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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