Book Review: The Equation That Couldn't Be Solved

The Equation That Couldn't Be Solved, by Mario Livio (amazon), is about the 18th century French mathematician, Evariste Galois, who invented Group Theory en route to proving that certain kinds of equations cannot be solved by formula. It is also about the role of symmetry in nature, and how Galois' invention, by providing the mathematical tools needed to reason about symmetry, has become a key tool in unlocking the secrets of the universe.

Unfortunately, this summary may be more focused and purposeful than Livio's book. The sweep of this short book (less than 300 pages) is ambitious -- it delves into the history of mathematics, the French Revolution, Relativity, String Theory, music, evolution and the role of symmetry in mate selection. I was never sure whethere Livio's intention was to reveal Galois' genius, convince the reader that symmetry drives the nature of the universe, or demonstrate the broad applications (and they are indeed broad) of Group Theory. The overall effect is a little scattered.