From 1897 to 1898 he was a mathematical master at Dundee High School, and in October 1898 he went to Cambridge and entered at Gonville and Caius College, gaining an Exhibition there in 1898 and being elected a Foundation Scholar of the College for his remaining years in residence. In 1901 he was Senior Wrangler, and in Part II of the Mathematical Tripos in 1902 he obtained a First Class.
In February 1903 he came to Cape Town to the South African College to act for the year as Deputy Professor of Applied Mathematics and Physics to Beattie, who had a year's leave of absence for the Magnetic Survey of South Africa, which was being carried out by him and Morrison. Brown's work was so efficient that at the end of the year the College Council resolved to split the Chair, to offer Beattie the professorship of Physics and to invite Brown to remain in Cape Town as Professor of Applied Mathematics. He accepted the invitation and was Professor of Applied Mathematics first at the South African College and later at the University of Cape Town from its inception in 1918 till his death on January 27, 1947.
In teaching, in advising and helping students, and in examining he proved an excellent professor: in the long tenure of his Chair, when the number of students in his department grew fourfold, he always - helped, I have no doubt, by his quiet sense of humour - had the respect and admiration of his students and their friendship in their post-university days.
In administrative work for the South African College and the University of Cape Town he did outstanding work. From 1908 to 1910 he was Senate assessor to the Council of the College, from 1912 to 1914 he was Vice-Chairman of Senate and in charge of the academical work of the College, and he was a member of many committees. His services in this way were more and more made use of in the days of the University from 1918; he was, with but a short break, a member of Council, of its Finance and General Purposes Committee and most of its sub-committees, in addition to being a member of most Senate Committees, till his death; his careful consideration of all questions and his sound advice were of the greatest value. He was Head of College House from 1923 to 1927 and Head of Men's Residence at the seat of the University in Rondebosch on the slopes of Table Mountain from its beginning in 1928 to 1932.
He was elected in 1938 the representative of the University on the Cape Hospital Board, and in 1939 Chairman of the Groote Schuur Hospital Committee.
He was elected a Fellow of the Royal Society of South Africa in 1918, was on its Council from 1931 to 1935 and again in 1941, was its Hon. Treasurer from 1936 to 1940 and President from 1942 to 1945.
With the work of his department and all his administrative work he had little time for research and published only a few papers in pure and applied mathematics, including "The Equivalent Mass of a Spring Vibrating Longitudinally", in Transactions of the Royal Society of South Africa, vol. v, 1916, p. 565, and "The Use of a Standard Parabola for Drawing Diagrams of Bending Moment and of Shear in a Beam Uniformly Loaded", Transactions of the Royal Society of South Africa, vol. v, 1916, p. 659. He also helped Beattie and Morrison with their work on the Magnetic Survey and assisted in writing the report for the Royal Society of London on the observations from 1898 to 1906.
In his little leisure he was a great reader and a keen musician.
He married Mary Graham in 1911 and is survived by her, a daughter and a son.
He was elected a Fellow of the Society in 1907.