Customer Reviews

Playing with Infinity: Mathematical Explorations and Excursions

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Infinity is fun. But most people have never been exposed to the fascinating theory of infinities. This book provides an extremely well presented introduction to the concepts of infinities. The presentation is at times a little forced, however overall it is clearly and simply written, and the basic analyses of enumeration by pairing of elements is explained in a simple and easily understandable manner. The elementary concepts of infinites are not difficult to grasp, and should and can be understood by anyone with an interest in mathematics. This book provides an easy to understand introduction to these concepts. I especially recommend it for parents wanting to study/learn math with their kids in middle and high school. It covers material that will not be covered at school, but is fun and not overly difficult to grasp, and will surely help both the parent and child.

This book will give you a good general introduction to the concept of infinity. I found the presentation informal and quite easy to follow. Since the book was first written in 1943 and revised in 1960 there are some units that are not used anymore. For example, the coinage of pounds, shillings, and pence is dead. Things like a chapter on "The Charts Get Smoothed Out", may seem round about but still interesting. My favorite chapter is "Mathematics Is One". The derivation of "visual forms" in functions is excellent.

Have pen and paper handy because to really enjoy the book I found myself doing some of the "the reader can solve for himself..." stuff. Another point is that you can more or less read the chapters independently and in no particular order and still reap huge benefits from the material.

Thank God for Dover which still publishes this book. My copy is a 1976 edition. If you are interested in getting back in touch with things you may have long forgotten get this book.

This book explains the why's behind math from principles as basic as counting to as complicated as series, geometry, and even some calculus principles. It is written in a conversational tone with lots of pictures (yes, and numbers). Each chapter builds upon the last, and it is easy to follow (though sometimes dense). It was my first "fun" math book and is still by far my favorite. There are other math books that take real situations and relate them to math, but this starts with math and sticks with it. Thus, not for the mathphobe, but great if you want to understand math from the ground up.

The author, Rozsa Peter, is a lady mathematician (or is one not supposed to notice?) who shares with George Gamow and Richard Feynman a flair of making the complicated seem simple. The preface states that the book is written for "intellectually minded people who are not mathematicians." The book explores various ways in which the concept of infinity enters into mathematics - and the dangers it poses. Along the way other concepts, drawn from topology and non-Euclidean geometry, are snuck in. While these are only peripherally concerned with infinity, they constitute some of the most appealing material. The "seven bridges of Koenigsberg problem" is an example. Perhaps the very best part of the book is the last chapter, devoted to Goedel's "unprovability" theorem.

My general impression of this book is that of a mathematical counterpart to Gamow's, "One, Two, Three ... Infinity" -- but not quite as good. Of course Gamow's work is such a masterpiece that "not quite as good" still leaves lots of room. And that is why this book is a gem in its own right. I recommend this book especially to high school students with a strong interest in mathematics.

So, why is the book not quite as good as Gamow's? For one thing it does not quite have the breathtaking sweep of Gamow. The other is that in the process of making things simple, Rozsa overdoes it at times. Concepts that great minds struggled with for centuries appear as child's play. The image of little ten-year-old Eva rediscovering the irrationality of the square-root-of-two all by herself seems a little strained. But then again -- maybe she did do it!

Prof. Peter (whose book on recursive functions is considered a classic among computer scientists) introduces the reader to the beauty that is mathematics by breaking down concepts that might appear intimidating to the neophyte. This charmingly written book takes readers by the hand and explains areas of mathematics that deal with the concept of infinity in a friendly, non-condescending manner, commencing with basic arithmetic and eventually progressing to logic and set theory and the works of Cantor, Hilbert, and Russell. A good introduction to mathematical principles for those looking to get their feet wet, Playing with Infinity is also fun for the more mathematically seasoned reader. Many thanks to Dover for keeping such books available and at such a reasonable price.

The book shows a number of ways the concept of Infinity has benefited us as mathematicians.

This book is a gem. I read it as a highschool student, and it
played an important role in enticing me to become a
mathematician. Its emphasis is not on practical applications
or on solving funny problems: instead, it is an inspiring
introduction to some of the great
intellectual challenges in the history of mathematics.