This article was published in Australian Dictionary of Biography, Volume 7, (MUP), 1979
Horatio Scott Carslaw (1870-1954), mathematician, was born on 12 February 1870 at Helensburgh, Dumbartonshire, Scotland, fifth son of Dr William Henderson Carslaw, Free Church minister, and his wife Elizabeth, née Lockhead. He was educated at Glasgow Academy and the University of Glasgow (M.A., 1891). That year as a scholar he entered Emmanuel College, Cambridge (B.A., fourth wrangler, 1894; M.A., 1898; Sc.D., 1908). In 1896 he became assistant to Professor William Jack at Glasgow and next year studied at the universities of Rome, Palermo, and Göttingen. A fellow of Emmanuel College in 1899-1905, he continued to teach at Glasgow until he was appointed to the chair of pure and applied mathematics at the University of Sydney in 1903 in succession to T. T. Gurney. On 12 February 1907 at Bowral he married a widow Ethel Maude Cruickshank, daughter of Sir William Clarke, but she died on 3 June the same year.
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).
In Glasgow Carslaw had been inspector of mathematics in secondary schools. In Sydney there was no inspection of schools offering secondary courses or co-ordination of standards and syllabuses, and the final examination was entirely in the hands of the university. He was also concerned both with the general nature of the schools' curriculum and with their relation to the university. While seeking quality in the curriculum, he deplored specialization at the school level. He became involved in the exchanges between the university and Peter Board between 1907 and 1912 and came to accept Board's suggested leaving certificate, and to welcome the principal features of A. C. Carmichael's University (Amendment) Act, 1912. Indeed, in a situation of recurrent tension, Carslaw's ultimate appreciation of the merits of the government's intentions, and his moderating influence in university circles helped to prevent a serious confrontation. He was a member of the first board of examiners established under the Act, and was chief examiner in mathematics for the next thirty years.
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. The latter was expanded with J. C. Jaeger into Conduction of Heat in Solids (Oxford, 1947; 2nd edition 1959); during work on it they produced Operational Methods in Applied Mathematics (Oxford, 1941; 2nd edition 1948), which was a successful attempt to replace the controversial Heaviside operational methods, of which he much disapproved as lacking in rigour, by an integral transform approach. 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.
J. C. Jaeger, 'Carslaw, Horatio Scott (1870–1954)', Australian Dictionary of Biography, National Centre of Biography, Australian National University, http://adb.anu.edu.au/biography/carslaw-horatio-scott-5518/text9395, accessed 26 May 2013.
This article was first published in hardcopy in Australian Dictionary of Biography, Volume 7, (MUP), 1979