well, but never ostentatiously.
When Hardy went to Oxford in 1920, J.E. Littlewood advised Collingwood on research. He obtained a Rayleigh prize in 1923, but failed to obtain a Trinity research fellowship. At the invitation of W.H. Young he went to Aberystwyth in 1922. There Professor G. Valiron of Strasbourg was lecturing in French on integral functions, and Collingwood made translations which eventually formed a book. In 1924–5 he held a Rouse Ball travelling studentship, mainly at the Sorbonne, and thus became the only one of the Hardy–Littlewood school to have close relationships with French mathematicians.
Collingwood took his MA degree in 1925 and, returning to Cambridge, read for a PhD degree (which he obtained in 1929) for a dissertation which included material from some already published papers on integral and meromorphic functions. He was made a member of the high table at Trinity, and in 1930 steward. Most unusually for a non-fellow, he was elected to the council of Trinity College. He still entertained well. He also regularly gave two advanced courses for the mathematical faculty, but did no regular undergraduate teaching. The six mathematicians Littlewood, Collingwood, Macintyre, Clunie, Rahman, and Joyal constituted a sequence, each the PhD student of the one before.
In the 1930s Collingwood became interested in pictures, and, when a family trust fell in on the death of an aunt, he bought some fine contemporary and eighteenth-century pictures through Geoffrey Agnew, one of his earlier Cambridge friends. He also made a collection of Chinese porcelain, becoming quite an expert on the subject. Collingwood was lieutenant in the Northumberland hussars in 1923–7 and became a JP in 1935. He was chairman of the bench for many years and deputy lieutenant for Northumberland in 1959. He gave much time and thought to the management of the Lilburn estate. When in 1937 he became high sheriff of Northumberland he gave up his Cambridge obligations, but continued to visit, in particular for the college commemoration feast.
In the Second World War Collingwood joined the Admiralty minesweeping division as an officer of the Royal Naval Volunteer Reserve, reaching the rank of acting captain. He served as director of scientific research with the Admiralty delegation in Washington in 1942, as officer in charge of the sweeping division in 1943, chief scientist, Admiralty mine design department in 1943–5, and as one of a delegation to Moscow on a special scientific mission. His all-round ability and wide experience, backed by his determination, were effective in getting the money needed for the scientists' work; he also impressed the scientists as having a sound grasp of physical principles. In 1946 he was appointed CBE, and became an officer of the American Legion of Merit.
Collingwood's first paper in 1924 generalized Nevanlinna's second fundamental theorem from 2 to p exceptional values, a result which Littlewood had, independently, stated in a letter to Nevanlinna. Collingwood's second paper, also in 1924, developed the idea of deficient values, questioning whether they were asymptotic. During the war this was proved false. After a gap from 1932 to 1948 Collingwood returned to this subject and discussed the islands in which |f(z)-a| < σ and f(z) takes no value more than p times, where σ and p may tend to infinity with |a|. These later papers seem less effective than the first two but led to fruitful discussions with Weitsman in June 1970. Collingwood's wide knowledge of the literature of mathematics enabled him and M.L. Cartwright to develop the theory of cluster sets in a joint paper in Acta Mathematica (87, 1952) which W.K. Hayman described as the beginning of the modern subject. If f(z) takes values on the Riemann sphere in |z| < , and there exists a sequence zn → eiθ such that f(zn) → w, then w belongs to the cluster set C(f, eiθ) of f(z) at eiθ. Their relationship to the range of values taken by f(z) near eiθ, and to neighbouring Fatou points, eiθn, θn → θ at which f(z) tends to a limit in any angle, and so on, formed the subject matter of the rest of Collingwood's mathematical papers. The standard textbook, written by Collingwood and A.J. Lohwater (1966) includes Collingwood's important applications to prime ends.
After 1945 Collingwood actively sought mathematical contacts. In particular he attended the new British Mathematical Colloquium, where he helped to organize special sessions on the theory of functions, and thus soon became a well–known figure. In 1959 he obtained a Cambridge ScD, in 1962 he was knighted, and in 1965 he was elected FRS and made an honorary LLD of Glasgow University where in 1961 he had given the seventh Gibson lecture. He joined the council of the London Mathematical Society (LMS) in April 1959 and was treasurer from 1960 to 1969, when he became its president. Collingwood made the fullest use of the benefaction of G. H. Hardy to strengthen and widen the activities of the society—including the founding of the Applied Probability Trust for the publication of the Journal of Applied Probability, edited by J. Gani, which began in 1964. Collingwood took a large part in drafting the petition, draft charter, and statutes for a royal charter (approved by the privy council in 1964) for the LMS to mark its centenary in 1965. An interest in bacteria, as well as in local affairs, led Collingwood into medical fields. He was an active supporter of Newcastle hospitals, vice-chairman of the Central Health Services Council (1959–63), vice-president of the International Hospital Federation (1959–67), a member of the Medical Research Council (1960–68) and treasurer (1960–67), and a member of the royal commission on medical education (1965–8). He was made an officer of the French Ordre de la Santé Publique, in 1963. He had a great effect on medicine by contributing to the technical development of the use of computers in that area. He spoke at the annual congress of the British Institute of Radiology in 1967 and at that of the British Dental Association in 1970. He also had a strong interest in history, and knowledge of it.
He was made an honorary DSc of Durham University in 1950, and was active in its affairs as chairman of its Council from 1955 until his death at home at Lilburn Tower on 25 October 1970. He never married. His large mathematical library and many manuscripts were left to the department of Mathematics at Durham, and Collingwood College was named after him.
