I came to this book via two others. I had enjoyed
50 Mathematical Ideas You Really Need to Know (50 Ideas You Really Need to Know Series), and wanted to give it as a present. However I felt it required more mathematical expertise than my friend had, so looked for a simpler book in the same style. I had read and enjoyed
The Little Book of Scientific Principles, Theories and Things, so was delighted to discovered there was a mathematical version. I bought the Kindle edition to check it out.
I feel The Little Book of Scientific Principles works better in the paper edition than it does on Kindle (see my review), and I assume the same is true of this. Also I know more on this subject than I do of general science, which makes me pickier. But even taking these into account, I don't feel this book is nearly as good as either of those mentioned above.
Overall the book has a muddled feel to it. It works better at the beginning, with a historical progression of ideas, subverted occasionally by a linking of related concepts. Later the progression disappears, and there is just a hotchpotch of topics. There is also a randomness to the type of entry - major fields are jumbled together with archaeological finds, biographies of famous mathematicians, entertaining puzzles and number related stories, both as different entries and within entries. This could be an excellent approach, helping to lighten the weight of theory while demonstrating the vast scope and real life applications of mathematics, but it's so unstructured that it is just frustrating.
The explanations are also better at the beginning of the book. Later they start clear and simple, but then tend to accelerate to more advanced aspects without taking time to properly explain all the concepts on the way. Topology, for example, starts off with a nice explanation of the difference between a sphere and a doughnut, then dives into Poincaré's conjecture without really explaining what a three-manifold is. Mobius strips and Klein bottles, however, each have their own entry.
The overwhelming feeling is of a good idea rushed into print before it has been properly worked out.