For many years it has been my custom to take the junior students, that is to say the lowest class, in Mathematics for one hour a week: and a part of the session has been given to what may be called the simpler treatment of the principles of Arithmetic. No attempt has been made to touch the more difficult parts of this subject: no effort has been made to base, for example, the idea of fractions upon a purely abstract foundation.

Those who have worked for the reform of mathematical education in this country, and the Mathematical Association in particular, have up to the present time concerned themselves mainly with reform in the school. A fairly complete survey of this field has been carried out. As a result the character of school mathematics has been transformed, the syllabuses, if not always the question papers, of most examining bodies have been regenerated, and even in the most academic haunts there has been a feeling of uneasiness. It would be unduly optimistic to suppose that the recommendations of the reformers have been universally adopted, or that there is not still a great deal to accomplish, but the progress achieved suggests that the time has come when the universities may be taken in hand.