The Readin Roos

One of the paradoxes of popular accounts of mathematics is that they tend to have little mathematics in them. Instead, authors tend to focus on the eccentricities of those who do mathematics. In this book, Marcus du Sautoy does present quite a lot of conceptual material on group theory and its importance in the mathematical expression of symmetry, in addition to the nearly-obligatory accounts of the strange lives of Evariste Galois and Sophus Lie. What also makes this book different than many other books on mathematics for general audiences is du Sautoy's personal narrative. The chapter structure moves through a year of his life, as he researches, collaborates, and presents material on the "Monster," a 196,883-dimension group object with a mind-boggling number of different symmetries (808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 symmetries, to be exact). For those of us who have trouble visualizing all of the geometrical symmetries in three dimensional space, this is obviously daunting. Du Sautoy shows how to make the leap from geometric visualization in three dimensions to group theory visualization of higher-dimensional objects (although not with mathematical rigor or the detail required for individual study).

Along the way, we meet many of the characters of modern group theory, including John Conway, Simon Norton, and other authors of the comprehensive "Atlas of Finite Groups" that maps out all the possible symmetric groups. Du Sautoy takes us from a beach in the Sinai, to the symmetric majesties of the Alhambra Castle, to conferences in Japan - while personally showing us his relationship with his son from an earlier marriage, his wife and their efforts to adopt children, and the challenges he finds in relating to other mathematicians.

This book is a very worthwhile read, and the effort to understand the mathematics conceptually is rewarded in developing a deeper appreciation for the beauty of mathematics and the human pursuit of symmetries.