Dr **Horatio Scott Carslaw** FRSE LLD (12 February 1870, Helensburgh, Dumbartonshire, Scotland – 11 November 1954, Burradoo, New South Wales, Australia) was a Scottish-Australian mathematician.^{[1]}^{[2]} The book he wrote with his colleague John Conrad Jaeger, *Conduction of Heat in Solids*, remains a classic in the field.

He was born in Helensburgh, Scotland, the son of the Rev Dr William Henderson Carslaw^{[3]} (a Free Church minister) and his wife, Elizabeth Lockhead.^{[1]} He was educated at The Glasgow Academy. He went on to study at Cambridge University and then obtained a postgraduate doctorate at Glasgow University. He was elected a Fellow of the Royal Society of Edinburgh in 1901.^{[4]} He was a Fellow of Emmanuel College, Cambridge and worked as a lecturer in Mathematics at Glasgow University, when in late 1902 he moved to Australia.^{[5]}

In 1903, upon the retirement of Theodore Thomas Gurney,^{[6]} Carslaw was appointed Professor and the Chair of Pure and Applied Mathematics in the now School of Mathematics and Statistics at the University of Sydney. He retired in 1935^{[7]} to his house in Burradoo where he produced most of his best work.^{[1]} The Carslaw Building at the University, completed in the 1960s and containing the School, is named after him.^{[8]}

He died at home in Burradoo and was buried in the Anglican section of Bowral Cemetery.^{[1]}

He married Ethel Maude Clarke (daughter of Sir William Clarke, 1st Baronet^{[1]}) in 1907 but she died later in the same year.^{[4]}

*An introduction to infinitesimal calculus*, 1905*Introduction to the theory of Fourier's series and integrals and the mathematical theory of the conduction of heat*, London 1906, revised 2nd edn. 1921, published under the title*Introduction to the mathematical theory of the conduction of heat in solids*;^{[9]}revised and enlarged 3rd edn. 1930, published under the title*Introduction to the theory of Fourier's series and integrals*^{[10]}*The Elements of Non-Euclidean Plane Geometry and Trigonometry*, London 1916- with John Conrad Jaeger:
*Operational methods in applied mathematics*, 1941,^{[11]}1948 - with Jaeger:
*Conduction of Heat in Solids*, Oxford 1947, 1959