An interesting history of algebra, but not as good as Prime Obsession. ( )

Really nice history of mathematics. The author touches upon most algebraic topics including vectors, groups, and fields, and does a good job giving examples and motivation as to why each area was interesting to the mathematicians of the time. Anyone who enjoyed high school algebra should be fine with the level of mathematics discussed. Also check out the author’s previous book “Prime Obsession” which I found slightly more difficult but also more engaging. ( )

John Derbyshire's "Unknown Quantity" is a readable, fascinating history of algebra. In the process of teaching the history of the subject, the author cannot but help teach the reader a bit of the substance. Derbyshire is not one of those authors who fears that any equation will reduce his readership. How could he be - he is writing about the study of equations.

I'm not up to the effort to transcribe the most interesting things in the book in algebraic form, so I'll try to put some of the ideas in verbal English. Along the way, I learned that "i" has a rather simple square root, namely [1 over the square root of 2 times (1 over the square root of 2 times i)]. Multiply it out for yourself - it works. Moreover, any number has n nth roots that are fairly easy to determine geometrically in the complex plane: they are all the same magnitude, so they all lie equally spaced on a circle around the origin, the radius of which is the module of the real nth root of the original number.

We also learn that "an algebra" is a vector space in which 2 vectors can not only be added, but also multiplied, giving another vector as the result.

Determinants are numbers, but matrices (which look an awful lot like determinants) are merely arrays. Nontheless, matrices can be manipulated in many of the same ways as numbers.

Derbyshire also covers fields, groups, set theory, manifolds, and Riemann spaces. By the end of the book, the material has become dauntingly abstruse. In fact, in writing about a modern algebraist, Alexander Grothendieck, the author confesses, "...I myself cannot understand much of his work" but the comments of several emminent mathematicians "are sufficient to persuade me of his genius."

The book remains an eye-opener for the interested layman with a mathematical bent.

(JAB) ( )

John Derbyshire writes a good book! And for those not opposed to learning the history of a concept, and a little of the concept itself, I highly recommend it.

If you make it to at least high school there is a very good chance you will be confronted with the concept of algebra. while you may or may not learn this concept, it is absolutely pervasive in everyday life and, like it or not, if you are over th eage of 13 or so, you use it fairly regularly.

Algebra has developed over thousands of years from the merchant figuring out a procedure to repeatedly assign values to different quantities of the same ingredient, to abstract applications in topology, quantum physics or number theory.

When you read Unknown Quantity, you will learn some very interesting history, and by default will learn a little algebra along the way. I would love to see a similar work by Derbyshire on the calculus! ( )

This book was interesting stories about history interspersed with very badly explained math. It's definitely not for someone who isn't a mathematician, but I feel real mathematicians would probably be bored by all the math. So I'm not sure who would like the whole thing. I read it mostly for the interesting history, which was generally well done. ( )