This book, by a world famous dynamicist and mathematical physicist, is a kind of digression about mathematics, mathematicians, ethics, politics, philosophy, and more. His discussions of mathematics, in the chapters "What is Mathematics?", "The Erlanger Program", "Mathematics and Ideologies", and "The Unity of Mathematics", are extremely well done, even enlightening. Some other chapters are less compelling. Overall: a book that certainly deserves to be read. ( )

The man who coined the term 'strange attractor' provides a contemporary and a personal look at mathematics in an easy to read fashion. This book is a little bit eclectic which may be considered as a positive point for people outside the world of mathematics, and Ruelle does not adhere to a linear organization, preferring to jump from one subject to another but manages to provide good connections and insights.

Among the mathematicians he writes about, I found the case of Alexander Grothendieck very remarkable, inspiring, sad and hilarious [1]. This is a very interesting part of the history of mathematics which includes important lessons about organizations, politics and power relations.

Ruelle's discussion on some messy parts of math and proof-checking is very good and he poses important questions about proofs getting longer and longer and formalisms required to handle things as rigorously as possible.

The closing chapters are devoted to Ruelle's area of expertise and he writes very strongly on mathematical physics and give very good examples how diverse scientific fields help each other.

1- See my blog entry 'Corporatism in Science and Math: Mathematician Missing - Part 2':

http://ileriseviye.org/blog/?p=2223 ( )

These ~150 pages harbor quite a variety of opinionated but meaty little chapters on the basic nature of mathematics and what it means to be a mathematician.

The book keeps the promise of its title: it's a personal, sometimes idiosyncratic tour of many aspects of mathematical thinking and mathematical work, containing original thoughts and ideas and many anecdotes that keep the book flowing. In the end it doesn't offer any revolutionary new ideas, but it reaches a goal similar to Gower's Very Short Introduction to Mathematics using very different means: it introduces the reader to what mathematics is. ( )