
Mario Livio
The equation that couldn't be solved
Symmetry has always played a large part in the development of mathematics. This book shows how ideas of symmetry were used to settle a long standing question  for which polynomial equations could a formula be found for their roots? The book gives biographical details of the mathematicians working on this problem, and in particular the tragic story of Evariste Galois who was killed in a duel at the age of twenty, having spent the night before hurriedly writing down some of his most important mathematical ideas. Thus Livio makes an abstract mathematical topic accessible to the reader with no previous knowledge of the subject.
Galois work was the start of Group theory, which is the mathematical description of symmetry. Livio goes on to show the important part this theory has come to play in the study of physics, for instance Noether's theorem which relates symmetries to conservation laws, and the use of group theory in particle physics.
My one criticism of the book is that sometimes Livio seems to discuss a subject just of the sake of it. Of course symmetry gives a wide scope for discussion, and some people might enjoy the variety, but I felt that a more focussed approach would have been better.