Unknown Quantity: A Real and Imaginary History of Algebra
John Derbyshire
This is allegedly written for the educated layman but I know few who could grasp (or care about) field vs group theory, rings, tensors or manifolds much less "movements" like "Intuitionism" and "Constructivism". The author thankfully does not attempt a deep inquiry into every crevice of modern math but instead presents a breezy if sometimes obtuse overview.
Even mathematicians can be informed here, particularly on the personalities. The author attempts to stay within the bounds of algebra while explaining that various disciplines necessarily cross lines with geometry, topology other algebras. The author thankfully includes illustrations although many more are required. Many times, it was next to impossible trying to picture the prose. Then again, much of the latter part of the book is conceptual without basis in reality - parallel lines that meet, many dimensions (presented in three, of course), complex numbers, vectors, etc. Many times, the creation of the mathematical concept (matrix, field permutation, etc) is as astounding as the principles by which they are solved. My Grade - B+
