This was a difficult book for me to review. I wanted to love it, but didn’t.
Loving and Hating Mathematics: Challenging the Myths of Mathematical Life is, in essence, about our culture: who we are, how we communicate, our traditions and relationships. Throughout the book, these themes are illustrated with anecdotes about famous mathematicians, the folklore of our culture, many of which you will already know.
I can see two disjoint audiences for this book: us, and them.
Us, being the mathematicians (including pure and applied mathematicians, theoretical statisticians, theoretical physicists… i.e. all our highly quantitative cousins) will enjoy the stories that are new to them. I suspect, however, they will find themselves silently nodding in agreement to the arguments made against the myths, mouthing the words “yes, of course.” By this I mean that although the stories are fun, and part of our tradition, there is not much that is new in the book.
Them, being our friends, families, etc., are all the people who upon hearing that you are a mathematician want to know if you are adding longer and longer lists of numbers each day. These people will probably enjoy the book for its stories, but I suspect they will come away unchanged in their view of mathematics. Sure, they will know some amusing anecdotes, but the conclusions of the chapters don’t hit hard enough to convince anyone of anything. The plural of anecdote is not evidence.
For example, Hersh reports a survey he did of 250 mathematicians he was acquainted with concerning declining ability with increasing age. Sixty six responded, and their stories are no doubt interesting, but there is no systematic study of the results of this (admittedly) biased sample. If you are seeking that, look elsewhere. On the other hand, if someone is boldly stating the maxim “If you haven’t done anything significant by the time you’re 30, you never will,” then there are a few counter-examples in the book you will want to have in your quiver.
Lest the reader think I hated the book, let me state that in fact I enjoyed reading it very much. It was well written and entertaining. It just didn’t, in my opinion, build a strong enough case against the stereotypes.
Peter Rabinovitch is a Systems Architect at Research in Motion and a PhD student in probability. He is significantly over 30.