JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. WHAT is the use of mathematics ? There are many parents who would find it extremely difficult to answer this question, and if they attempted to give an answer,

more »

... hey would in many cases repeat what appears to be a widespread current belief, namely, that mathematics is of no use in itself, but that a school course in the subject affords valuable mental training and develops the brain. If this were all that could be said in favour of mathematics, a strong case could be made out for the rival claims of philately to be included in the curricula of our schools and universities. The intelligent study of a collection of postage stamps may be made of greater educational value than the unintelligent manipulation of mere mleaningless collections of algebraic symbols. The detection of watermarks and the measurement of perforations may be used to afford valuable mental training, and are well calculated to develop a child's powers of observation and accurate measurement. This statement of the educational claims of philately must not be taken seriously. It must only be regarded as indicating that, if mathematics is to be defended against the many competing claims for recognition of other subjects in our educational systems, a much stronger case must be made out than that based on the mere acadenmic ideal and the considerations associated with it as to the value of the mental training afforded by the study of mathematics. Now there are two aspects of mathematics which in my opinion place that subject far and away in front of any other branch of human study. These are the research aspect and the practical aspect. Of both of these the British public is as a rule profoundly ignorant. The claims of scientific research for recognition are being slowly forced upon our country by the successes of Germany and America, but those who associate any meaning with the word "research," contemplate the building of palatial laboratories to which the mathematician finds no admittance. Yet the mathematical researches of to-day become the practical applications of to-morrow and culminate in the commercial successes of the near future. It cannot be too strongly made known that the mathematician who shuts himself up in his study, and who is content to live on a starvation income turning out pages of foolscap covered with x's and ys, may be a pioneer, who, without knowing it, is building up the foundations of a great industry. But, people will say, this may be very true of applied mathematics, but surely those long and mystical hieroglyphics in pure mathematics can never lead to anything practical. A greater mistake could not be made. When the engineer passes on a problem to the applied mathematician, it is the want of further knowledge of the highest and most advanced parts of pure mathematics which frequently stands in the way of the final solution. Let us take one example of the way in which the study of what appeared to be purely symbolical abstractions has conduced to the progress of civilisation. When mathematicians first began to solve quadratic equations, they soon found the square roots of negative quantities occurring in their solutions, and a "practical man" of the ordinary type would naturally infer that the problems could not be solved, and that it would not pay K2