A pilgrimage through the uncanny world of symmetry.
Du Sautoy (Mathematics/Oxford; The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics, 2003, etc.) has two concerns. The first is defining the role of symmetry as a key to understanding many of nature’s intimate relationships: how it reveals genetic superiority through the conspicuous display of energy required to produce such beauty; how it signals to creatures (in “a very basic, almost primeval form of communication”) to go about the important business of reproduction. Du Sautoy’s second concern regards the ways in which symmetry achieves economy, efficiency and stability in nature, as in the comb of a honeybee hive or in spheres like bubbles and raindrops, which place a premium on surface area relative to a given volume. The author’s prose is equally economical and elegant, but when he gets going on the math behind the symmetry he enters a realm dense with equations and jargon, likely to give the math-challenged a case of the fantods: “I dive into an explanation of how I think you could use Galois’s groups PSL(2, p) built from permuting lines, mixed with zeta functions to try to prove that there are infinitely many Mersenne primes…” Still, du Sautoy doesn’t leave readers dangling; he takes pains to explain the secret language of math, even if it requires considerable backing-and-filling to keep pace with him. Impressively, he conveys the thrill of grasping the mathematics that lurk in the tile work of the Alhambra, or in palindromes, or in French mathematician Évariste Galois’s discovery of the interactions between the symmetries in a group.
Not for the faint of mathematical heart, but a dramatically presented and polished treasure of theories.