The Mind of the Mathematician offers a tour of the extensive literature on the psychology of mathematicians and the sources of mathematical creativity, as well as a collection of biographical cameos to illustrate the authors’ analysis. The intent of the authors is to make their review easily readable by both mathematicians and psychologists, so they limit technicalities in both fields or explain technical terms when necessary. The authors are a mathematician (James) and a psychologist (Fitzgerald).
The book is divided into two parts. The first part focuses on a review of the literature on the psychology of mathematicians, and the second part profiles twenty well-known mathematicians whose personalities the authors found particularly interesting. The profiles are designed to illustrate various elements discussed in the first part.
The first chapter attempts to describe the special attraction of mathematics and the distinctive culture of mathematicians. The authors take pains to point out examples of mathematicians who have contributed to music and the other arts, partly — I suppose — to dispel the belief that mathematicians have no outside interests. The next chapter takes up the literature on mathematical education, and includes an amalgam of topics from gender differences to child prodigies to the apparent decline in productivity with age. The final chapter of the first part takes up mathematical creativity and the role of intuition.
The mathematical profiles include three women and seventeen men and span an historical period from Lagrange and Gauss to Wiener and Gödel. Each profile is four pages or less in length, so biographical details and analysis are sketchy. The authors seem to have a special interest in Asperger syndrome, a “mild form of autism” said by them to be far more common than classical autism. They say: “People with the syndrome are attracted to mathematics and kindred subjects; indeed, such people are so common in the mathematical world that they pass almost unnoticed”. In several of the profiles the authors identify evidence to suggest that their subject displayed behavior characteristic of Asperger syndrome. Sometimes diagnoses of bipolar disorder and other mood disorders are offered as well.
In many respects, I found this book to be both intriguing and unsatisfying. There are many fascinating issues raised here, but the treatment is often rather superficial and it wants for synthesis and conclusions. I also found it rather short on ideas. For example, the discussion of mathematical creativity has very little to add to Hadamard’s The Psychology of Invention in the Mathematical Field (aka The Mathematician's Mind). Similarly, the questions of gender differences and decline in productivity with age get very shallow treatments. I was also troubled by retrospective psychological analyses of mathematicians based on biographical materials. While it appears that some important figures like Gödel suffered from debilitating psychological ailments, I am bothered by this apparent “line them up and diagnose them” approach. I suppose we should be happy that, as the authors say, “Some of them are quite normal.”
Bill Satzer (firstname.lastname@example.org) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.