Mark Ronan has written a beautiful book intended for the general public on Symmetry and the Monster. The book’s main theme is the classification of the finite simple groups. It starts off with the introduction of groups by Galois, gives the classifivcation of the finite Lie groups, the Feit-Thompson theorem and the construction of several of the sporadic groups (including the Mathieu groups, the Fischer and Conway groups and clearly the (Baby)Monster), explains the Leech lattice and the Monstrous Moonshine conjectures and ends with Richard Borcherds proof of them using vertex operator algebras. As in the case of Music of the Primes it is (too) easy to be critical about notation. For example, whereas groups are just called symmetry groups, I don’t see the point of calling simple groups ‘atoms of symmetry’. But, unlike du Sautoy, Mark Ronan stays close to mathematical notation, lattices are just lattices, characer-tables are just that, j-function is what it is etc. And even when he simplifies established teminology, for example ‘cyclic arithmetic’ for modular arithmetic, ‘cross-section’ for involution centralizer, ‘mini j-functions’ for Hauptmoduln etc. there are footnotes (as well as a glossary) mentioning the genuine terms. Group theory is a topic with several colourful people including the three Johns John Leech, John McKay and John Conway and several of the historical accounts in the book are a good read. For example, I’ve never known that the three Conway groups were essentially discovered in just one afternoon and a few telephone exchanges between Thompson and Conway. This year I’ve tried to explain some of monstrous moonshine to an exceptionally good second year of undergraduates but failed miserably. Whereas I somehow managed to give the construction and proof of simplicity of Mathieu 24, elliptic and modular functions were way too difficult for them. Perhaps I’ll give it another (downkeyed) try using ‘Symmetry and the Monster’ as reading material. Let’s hope Oxford University Press will soon release a paperback (and cheaper) version.

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Posted in groups
Written on Fri, 02 June 2006 at 10:49 am
Tags: Borcherds, Conway, Galois, groups, Mathieu, modular, monster, moonshine, symmetry
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