Page:Essays on the Higher Education.djvu/142

 The relation in which mathematics stands to the science of nature is somewhat akin to that in which language stands to literature. In a true and important meaning of the figure of speech, mathematics gives the key into the hand of him who wishes to make a scientific study of nature. The man who is to have any education whatever must have some knowledge of mathematics; he must know enough to be honest and accurate in his business transactions, if he wishes to exercise those virtues. To conduct well many forms of business, one must know much more than the rudiments of mathematics; while the successful pursuit of certain branches of mechanical industry and invention requires a considerable training in this branch of education. But it is for a certain amount of the scholastic study of mathematics, as a necessary factor in a liberal education, that I now plead. Much has been made, by the advocates of a high value for the mental training that comes through this form of study, of the kind of close deductive reasoning which it employs. Such an estimate is partially justified; although it has, I think, very often been exaggerated. Of more educational value is that training which mathematics imparts in respect of quickness of insight and deftness of handling bestowed upon set problems. To enjoy, and to be skilful in, attacking problems is a not insignificant attainment for any educated mind.