To appreciate mathematics at its deeper level we must pass from naked formulas to the ideas that lie behind them.
In the present volume, we have selected for reprinting a number of pieces that appeared principally in Science World, a periodical with a wide circulation among students and teachers. In writing these articles it was our aim to deal with a number of diverse areas of current mathematical interest and, by concentrating on a limited aspect of each topic, to expose in a modest way the mathematical ideas that underlie it. It has not been possible, in the few pages allotted to each essay, to present the topics in the conventional text-book sense; our goal has been rather to provide a series of appetizers or previews of coming attractions which might catch the reader's imagination and attract him to the thoroughgoing treatments suggested in the bibliographies. Each article is essentially self-contained.
What reason can we put forward for the study of mathematics by the educated man? Every generation has felt obliged to say a word about this. Some of the reasons given for this study are that mathematics makes one think logically, that mathematics is the Queen of the Sciences, that God is a geometer who runs His universe mathematically, that mathematics is useful in surveying fields, building pyramids, launching satellites. Other reasons are that life has become increasingly concerned with the manipulation of symbols, and mathematics is the natural language of symbols; that "Euclid alone has looked upon beauty bare"; that mathematics can be fun. Each of these has its nugget of truth and must not be denied. Each undoubtedly can be made the basis of a course of instruction.