Carslaw, Horatio Scott

(1870-1954), mathematician

by Michael A. B. Deakin

© Oxford University Press 2004 All rights reserved

Carslaw, Horatio Scott (1870-1954), mathematician, was born on 12 February 1870 at Helensburgh, Dunbartonshire, Scotland, the fifth son of William Henderson Carslaw, a Free Church minister, and his wife, Elizabeth, née Lockhead. After an early education at Glasgow Academy he attended Glasgow University where he studied under Professor William Jack, gaining his MA in 1891. He went on to study mathematics at Emmanuel College, Cambridge, and was fourth wrangler in 1894. His first academic appointment was as assistant to Jack at Glasgow in 1896. In 1897 he made study visits to Rome, Palermo, and Göttingen. He was made a Cambridge MA in 1898 and subsequently took doctorates at both Glasgow (1899) and Cambridge (1905).

Carslaw's visit to Göttingen was the principal influence shaping his future research. During his stay the theoretical physicist Arnold Sommerfield introduced him to continental advances, then poorly known in the English-speaking world, and to modern notions of mathematical exactitude, especially the rigorous attention to detail in the application of mathematics. Carslaw worked intensively to apply advanced complex variable analysis to problems of heat and diffraction. In 1903 he took up an appointment to the chair of pure and applied mathematics at the University of Sydney. Aquiline, keen-eyed, bespectacled, already balding, he was by office the leading mathematician in New South Wales, indeed in Australia as a whole. This context drew his attention to matters of mathematical education. He once described himself as a teacher who enjoyed teaching; others saw him as something of a showman in the lecture room. He was active in both the administrative and the expository aspects of school and undergraduate mathematics, and wrote texts on calculus, trigonometry, and non-Euclidean geometry. His many students included E. M. Wellish (later his deputy) and J. C. Jaeger, his subsequent collaborator.

More than a textbook, and incorporating then recent results, was Carslaw's Introduction to the theory of Fourier's series and integrals and the mathematical theory of the conduction of heat (1906). Work on Fourier (trigonometric) series and their applications was a lifelong preoccupation, and this text was several times revised and reissued.

Carslaw married a widow, Ethel Maude Cruickshank, née Clarke, on 12 February 1907. She died on 3 June of the same year, and he never remarried. Not surprisingly, these events correspond to a hiatus in Carslaw's mathematical output; he published nothing during 1907-8. However his research work in time resumed and he contributed many papers, both innovative and expository, some seventy in all. Honours came to him, including doctorates of science (Adelaide, 1926) and laws (Glasgow, 1928). He was a fellow of the royal societies of Edinburgh and of New South Wales. He retired in 1935.

Carslaw's most enduring mathematical legacy, Operational Methods in Applied Mathematics (1941; 2nd edn, 1948; co-authored with Jaeger), is a product of his retirement. This book introduced into undergraduate curricula the 'Laplace transform', a front-line research topic which became in record time standard fare, displacing the earlier, unsatisfactory 'operational calculus'.

Carslaw continued to work after his retirement, despite failing eyesight. Ever humanely left-leaning, he devoted his later years to another long-standing interest, the pursuit of equitable income tax schemes. He died at his home, Thule, Osborne Road, Burradoo, New South Wales, Australia, on 11 November 1954 and was buried the next day in the Anglican section of Bowral cemetery.

MICHAEL A. B. DEAKIN

Sources  
Journal of the London Mathematical Society, 31 (1956), 494-501
AusDB, 7.578-9
J. C. Jaeger, 'Horatio Scott Carslaw, 1870-1954: a centennial oration', Gazette [Australian Mathematical Society], 8 (1981), 1-18
The Australian Mathematics Teacher, 11/3 (Nov 1955)
I. S. Turner, 'The first hundred years of mathematics at the University of Sydney', The Australian Mathematics Teacher, 9 (1953), 12-17, 26-34
M. A. B. Deakin, 'The ascendancy of the Laplace transform and how it came about', Archive for History of Exact Sciences, 44 (1992), 265-86
Sydney Morning Herald (12 Nov 1954), 3, 10
The Times (26 Nov 1954), 10
Journal and Proceedings of the Royal Society of New South Wales, 89 (1956), xxvii
M. S. Paterson, Memoirs FRS, 28 (1982), 162-203 [obit. of J. C. Jaeger]
M. S. Paterson, 'John Conrad Jaeger, 1907-79', Historical Records of Australian Science, 5/3 (1982), 64-88
Sydney Morning Herald (16 Feb 1907), 12
Sydney Morning Herald (5 June 1907), 8
H. O. Lancaster, 'The departments of mathematics at the University of Sydney', Gazette of the Australian Mathematical Society, 13/2 (1986), 29-38

Archives  
Basser Library, Canberra

Likenesses  
three photographs, 1903-39, repro. in Australian Mathematics Teacher

Wealth at death  
A$55,579: AusDB


© Oxford University Press 2004 All rights reserved

[http://www.oxforddnb.com/view/article/51741]

GO TO THE OUP ARTICLE (Sign-in required)