Charles Weatherburn studied under H S Carslaw at the University of Sydney graduating with an M.A. in 1906. He then came to England, after the award of a scholarship, and studied at Trinity College Cambridge where he attended lectures by Whitehead, Whittaker and Hardy. He sat the Mathematical Tripos examinations in 1908, the same year as Brodetsky, and was awarded a First Class degree.
Returning to Australia, Weatherburn was appointed to Ormond College of the University of Melbourne. Pitman, writing in , describes how Weatherburn taught him as a student at the University of Melbourne (1916,1917,1920):-
There were very few honours students, and I was the only Ormond student doing honours mathematics in my year. I went to his room once a week, and sat near his desk while he talked and wrote notes for me. Always he wrote on the back of foolscap paper, the front of which was filled with an early draft of a section of one of his books. He took me through the topics in his two books on vector analysis, and perhaps also some differential geometry... He was neat and clear and interesting, and for me it was a very easy and efficient way of mastering vector analysis.
Certainly vector analysis was not universally accepted at this time and Weatherburn fought the battle for its acceptance against opposition from people such as Harold Jeffreys. Gibbs and Heaviside had been early exponents of the vector calculus while its chief opponents had been Tait. When Weatherburn published the first of his two volumes on vector analysis in 1921 he wrote in the introduction:-
The work of Gibbs and Heaviside drew forth denunciations from Professor Tait, who considered any departure from quaternionic usage in the treatment of vectors to be an enormity.
Weatherburn left Sydney in 1923 to take up the chair of mathematics in Canterbury College, University of New Zealand. At about this time his research interests changed from vector analysis to differential geometry. He wrote two major volumes Differential geometry of three dimensions (1927, 1930) as well as nearly 30 papers on this topic. Hodge, reviewing the second volume, wrote:-
Much of the volume is devoted to subjects to which the author has himself contributed in the last few years, particularly in the theory of families of curves and surfaces, and of small deformations. Other topics are however included, with the result that the two volumes together give an account of most of the principal branches of classical differential geometry. An elementary account of Levi-Civita's theory of parallel displacements is given.
In 1929 Weatherburn returned to Australia taking up the chair of mathematics at the University of Western Australia (founded 1911), becoming the first holder of this chair. He held this post until he retired in 1950 but his excellent sequence of research papers stopped in 1939. He published An Introduction to Riemannian Geometry and the Tensor Calculus in 1938 and it was reissued in 1966. After 1939 his only publication was a textbook on statistics which he published in 1946.
Article by: J J O'Connor and E F Robertson