This is a highly recommendable reading for mathematicians, of course, but also, with some cautions, for non-mathematicians. The sheer description of the book as a set of papers on the lives and scientific results of several important mathematicians does not express well the nature of the book. Let us try to do better.
Being a collection of independent chapters, the reader can proceed by browsing through the sections guided by the contents table. The table sure contains so famous names that this will give immediate spontaneous choices according to the reader particular interests. Not surprisingly, our reader could discuss the list of mathematicians present: some are missing, some are not that important (or are they?, there is something to learn, then). Also, our reader can find the papers a little unbalanced: some very short, some too technical, some too well known information (how to tell new on John Nash?). But we can be sure that this appreciation goes with him, and another reader will find enough the very short paper, quite interesting those technical details, and a pleasure to find once again the same information with a somehow different twist. Furthermore this double impression will most likely be felt by all readers. In fact, this quality shows the book is right in its tone and scope, and guarantees some good pieces to anyone.
Now, the reader can pick the book as a novel and read it from first page to last. This is relevant, because the organization and ordering of the chapters contribute to the overall effect, by combining in different doses mathematics and life, research and civil or political activism, detail and overall view. Not to be forgotten the great mathematicians appearing in this book are men who have lived through the Second World War and the posterior Cold War, and at one time or another many have taken definite positions. Often great man take very strong positions, which their prominence can amplify, and this is also explained in the corresponding place.
It is clear that a mathematician is best prepared to extract the most from this kind of book. So what for non-mathematicians? Clearly, lives and miracles, true (or imaginary) stories, will interest them. And there is a lot of this stuff for them in the book (beaches of Rio de Janeiro included). But this does not mean they must limit their reading to that. Clearly they should discard many technicalities. Despite the efforts made in many parts, Mathematics are for specialists, for professional mathematicians. However, a sensible diagonal reading of those parts should help anyone to understand the high quality and deep difficulty of the achievements that matter, and the ways they were reached. Those ways may take many years and involve many people, but most often an outstanding scientist can be singled out as leading the track. As a mathematician myself, I find difficult to transmit my own amazed view of the really great mathematics made by really great mathematicians. This book is another try at this, and very welcome.
This review is deliberately imprecise, to avoid spoiling the pleasure of the surprise. However one cannot help listing some unusual names to be found in the book: Verlaine, Musil, Queneau, Borges. (These mentioned in the hope of promising further surprises.) This is a book to read and enjoy, not to study, which for a book classified as Mathematics is not common.