Symmetry and the Monster: One of the Greatest Quests of Mathematics

6 September 2006

by Mark Ronan, Oxford University Press. Hardback ISBN 0192807226, £14.99 ($27).


Simple symmetry groups are groups of geometric operations (rotations, reflections, etc) that cannot be decomposed into simpler groups. Symmetry and the Monster is about identifying and classifying the finite simple symmetry groups and discovering exceptions that do not fit into the overall pattern. The largest exception is the Monster. This book is the first telling of a mathematical odyssey spanning two centuries and the biographical accounts linking the technical sections are lively and informative, although they become more reticent as we reach modern times with living protagonists.

Ronan insists on calling simple groups the “atoms of symmetry” (atoms are not simple) and classifying them in “periodic tables”. However, even Ronan’s first table is mysterious, with Lie groups classified in “families”, labelled A through G (rows), operating in dimensions 1 through 9 (columns). Ronan does not tell the reader what the family members have in common, but says that some groups don’t appear because they are not “simple” or are the same as others. For example, D3 is apparantly the same as A3. And it doesn’t get any easier.

Oxford University Press considers this book “a must-read for all fans of popular science”. In his blog, Lieven le Bruyn, professor of algebra and geometry at the University of Antwerp, suggests that “Mark Ronan has written a beautiful book intended for the general public”. However, he goes on to say: “this year I’ve tried to explain […] to an exceptionally good second year of undergraduates, but failed miserably […] Perhaps I’ll give it another (downkeyed) try using Symmetry and the Monster as reading material”.

As an erstwhile mathematician, I found the book more suited to exceptional maths undergraduates than to the general public and would strongly encourage authors and/or publishers to pass such works before a few fans of popular science before going to press.

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