
Ian Stewart
Why Beauty is Truth
Although symmetry seems to be predominantly a geometrical property, Why Beauty is Truth: A History of Symmetryshows that it really gained its importance in mathematics and physics via a different route  that of the solutions of polynomial equations. Ian Stewart starts at the time of the Babylonians, who were able to solve quadratic equations, and moves through the solutions of the cubic and quartic in the Renaissance. Hence we get to the work of Abel and Galois, who demonstrated the insolubility of the quintic by radicals. This was the start of group theory, and the rest of the book shows how this had much influence in later mathematics and physics.
Stewart shows how Sophus Lie applied the notion of a group to continuous systems. He describes the work of Einstein, as well as the development of quantum theory, showing how symmetry has a natural place in modern physics. There is also a chapter on Edward Witten and Superstring theory. Stewart also clearly has a soft spot for quaternions and octonions, showing how these almost forgotten structures may yet play an important part in physics.
The book gives prominence to biographies of the mathematicians concerned, and some people might feel that there isn't enough maths, however I felt that Stewart struck the right balance, and so kept the book accessible to a wide readership.