Numbers: A Very Short Introduction
In most people’s minds, math is about numbers and numbers are math. The connection is so prevalent that sometimes it’s very hard to explain to people that you are actually doing math when all you do is write unrecognizable symbols on a blackboard or a piece of paper. Nonetheless, the study of numbers can open up vistas to all sorts of interesting mathematical objects, as well as a lot of interesting and non-trivial research on numbers themselves. For instance, integers are probably the most accessible of all numbers, and yet certain properties of integers are so hard to understand that even those professional mathematicians who have worked on them all their lives feel like they have only been scratching the surface of all the problems that one can possibly dream of.
This short introduction introduces the reader to the full richness of numbers, the way in which various sets of numbers arose, and various intriguing and fascinating properties that various collections of numbers have. The book is particularly detailed and comprehensive when it comes to discussing various sets of integers and their properties. I am a theoretical physicist with a lifelong armature interest in math, but even I have never heard of several collections of integers that had been discussed in this short introduction.
The book is very detailed, and it doesn’t condescend to the reader. Many examples are given somewhat detailed proofs, and at no point does the reader get the impression that this is a watered-down popular math book. Many arguments can be challenging and need to be read carefully and if you are not willing to untangle them you will not benefit too much from the text. I certainly appreciated all the effort that has been put into making this book this educational and informative.
Unfortunately, the book’s biggest strength is also its biggest weakness. This book will probably be on the advanced side for the most general readers. It is certainly amongst the most intellectually demanding of all VSI books. If you are up for a challenge, however, it will be the best introduction to numbers short of actually opening a textbook on the subject.
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