Unknown Quantity

X: The unknown quantity. But how did the idea of using letters to represent numbers in this way originate. That's one of the questions that John Derbyshire investigates in Unknown Quantity A Real and Imaginary History of Algebra. He looks at the work of early writers such as Diophantus, and describes how the development of the subject continued in the Arabic world. The book then moves on to the work done following the Renaissance in Europe, and in particular the solution of polynomial equations of one variable, leading to the work of Abel and Galois showing the insolubility of the quintic.

The second half of the book gets onto more recent developments in algebra, in particular the tendency towards abstraction which followed the work of Galois. Derbyshire looks at the origin of structures such as groups, fields, rings, vector spaces and many others.

The book has more maths in it than many of its type, but it shouldn't pose any problem to those with a reasonable grasp of high-school mathematics. This has the advantage that it gives a more complete description of the work done on solving equations, and the later parts give a useful taster of what is taught in university mathematics courses.