He was born on 12 February 1905, and educated at Hastings Grammar School and Jesus College, Oxford. His association with Edinburgh University began with the award to him of the Bruce of Grangehill Research Scholarship. From 1928 to 1937 he remained at Edinburgh as a Lecturer in Mathematics, except for a visit of one year in 1933-34 as a Rockefeller Research Fellow at Princeton University.
In 1937 he was appointed Professor of Mathematics at University College, Southampton, and left there for Leeds University in 1946 to take up an appointment as Professor of Pure Mathematics. Soon afterwards he became head of the Department of Mathematics and served in this capacity from 1948 to 1968, finally retiring as Chairman of the School of Mathematics in 1970.
He was a member of the London Mathematical Society from 1929 and had served on its Council from 1938 to 1945. He was also Vice-President of the Society in 1942-43. He was also a member of the Edinburgh Mathematical Society and served as its President for the year 1935-36.
His early research interests reveal the natural influence of his participation in the developments of the mathematical school of Sir Edmund Whittaker. They are concerned with problems arising from the differential equations of mathematical physics, particularly Laplace's equation, together with questions in relativity and in classical analysis. However, Ruse studied these matters with the instincts and characteristics of the pure mathematician. His papers are noticeable for elegance, concern with generalisation, geometric insight and the application of geometric methods. Above all there is a powerful exploitation of the tensor calculus, which is of course the natural technique for the study of local differential geometry. For these problems at that stage of development there was exceptional advantage in this approach and his contributions proved to be of value in the development of the theory of relativity.
This stream of research was interrupted to some extent when he left Edinburgh. His post at Southampton required a heavy teaching commitment and during the war years in a front-line town these matters had to be set aside for the pressing task of maintaining the department under difficult conditions. However, his creativity and enthusiasm for mathematical research returned with full vigour when the war ended and the opportunity was enhanced with his new appointment at Leeds in 1946.
A closer look at the earlier research papers reveals that the extension of Laplace's equation to an arbitrary Riemannian space depends on an implicit assumption that the appropriate form of the solution is a function of the geodesic distance alone. Ruse and E T Copson drew attention to this omission in their joint paper of 1939-40 and there they studied properties of the spaces, designated as harmonic spaces, for which the above property holds. This led to the study of completely harmonic spaces where this form of the solution of Laplace's equation holds at every point. It led to work by Ruse, Walker and Lichnerowicz and subsequently the theory of harmonic spaces developed into a significant contribution to local differential geometry. A full account of it can be found in the book, Harmonic Spaces, written jointly by H S Ruse, A G Walker and T J Willmore.
In 1948 Ruse became head of the mathematics department at Leeds, a post which he occupied until his retirement. During this period the natural growth of the university, together with the later impetus of the national expansion of higher education and its own extensive service teaching, all combined to produce a phenomenal growth in the size and complexity of the mathematics department. Eventually it became the School of Mathematics in 1968. Harold Ruse supervised every detailed change and initiated significant ones, notably the establishment of research chairs in pure and applied mathematics in 1963, which led to the rapid expansion of the postgraduate work and research of the department. During this period his own research work gradually contracted under these responsibilities, which he felt obliged to undertake personally. Since differential geometry had now undergone an internal revolution, being transformed into a subject concerned with global problems for which the new topological methods were appropriate, his own subject became a mystery to him in its new guise and his responsibilities prevented a gradual transition of research from the old to the new. Perhaps as a compensation, he played a prominent part in bringing forward young mathematicians and in fostering opportunities for meetings; thus with A G Walker he founded the Leeds-Sheffield Colloquium, now the Yorkshire Colloquium, and supported actively the inauguration of the British Mathematical Colloquium and spoke at its first meeting in Manchester in 1949.
He retired in 1970 and greatly enjoyed his leisure, so long due. He had an office in the School and often attended seminars. The day before his sudden collapse, he attended the algebra seminar and seemed to be in good health and spirits.
Harold Ruse was a man of gentle nature, with a deep concern for the welfare of students and colleagues. He was a dedicated Christian who took an active part in church affairs and his all-embracing capacity for friendship was combined with tolerance and wide sympathies.
My thanks are due to Professor E M Patterson for allowing me to read the draft of his tribute to Harold Ruse for the London Mathematical Society.