THE EQUATION THAT COULDN’T BE SOLVED

Evolution favors symmetry. So do people. So does just about everything in the universe.

Astrophysicist Livio (The Golden Ratio, 2002, etc.), no slouch at mathematics himself, crafts an entertaining exploration of how the laws of symmetry have shaped our chaotic little world, and how they inform our appreciation of art and music. One of his great heroes is someone whom mathematicians with a historical bent know well: the French wunderkind Évariste Galois, generally held to be one of the great minds in a field dominated by great minds and the progenitor of what is now called group theory. Galois (1811–32) was a brilliantly troubled kid who loved mathematics, which returned the favor, and a woman who did not. The young genius died in a duel whose occasion has long mystified historians. His last, supremely memorable, words were: “Don’t cry, I need all my courage to die at twenty.” Before he died, however, Galois impacted the course of history. Among other accomplishments, he formed a new branch of algebra known as Galois theory. Livio’s history is elegant but, suffice it to say, not for the innumerate or the scientifically faint of heart: it helps to know something of quadratic equations and other high-order concepts that would have been second nature to Galois but are harder going for us lesser souls. Galois’s research, Livio writes, helped turn other scientists to thinking about symmetry, which led to Einstein and quantum theory and other wonders of the modern age. It’s a complicated tale, with learned asides on the nature of creativity and, in the bargain, a convincing argument many years after the fact concerning the identity of Galois’s killer.

A lively companion to Bulent Atalay’s Math and the Mona Lisa (2004), John Barrow’s Book of Nothing (2001) and other recent popular studies in mathematical thought.