The future of mathematics appears bright, both for the investigator and for the teacher. When a country which has such an enlightened educational system as France increased the amount of time devoted to secondary mathematics so recently as 1902 and again in 1906, it furnishes one of the strongest possible encouragements to the teacher who may have been troubled by the thought that the educational value of mathematics was not being as fully appreciated as in earlier years. Naturally we may expect that there will be local changes of view as regards the value of mathematics as an educational subject, and these changes will not always be for the better, but the civilized world, as a whole, is learning to appreciate more and more the fundamental importance of early mathematical training, so that we should not be too much perturbed by local steps backwards, but we should move ahead with the assurance that we are engaged in a work of the highest pedagogical importance.
The boundless confidence in the importance of early and extensive mathematical training should, however, not blind us to the need of changes and new adaptations. As an important function of mathematical training is the furnishing of the most useful and the most powerful tools of thought, it is evident that the choice of these tools will vary with the advancement of general knowledge. All admit that the concept of a derivative is one of the most useful elementary tools of thought, and in a number of countries this concept has been introduced into secondary mathematics and used with success. At the last International Mathematical Congress, held at Rome, M. Borel, of Paris, reported that the notion of derivative had been introduced into French secondary education in 1902 and that it had led to satisfactory results. At the same meeting M. Beke, of Budapest, stated that this notion, together with the notion of function and graph, had been introduced into the courses of secondary education in Hungary.
At the recent joint conference of the Mathematical Association and the Federated Association of London Non-Primary Teachers, the chairman remarked: "I have always thought that a mathematician was a man who when he wants to find anything out, uses his brains for that purpose, whereas a physicist, when he wants to find out anything, resorts to experiment." Although this statement is not to be construed literally, yet it does involve a great partial truth and it calls attention to elements which insure mathematical appreciation as long as there is scientific thought. "It is the mind that sees as well as the eye," and the mind sees some of the greatest truths most clearly by means of mathematical symbolism. In fact, mathematical symbols serve both as a telescope and also as a microscope for mental vision, and as long as such vision is demanded the teacher of mathematics will be appreciated.
