# Horatio Scott Carslaw

Carslaw was born 12 Feb 1870 in Helensburgh, son of the Rev. William Henderson Carslaw, Free Church minister, and his wife Elizabeth, née Lockhead , and was educated at Glasgow University and Emmanuel College, Cambridge. He also studied in Rome, at Palermo and Gottingen. After taking his M.A in Glasgow in 1891 he became a scholar of Emmanuel College and Fourth Wrangler in 1894. He was appointed Lecturer of Mathematics at Glasgow University in 1896, and was elected a Fellow of Emmanuel College in 1899. In 1903 he became Professor of Mathematics in the University of Sydney and held the chair until 1935. He married in 1907 Ethel Maude, daughter of Sir William J Clarke, Bt, of Rupertswood, Victoria. She died within a year of their marriage.

Admirably fitted by inclination to cope with his neglected and run-down department, he described himself as 'a teacher who enjoyed teaching'. He faced a complete lack of suitable mathematics textbooks in English, and a further limitation was the importance attached to Euclidean geometry with its difficulties in the theory of parallels. Partly to interest schoolteachers, he wrote The Elements of Non-Euclidean Plane Geometry and Trigonometry (London, 1916).

Carslaw's most important and enduring work in mathematics was on the theory of conduction of heat. He extended Fourier's great work of 1822 and made the discussion of trigonometric series more rigorous in his book Introduction to the Theory of Fourier's Series and Integrals and the Mathematical Theory of the Conduction of Heat (London, 1906). As a first step he had to supply a satisfactory treatment in English of real variable theory and the integral calculus. In 1921 the book was enlarged into two, one on Fourier series and one on conduction of heat. In all he wrote ten books and some seventy papers.

In 1921 Carslaw attended the Second Congress of the Universities of the Empire at Oxford. He contributed many articles to the Sydney Morning Herald on such subjects as the need for a closer association with English universities, the development of progressive income tax schedules, and on Lewis Carroll. A fellow of the Royal Society of Edinburgh, he joined the Royal Society of New South Wales in 1903. He was awarded honorary doctorates—of science by the University of Adelaide in 1926 and of laws by the University of Glasgow in 1928.

Although rather shy Carslaw enjoyed company, was a member of the Australian Club and had a large circle of friends, both at home and overseas, with whom he had a prodigious correspondence. This, coupled with sabbatical leaves spent at Emmanuel, kept him in touch with developments overseas and assisted in placing students in whose welfare he took a keen interest. In his earlier days he enjoyed sailing with his close friend Sir Alexander MacCormick and, later, gardening and country life.

In 1935 Carslaw retired to his house at Burradoo where he produced much of his most important work until stopped by failing eyesight. He died there on 11 November 1954 and was buried in the Anglican section of Bowral cemetery. His estate was valued for probate at £55,579

In the 1960's the building containing the School of Mathematics and Statistics at the University of Sydney was named the Carslaw building in honour of the man from Helensburgh.