Postgraduate Mathematics Blog
The book that (I believe) all mathematicians should have
9/2/21 - I want to have an opening blog post in each of my three sections before I publish my website, so I decided to share my favorite mathematics book I've come across: The Princeton Companion to Mathematics.
The book is almost an encyclopedia to (mostly) pure mathematics, but was constructed, and indeed intended, to be read cover-to-cover. What's so great about this intent is that the creators do their best to introduce background knowledge of each topic in an earlier section. They admit that it's not always possible, and Wikipedia is still a great "reference to the reference". But by-and-large the book is an easy-enough read for the early postgraduate in mathematics.
I'll admit as well, however, that at ~1000 sizeable pages, I'm still in the middle of digesting it. Already the wealth of knowledge I've gained is massive, and I expect it to continue. More or less, this book introduces the relevant topics of modern mathematics to a point where, when observing a conference/seminar presentation, most of the talk will still go over my head. However, it seems as though now I am versed in the subject enough to understand the motivation of each presentation, and I can see where it fits into the modern mathematical landscape.
Soon I'll be starting on the book's "sequel": The Princeton Companion to Applied Mathematics, which I can only hope will be just as good.