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

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 ...