The Power of Symmetry Why Beauty is Truth: A History of
Symmetry. Ian Stewart. xiv + 290 pp. Basic Books, 2007. $26.95.
Symmetry is a fundamental concept pervading both science and
culture. In popular terms, symmetry is often viewed as a kind of
"balance," as when Doris Day's character in the 1951 movie On
Moonlight Bay insists that if her beau kisses her on the right
cheek, then he should kiss her on the left cheek too. But in
mathematics, symmetry has been given a more precise meaning. In
his new history of mathematical symmetry, Why Beauty Is Truth,
Ian Stewart gives this definition: "A symmetry of some
mathematical object is a transformation that preserves the
object's structure." So a symmetrical structure looks the same
before and after you do something to it. A butterfly looks the
same as its mirror image. The (idealized) wheel of a car may
look the same after being rotated on its axle by 90 degrees (or
possibly by 72 or 120 degrees, depending on the particular
design). Although mathematical symmetry m