Von Zahlen und Figuren: Proben mathemalischen Denkens für Liebhaber der Mathematik

Abstract

IT has been rightly said that the high walls built up round mathematics by the signs of integration and summation, cause mathematics to be a permanent mystery for the average thinking person. It is true that a thorough insight into higher mathematics requires special training; yet within these abstruse theories, there must be some parts and some examples, at least, which, properly explained, could enable non-experts to peep through the complex texture of mathematics, and derive thereby some measure of enjoyment. This is the spirit which underlies the little work under notice. Although this book will teach nothing new to mathematicians, it will be found most interesting and helpful by those who are interested in mathematics. Without using anything but logic and the most elementary notations, the authors are able to guide one through the mysteries of the prime numbers, of incommensurable lines and irrational numbers, the theory of aggregates and the paradoxes of transfinite numbers, the doctrines of the polyhedra and the measurement of the circle. Although their exposition is based on mathematical facts, the authors lay more stress on the general form and method of the questions treated; while occasional historical remarks add to their interest. Thus, instead of showing the pragmatical aspects of mathematics, or their philosophical importance, the book emphasises the internal and structural characteristics of pure mathematics. The student of logic, in particular, will find in this very able book an ample field for his speculations. Von Zahlen und Figuren: Proben mathemalischen Denkens für Liebhaber der Mathematik. Prof. Hans Rademacher Prof. Otto Toeplitz . Pp. vi +164. (Berlin: Julius Springer, 1930.) 9.60 gold marks.