Mathematics existed prior to the mathematician. Before Man calculated, Nature multiplied and divided; her products were based on geometrical forms. Mathematics, in reality, is not a creation of the mathematician. It is a vital spirit, immanent in Nature and Man, and expressed in the forms and processes of Nature and the manifold works of Man. This spirit functions only partly through the mathematician, who limits both its sphere of operation and its method of working. These limitations constitute a serious difficulty for the pupil by cramping the expression of his personality. His love of beauty is ignored, his social sympathy is untouched, his sense of humour lies dormant, his interest in Nature is not aroused, his imagination has little outlet, his artistic, musical and religious tendencies find no contact. On the whole his emotions are starved, his intellectual development is limited and his spiritual life is uninfluenced. These are hardly the conditions for the successful teaching of any subject. Nor does such limited mathematics contribute adequately to the general culture of the pupil. Its limitations are also a serious obstacle to the integration of the school curriculum, one of the most pressing problems.