Taming the Infinite: The Story of Mathematics [Paperback]

This is a fantastic book on the history and applications of mathematics. It starts with Hindu Arabic numerals and ends with Chaos Theory. Of course every major mathematical theorem or topic during this period could not be stated in a book of this size and as the author states he had to be selective. My only complaint about the selection is the lack of `linear algebra' because it is perhaps the second most (first being calculus) powerful mathematical tool ever invented.
To fully appreciate this book you must have a reasonable mathematical ability such as a good pass at Further Mathematics A level or equivalent.
Stewart does write in a way that will appeal to most readers and also you can dip into any chapter without digesting the previous chapters. The author has hit the right tone and progression.
A lot of research and time must have been invested into writing this book because of the coverage of applications, the history behind important mathematical developments, profiles of the leading mathematicians etc. I really do like the broad range of mathematical applications throughout the book. The author explains where differential equations are used in the field of physics and modern technology such as radio, tv and commercial jet aircraft and how important Navier Stokes Equation is in fluid mechanics. It goes on to explain where coordinate geometry and trigonometry are used in real life such as graphics, stock market fluctuations, navigation, surveying etc. This is an excellent resource for any A level mathematics teacher who wants to inspire his/her pupils.
The history of mathematics starts with the Hindu Arabic numerals and how they were brought to Europe by Fibonacci. It highlights major historical figures in the mathematics by placing a brief biography in a light shaded grey with an image of the mathematician. However I did not find this sort of feature for Leibniz which is a serious omission since he and Newton founded calculus.
I found the following minor typos:
1. Page 73 the result `sin(theta/2)=sqrt(1-cos(theta))/2' should be `sin(theta/2)=sqrt(1-cos(theta)/2)'.
2. On page 156 the statement of Riemann Hypothesis should read `complex zeros lie on the line z=1/2 plus or minus it' not `z=1/2 plus it'.
3. Page 260 the statement is written `x(t+3)' should be `x(t+ epsilon)'.
This is an excellent book and would recommend that anybody interested in mathematics should purchase this book. The book is a fantastic resource for any college or university library.
Kuldeep Singh
Sunday, 12 April 2009

This is university level pure mathematics so the Waterstone reviewer who wrote "guaranteed to illuminate even the most number-shy" could not have read it. I don't know where this paperback is supposed to fit in: it is not a text book and nor is it a layman's paperback but requires a good level of mathematical knowledge and a high intellect to get anywhere near grasping the concepts. A number of tantalising concepts could have made this book more interesting if they had been explained eg. what is 196,884 dimensional algebra and although it is good to know that the Greeks solved cubic equations using conic sections how did they do it? The index is not very good. I don't know who this book could be recommended to.

I found this book disappointing. It seemed to me to have been written without a clear enough view of the intended readership. It contains brief biographies of leading contributors to the development of maths, and these are often written in a fairly chatty style; and boxed text gives short illustrations of the usefulness of different aspects of maths. These parts of the book seem intended to be comprehensible to non-specialists, though they contain passages that require more expert knowledge to be fully understood. The core of the book is an outline of the history of maths, and much of this, especially for Renaissance and later maths, is incomprehensible to someone who has not had at least university-level mathematical education. (I suspect some will be not fully comprehensible even to some maths graduates.) The problem is that many mathematical discoveries are presented in a fairly technical but very summary form, without clear explanations of what they are about, and at times without a clear exposition of the mathematical notation used. Specialist terms are often used without explanation of what they mean.

Unless you are an expert mathematician, you are likely to feel that you are often reading an unknown foreign language, without a crib or dictionary.