38 of 48 people found the following review helpful
This review is from: The Princeton Companion to Mathematics (Hardcover)
I learned about this book while I was reading a blog post on Timothy Gower's first blog post.
I have read quite a bit and I think is a wonderful book. While it does lack a lot of detail. It does excel at giving a general view at what mathematics is all about.
If you ever wonder
What is mathematics?
or what do mathematicians do. This book is a good start. The book is a compilation of essays in different topics in mathematics many written by first class mathematicians including Timothy Gowers and Terence Tao both recipient of the Fields Medal in mathematics the equivalent to the Nobel prize and many others.
I believe the book should be part of any mathematicians or aspiring mathematician library.
The book covers mathematical history and also mathematics itself. Great parts of the book could be read by high school students but for some other parts is necesary to have at least and undergrad degree to be able to understand it. I wonder if a new Ramanujan found this book if he will be able to reivent the whole of mathematics from this book?
Someone asked in Prof. Gower's Blog What knowlege prerequisites are required to be able to profit from this book and what follows is part of the answer that professor Gower's gives and I believe it could be also very useful to others considering buying this book.
"That's a good question and one that doesn't have a straightforward answer. When we started out on the book, we hoped to have a more or less uniform level of difficulty throughout. But it fairly soon became clear that that was not practical, since some parts of mathematics are much harder to explain than others, so we modified our goal to one of trying to explain everything as accessibly as possible (and ideally more accessibly than one could easily find elsewhere), even if that level of accessibility varied from article to article.
The result? I would say that if you have done high-school mathematics and were good at it, then you will understand at least some of the book, enough to make it worth reading if you have a genuine interest in the subject, a wish to learn more, and a willingness to think quite hard as you read. If you are taking university courses in the subject, then the proportion you will understand will be much higher: some parts will be heavy going, but other parts will give you very useful insights into the concepts that are being thrown at you all the time. And if you are a graduate student or professional mathematician, then the book will be a very helpful resource if you are interested in getting at least some understanding of parts of mathematics that are not your own speciality."
My simplest advice is
If you love mathematics or like mathematics this is a book to get and treasure!