Now the person who influenced Davies most during these years was Paul Dienes, a Hungarian who had worked under Émile Borel and Jacques Hadamard in Paris. Dienes was appointed to University College, Aberystwyth, in October 1921, joining William Henry Young. Davies was taught by both Dienes and Young during his undergraduate years in Aberystwyth. In 1923 Young left Aberystwyth and, as a consequence, Dienes took up a lectureship at University College, Swansea, in that year. At Swansea, Davies had worked under Dienes who advised him to work on the absolute differential calculus. Dienes had become interested in this topic after leaving Paris because of its applications to relativity theory. The leading expert on the absolute differential calculus was Tullio Levi-Civita who lectured in Rome, so in August 1926, following Dienes' advice, Davies travelled to Rome.
This was the first visit of many that Davies made to Rome where, as intended, he studied under Levi-Civita. He was awarded a doctorate for his thesis which he defended in an oral examination conducted by eleven professors. He had many adventures in Rome which he enjoyed recalling. For example, on one occasion :-
... a party of students were making merry in the Colosseum and since many nationalities were represented among them, they decided that each should sing a song of his native land. As Wales begins with a W, Ianto had the honour of singing last. The strains of "Land of my Fathers" were ringing strongly through the Colosseum when the police arrived.Rome was an enjoyable but stressful experience and Davies' health broke down through overwork. He returned to Wales to recover, which took the best part of a year, before moving to his next European capital Paris in 1928. In Paris he spent time at the Sorbonne and at the Collège de France where he was greatly influenced by Élie Cartan.
In 1930 Davies returned from the Continent to take up a post as assistant lecturer at King's College, part of the University of London. He was promoted to Lecturer in 1935 and, in 1946, he was promoted to Reader :-
His steady stream of publications is testimonial to his authority in the fields of Riemannian geometry and the calculus of variations. His Celtic fluency and enthusiasm, together with his fertility of ideas, surrounded him with research students, in whom he took a keen and friendly interest.Davies loved spending time on the Continent, both for holidays and for discussing research at various universities. Being an excellent linguist aided his enjoyment of the countries he visited. One of his great joys was sport :-
Every Christmas he would join a party of friends for winter sports and he soon acquired some ability as a skier. In those pre-war days in Switzerland the atmosphere in the evening was elegant and relaxed. Ianto was an excellent raconteur and these were the hours in which he shone most brilliantly. He also became a keen Wimbledon tennis fan and for many years he would take an early place in the queue for the Centre Court on the First Thursday and the Second Wednesday of the tournament.In 1939 with the outbreak of World War II, the government passed the University and Colleges (Emergency Provisions) Bill. Under the terms of this bill students from King's College London, were evacuated to the University of Bristol where it was 'business as usual'. Davies moved to Bristol to carry on with his university duties. However, in November 1940, Bristol was bombed and the building housing the library of King's College, which had been removed to Bristol for safety, was hit destroying thousands of books. In Bristol he met Margaret Helen Picton; they were married in 1941. Sadly Margaret died in 1944 in London.
The University College, Southampton, offered Davies the chair of mathematics in 1946, a few months after his promotion to a Readership at King's College. He accepted and, rather remarkably, this gave him the distinction of becoming the only professor of mathematics in Britain who had not studied at either Oxford or Cambridge. He met Hilda Gladys Boyens in Southampton; they married in 1955 and had one son, Geraint. Davies spent the rest of his career at Southampton until his retirement in 1969 at the age of 65 :-
Research flourished under his guidance and the department's growth from a staff of six to a multi-professorial one of more than sixty was accomplished with typical zeal.Retirement did not mean an end to mathematical research for Davies for, after he retired, he went to Canada to spend two years as Professor of Mathematics at the University of Calgary. In 1971 Davies, remaining in Canada, took up an appointment as Professor of Mathematics at the University of Waterloo. He was on the University of Waterloo campus when he was suddenly taken ill and died within a few hours.
Davies was an editor of Aequationes Mathematicae and, on his death, his fellow editors, writing in , described him as:-
... a mathematician of great breadth. His steady stream of publications in differential geometry and the calculus of variations attests to his authority in this field.In his first few papers, Davies used the Lie derivative to examine the action of an infinitesimal transformation on a submanifold of a Riemannian manifold. These papers included: On the infinitesimal deformations of a space (1933), On the deformation of a subspace (1936), (with P Dienes), On the infinitesimal deformations of tensor submanifolds (1937), On the second and third fundamental forms of a subspace (1937), and Analogues of the Frenet formulae determined by deformation operators (1938). He extended the ideas in these papers to generalisations of Riemannian manifolds such as Finsler manifolds and Cartan manifolds in later papers, for example: Lie derivation in generalized metric spaces (1939), Subspaces of a Finsler space (1945), Motions in a metric space based on the notion of area (1945), and The theory of surfaces in a geometry based on the notion of area (1947). In papers such as On the invariant theory of contact transformations (1953) Davies studies invariant theory of contact transformations by using tensor calculus. Later, in Parallel distributions and contact transformations (1966) he re-examines the invariant theory of contact transformations from the point of view of parallel distributions.
Davies had many interests outside mathematics. He was a linguist who, again quoting :-
... was fluent in five languages and delighted in the friendship of people from all walks of life in countries throughout the world. He had a passionate regard for the Welsh culture and his Celtic enthusiasm and fine spirit endeared him to us all.
Article by: J J O'Connor and E F Robertson