From Zero to Infinity: What Makes Numbers Interesting

摘要

It would be difficult for anyone to be more profoundly interested in anything than I am in the theory of primes. - G. H. Hardy (see book). From Zero to Infinity by Constance Reid has been inspiring the mathematically keen for over 50 years now. Written in informal style, the book offers an introduction to the beauty of natural numbers. It is organized into 12 chapters, with a chapter each for the first ten natural numbers. A special chapter is dedicated to the Euler identity, and another one to Aleph-0. Tracing the discovery of the numbers, the chapters expand upon features and facts, all of which tells us why these numbers are interesting. While perhaps many of such facts can be found in elementary undergraduate texts, it nonetheless attempts a holistic picture describing relations between prime, composite, perfect, rational and irrational numbers. As the author explains in the preface, the book has a story. The advent of computers enabled the discovery of a new set of perfect numbers, which started the chapters. While it may be hard to imagine how a whole chapter could be written about the most common of numbers, the author does so in a very satisfactory manner. The chapters usually end with some notes, open problems and hints about these problems. The reader is often encouraged to tackle them, and not all are that elementary!