In spite of the achievements of mathematics, and of a very general recognition of the fact that mathematics is essential to the progress of knowledge in most of its departments, there exists a certain amount of contempt for the symbols, the formulae, and the abstractions of the subject. For a generation we have struggled against this feeling, and have endeavoured to correct the defects to which the feeling is due, but I do not think that many are satisfied with the success of our efforts. Those who have attended to the widespread demands for a more generous and thorough provision for education, as representing the only sure foundation for national efficiency and progress, have remarked with dismay the little interest that is shown in mathematical education. Surely this state of things demands, at the present time, our most urgent attention.