H T H Piaggio's father was Francis Piaggio (born at Hoton, London about 1839) who was a school teacher of dancing. His mother was Mary Piaggio (born at St Pancras, London about 1855) who was a cloakroom attendant. H T H Piaggio had a younger sister Edith Mabel (born about 1888) who became a shorthand typist. He also had a younger brother Edward Ernest (born about 1894) who became a clerk.
H T H Piaggio was educated at the City of London School and at St John's College, Cambridge. In 1908 he was appointed Lecturer in Mathematics at the University of Nottingham although at that time there was no separate Department of Mathematics there. A chair of mathematics was created at Nottingham and Piaggio was appointed to it in 1919. His most famous work, An Elementary Treatise on Differential Equations, was published by G Bell & Sons in 1920.
Full details of his life appear in the obituary by D A Young. We give a version at THIS LINK.
Here list a few articles which Piaggio published in The Mathematical Gazette: Relativity rhymes with a mathematical commentary (January 1922); Geometry and relativity (July 1922); Mathematics for evening technical students (July 1924); Mathematical physics in university and school (October 1924); Probability and its applications (July 1931); Three Sadleirian professors: A R Forsyth, E W Hobson and G H Hardy (October 1931); Mathematics and psychology (February 1933); Lagrange's equation (May 1935); Fallacies concerning averages (December 1937); and The incompleteness of "complete" primitives of differential equations (February 1939). In Nature Piaggio published articles such as The operational calculus (1943) and The significance and development of Hamilton's quaternions (1943). In the Proceedings of the Glasgow Mathematical Association he published Exceptional integrals of a not completely integrable total differential equation (1953). J M Thomas writes in a review:-
The usual theory of a single Pfaffian equation holds if the coefficients are of class C'. The author effectively remarks that this is not a necessary condition for the existence of a solution.Piaggio was a member of the Edinburgh Mathematical Society, joining the Society in May 1912. He read papers to the Society such as Note on Linear Differential Equations with constant coefficients on 10 May 1912.
Article by: J J O'Connor and E F Robertson