Review Symmetry : A Journey into the Patterns of Nature Reviewed by Brian

In January 1975, Jacques Tits gave a lecture during which he wrote down the order, 246 · 320 · 59 ·76 ·112 ·133 ·17·19·23·29·31·41·47·59·71, or about 8 · 1053, of a sporadic simple group M that Bernd Fischer and, independently, Robert Griess had predicted in 1973. Andrew Ogg, an expert in modular functions who happened to be in the audience, was uniquely qualified to recognize something peculiar about this order: he had recently determined the primes that give rise to a certain family of genus 0 modular curves, and the primes he had discovered were precisely the fifteen prime divisors on the blackboard. It was an astonishing coincidence. At the time, to suggest anything more than that would have been moonshine. Three years later, in 1978, Fischer, Donald Livingstone, and Michael Thorne calculated the character table of the Monster, as John Horton Conway had christened M , by assuming an additional prediction of Griess, the existence of an irreducible character of degree χ1 = 196883. Shortly thereafter, John McKay noticed that the