*The Wealth of Nations*(Polya, 2006), was a lawyer whose academic ambitions were thwarted by institutional anti-Semitism, until he converted to Roman Catholicism. His brother Eugen (Jenö) was a surgeon, famous for a type of gastrointestinal bypass surgery for the treatment of stomach ulcers, who died at the hands of the Nazis; another gifted brother, Laszlo, was killed in the First World War. His great-nephew is the controversial artist and biochemist, Gideon Polya. George seems to have limited his misfortunes to an early punch-up with a student with royal and high level political connections in Göttingen: fortunately for mathematics, this incident partly led to his appointment at ETH Zurich.

*How To Solve It*, is the subject of this review.

*How To Solve It*is an unusual book. There are in fact only 36 pages in all which outline Polya’s method: these form Parts I and II of the book, In The Classroom and How To Solve It – A Dialogue, respectively. These chapters are preceded by a two-page outline of the method, presumably intended as an aide memoire, and an Introduction, which outlines and explains the book’s rather unique structure. Part III, the largest section of the book, is entitled a Short Dictionary of Heuristic, essentially an appendix expounding in detail on the problem-solving techniques and ideas mentioned in Parts I and II, together with potted biographies of a few mathematicians and definitions of a few pertinent terms. The final section, Part IV, is the aptly-titled Problems, Hints, Solutions. Throughout the book, subsections within the chapters are numbered, rather more like a textbook or business document. Initially a little disturbing to the reader expecting something a little more literary, this does however reinforce the fact that this book is very much a guide: a textbook in mathematical guidance.

- Helping the student
- Questions, recommendation, mental operations
- Generality
- Common sense
- Teacher and student. Imitation and practice.

*thing*, and supplies a structure, a logic, and a process from which something might reliably emerge. It is not a book to be read through, short as it is. It is a book that should be kept on a convenient bookshelf, to be referred to, dipped into, and mulled over. Frequently.

References

J J O’Connor, J.J., & Robertson, E.F. (2002). MacTutor: *George Pólya.* [online]. University of St Andrews: MacTutor. [Cited 26/03/2010].

*How To Solve It: A New Aspect of Mathematical Method*. Princeton, New Jersey: Princeton University Press.

*Global Avoidable Mortality*. [online]. Blogger. [Cited 26/03/2010].

*Eugen (Jenö) Alexander Pólya*. [online]. Oslo: Who Named It? [Cited 26/03/2010].