Friday, December 4, 2009

Unknwon Quantity

Book Review : Unknown Quantity
Author : John Derbyshire
My Rating : 4 out of 5 star

The complete title of the book is "Unknown Quantity: A Real and Imaginary History of Algebra".

John Derbyshire is a brave author. He first had the audacity to write Prime Obsession, about Riemann Hypothesis and make it accessible to an average reader. He was immensely successful. In this book, he is trying to pull off the same trick about entire Algebra.

He starts with very primitive - by today's standards, but no small feat then - algebra that existed in Fertile Crescent. From there, he proceeds to solving general polynomial equations and complex numbers. Things get more abstract, as he moves on to vector spaces, groups, fields and other advance topics such as category theory.

This is a significantly harder undertaking. He has to cover a lot of history and a lot of math. Derbyshire is a master at mixing these two aspects. Great anecdotes and biographic sketches are delightfully mixed with mathematical explanations. We all learned algebra in school. But we hardly learned anything about the mathematicians who advanced the theory. This book will fill many, if not all of those gaps.

But eventually the scope of the topic is just too immense to be covered in one book. I think that will restrict the target audience. You have to be really interested in math to enjoy this book. I am, and long time ago when I was doing my graduate studies, algebra was my favorite subject. Still that really was long time ago, and it was not easy to follow the latter half of the book. But if you want to learn why groups and fields are important (and interesting), this is very good gentle introduction.

This is a wonderful book, but you have to be willing to work with it. Even if you just want to browse the historical sections and skip the math, there is a lot to enjoy here.

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