The last half-century has seen a great and significant change in the popular estimation of mathematics. Formerly the subject was regarded as utterly unpractical, and therefore useless in the narrow sense of this term, though it was recognised as providing a training, unique in its character, in logical thought and accurate expression. Now it is regarded, and correctly regarded, as having enormous practical importance in science and engineering. Most, if not all, of those discoveries and inventions which are so profoundly modifying civic and national life have found their origin, or development, or both, in the labours of mathematicians, and this fact is widely known. The mathematician is no longer regarded as a dreamer of dreams; he is classed with the doctor, the engineer, the chemist and all those whose specialised labours have had immense import for the human race.