The Princeton Companion to Mathematics

Product Reviews

Human treasure
Seldom one could identify this kind of object in human history. This book is treasure of human beings. It collects first-rate insights from first-rate mathematicians of human world, in the way of first-rate (I would say the editor has devised such a wonderful 'function' to transform the input to such output).

Anyone seriously interested in mathematics and any college student shall own this book. It is the best introduction to mathematics than any other book because it contains many lens rather than one. One could be exposed to different perspectives in the book, rather than an algebraist's, geometer's, analyst's, or a number theorist's view. T. Apostol's Calculus is great. But it's not the best math introduction because it's through a great analysis teacher's len and it purely focuses on rigorous analysis way of seeing and doing math. So for others, you need this book.

And this book is better than encyclopedia because it expresses the authors' personal insights, which are all first-rate. We love insights/wisdom more than cold facts. Facts of mathematical objects could be found anywhere. But how do some first-class mathematicians "see" such objects? How do they explain the object? This may be the gem they learned/reflected during their past years (and successful ones). Now some of the gem is here in the book.

An apprentice needs a general master for guidance on the overall picture of each specific field that the apprentice could further study from masters of each specialty. This book is the general master to math beginners. It opens a door to the math world. What a wonderful world.
[2010-08-23]

Good content, poor format
This is a review of the Kindle version of the book. I own the physical version as well, and heartily agree with reviews of the overall excellent content, clear explications and wonderful cross-references in the original volume.

I do not give the Kindle edition five stars for two reasons: The frequent and highly relevant cross-references, which are ripe for an electronic hypertext cross-linking capability, are not at all exploited on the Kindle. This is, I am certain, far more the fault of the publisher than the Kindle device itself. One of the things I was looking forward to with the ebook version was being able to skip around dynamically, guided by the cross-linked articles. Now, that is very difficult. The only way to accomplish it is via manual searches.

Also, many of the more esoteric symbols, such as matricies or entities with super/sub-scripts seem to be "washed out". This isn't a terrible issue, as they are still legible.

Overall, the lack of hyperlinked cross-references is the most significant shortcoming.

For such an expensive ebook, one would have expected more attention to detail.
[2010-08-13]

For the Expert Only
Very briefly: This volume is about as complete a compendium of things mathematical as one will currently see. But it is for the expert, the man or woman who is versed in (pure!) mathematics. It is completely over the head and beyond persons like me who have some knowledge of applied math or accounting or business math. I therefor advise anyone who is like me to save a bunch of cash and, if interested in math, buy instead some popular exposition written for the likes of us.
[2010-08-10]

Kindle version technically poor
This is a wonderful book. I have the Kindle version, but disappointingly found that the
purely mathematical portions, i.e., equations, etc. has not been incorporated into the text.
Equations, etc. appear to be low resolution images that are barely readable and need to be
"double tapped" and then appear independent of the text and are nearly pix elated.
This is obviously an example of a great book that was converted to the e-book version
in haste and has proven an obstacle to reading it in this format.
Too bad because this practice will set back adoption of the e-book revolution.
My advice: Do not buy it in the Kindle format.
[2010-07-18]

An authoritative reference with encyclopedic scope
This enormous book covers the world of mathematics authoritatively and deeply: Different sections are written by experts in the specific area. Nonetheless, each section is reasonably comprehensible.

It would be unreasonable to try to read through the entire book end-to-end, although you could do that if you have nothing else to do for a year. However, if you like reading and thinking about mathematical ideas, this book will be a great place to get up-to-speed on any topic you may stumble across. Each section also has suggestions for further reading, so you can keep going beyond what has been included in the book.

If you enjoy mathematics beyond the recreational level, this book deserves a place in your personal library.
[2010-07-14]