The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry

For thousands of years mathematicians solved progressively more difficult algebraic equations, until they encountered the quintic equation, which resisted solution for three centuries. Working independently, two great prodigies ultimately proved that the quintic cannot be solved by a simple formula. These geniuses, a Norwegian named Niels Henrik Abel and a romantic Frenchman named Évariste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory.

The first extensive, popular account of the mathematics of symmetry and order, The Equation That Couldn't Be Solved is told not through abstract formulas but in a beautifully written and dramatic account of the lives and work of some of the greatest and most intriguing mathematicians in history.

What do Bach's compositions, Rubik's Cube, the way we choose our mates, and the physics of subatomic particles have in common? All are governed by the laws of symmetry, which elegantly unify scientific and artistic principles. Yet the mathematical language of symmetry-known as group theory-did not emerge from the study of symmetry at all, but from an equation that couldn't be solved.

For thousands of years mathematicians solved progressively more difficult algebraic equations, until they encountered the quintic equation, which resisted solution for three centuries. Working independently, two great prodigies ultimately proved that the quintic cannot be solved by a simple formula. These geniuses, a Norwegian named Niels Henrik Abel and a romantic Frenchman named Évariste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory.

The first extensive, popular account of the mathematics of symmetry and order, The Equation That Couldn't Be Solved is told not through abstract formulas but in a beautifully written and dramatic account of the lives and work of some of the greatest and most intriguing mathematicians in history.

Publishers Weekly

The idea of symmetry has been heavily deployed in recent science popularizations to introduce advanced subjects in math and physics. This approach usually backfires-mathematical symmetry is much too difficult for most laypeople to understand. But this engaging treatise soft-pedals it in a crowd-pleasing way. The title's formula is the "quintic" equation (involving x raised to the fifth power), the analysis of which gave rise to "group theory," the mathematical apparatus scientists use to explore symmetry. Inevitably, the author's attempts to explain group theory and its applications in particle physics and string theory to a general audience fall sadly short, so readers will just have to take his word for the Mozartean beauty of it all. Fortunately, astrophysicist Livio (The Golden Ratio) keeps the hard stuff to a minimum, concentrating instead on interesting digressions into human interest (e.g., the founder of group theory, Evariste Galois, was a revolutionary firebrand who died in 1832 at age 20 in a duel over "an infamous coquette"), pop psychology (women have more orgasms when their partners have symmetrical faces), strategies for finding a soul mate and some easy math puzzles readers might actually solve. The result is a somewhat shapeless but intriguing excursion. Photos. Agent, Susan Rabiner. 50,000 first printing; 9-city author tour. (Sept.) Copyright 2005 Reed Business Information.

Mario Livio is a senior astrophysicist and the Head of the Office of Public Outreach at the Space Telescope Science Institute (STScI) in Baltimore, Maryland. He is the author of The Golden Ratio, a highly acclaimed book about mathematics and art for which he received the International Pythagoras Prize and the Peano Prize, The Equation That Couldn't Be Solved, and The Accelerating Universe.  He lives in Baltimore, Maryland.