Several years ago (wow, it was 2008 – how time flies!), I wrote about The Princeton Companion to Mathematics. At the time I dubbed it, “the nicest math book I own”, and to this day, it has stood the test of time.

What not everyone might know is that Princeton University Press recently released a second companion. Unlike the first, which focused on a wide spectrum of, mostly pure mathematics, this new tome centers on applied mathematics.

Aptly named, The Princeton Companion to Applied Mathematics, it was released in late 2015 and my short and sweet take on this title is that it too is a remarkable book in its own right.

Due to its hefty size (over 1,000 pages) I’m still working my way through it, but I’m impressed with what I’ve seen so far. It is a great reference for sure and, honestly, I don’t know of any other math book quite like it.

The Princeton Companion to Applied Mathematics is a book that will be appreciated by mathematicians, as well as physicists, engineers, computer scientists, and virtually anyone with an interest in deepening their understanding of the lingua franca of the scientific world. One is able to do so thanks to the numerous examples in this book, which span an engaging array of different scientific disciplines and fields.

It is a companion in its own right, most definitely, but it also acts as a companion to the previous companion. Particularly because basic concepts from the first one are assumed in this second (and the editors admit as much in the book’s preface).

You might naturally wonder then, which one is better, and when it comes to this this point, I’m personally conflicted. On one hand, The Princeton Companion to Applied Mathematics is not the masterpiece of cohesive mathematical discussion that gives you an almost unified view of the field like the first companion was. Instead it is much more of a reference in that sense.

On the other hand, it is a delightful and approachable journey through the beauty, practicality, and interdisciplinary nature of applied mathematics. And I have a weakness for applied mathematics.

I think that the original companion is the better book, but you would do yourself a hefty disservice if you were not to get this second one as well.

My fingers are crossed that a companion to Statistics ends up being released at some point in the future – and I say that fully realizing what an epic multi-year, multi-author effort each of these books is. On the plus side, if they do, I should be done with The Princeton Companion to Applied Mathematics by then.