I recently got a hold of what I consider to be the nicest mathematical book in my collection. As a matter of fact, it’s the nicest book I own, period – even though I posses bookshelves teaming with terrific titles on mathematics, science, programming, computer science, photography and so on. The book I’m talking about is The Princeton Companion to Mathematics. If you are in an absolute rush, the short version of my post today is, buy this title. You don’t have to click on the link with my referral if you don’t want to, seriously just pick up a copy of this book, I can guarantee you that it will be love at first sight.
I’d like to claim that I’ve read it cover to cover. But I haven’t. At 1014 pages (and a hefty five and a half pounds), this recently published hardcover tome will probably take me a while to properly read through in its entirety. It can serve as a reference that can be randomly accessed if you so chose, but from what I’ve read so far, I’m extremely impressed and am eager to pursue my way through it systematically. It will be time really well spent, and dare I say, a life changing experience. This is the book to bring on a proverbial desert island, if you were allowed only one title.
The Princeton Companion to Mathematics is not only a beautiful book from an aesthetic standpoint, with its heavy, high quality pages and sturdy binding, but above all it’s a monumental piece of work. I have never seen a book like this before. It rigorously illustrates the (pure) mathematical field while remaining as accessible as possible to the general reader. There is no mathematician in the world who, upon reading this book cover to cover, would not have learned a great deal from it. And I’m sure this includes Timothy Gowers himself, who was the book’s Chief Editor and who brilliantly managed to coordinate a team of world class experts to cover (again in an accessible manner) their respective fields of expertise. Such experts not only are the best mathematicians alive today in their respective areas of expertise, but are also absolutely wonderful teachers who have the uncanny ability to divulge information in a understandable manner, under the editorial guidance of Professor Gowers. Timothy Gowers, by the way, also has a blog, which contains discussions about the book and a helpful errata.
This book is what I now consider to be the bible of mathematics, and unlike a typical reference or encyclopedia, The Princeton Companion to Mathematics never fails to provide a sense of unity and cohesion, both of which are essential if you want to truly provide an (nearly) complete panorama of a subject. While all the basics are well explained with the clarity and simplicity of really good popular science, this tome doesn’t skimp on details or theorems when it comes to highly advanced topics that few people are familiar with. The style remains geared towards providing a good introduction to each subject, as opposed to a PhD thesis, and as such it will prove useful to the ambitious high school student, as well as professional mathematicians or graduate students. And as if all this wasn’t enough, they managed to squeeze in a biographical overview of the most important historical mathematicians from Pythagoras to Bourbaki, as well as a respectable (yet not overly comprehensive section) about applied mathematics, and math’s influence on other disciplines.
I believe this is the kind of book that will still be is use a hundred years from now, even though by then it will be slightly outdated. This title is destined to be fully revered as a classic and monumental review of the subject of pure mathematics. I salivate like Pavlov’s dogs at the idea of the amount of fun I will have exploring this book, which will no doubt expose my ignorance about several key areas of math, and yet at the same time help me to remedy such things.
This Christmas, give yourself a great gift and get this book. If you are looking for the perfect gift for people who’re interested in mathematics, this is the right book. If you are a parent, I especially encourage you to pick it up for your son or daughter, it could change their lives. Ladies, your geeky boyfriend will likely propose to you if you put a copy under the tree. Jokes aside, The Princeton Companion to Mathematics makes for a great read to start 2009 off with.