Good Reads: The Princeton Companion to Mathematics
Next up on Good Reads: The Princeton Companion to Mathematics, edited by Fields medalist Timothy Gowers. This book is an exceptional resource! With over 1,000 pages of mathematics explained by the experts for the layperson, it's like an encyclopedia for math, but so much more. Have you heard about category theory but aren't sure what it is? There's a chapter for that! Seen the recent headlines about the abc conjecture but don't know what it's about? There's a chapter for that! Need a crash course in general relativity and Einstein's equations, or the P vs. NP conjecture, or C*-algebras, or the Riemann zeta function, or Calabi-Yau manifolds? There are chapters for all of those and more. Seriously, just browse through the table of contents. You'll see what I mean!
This is a great reference for those times when you want to know what [enter-new-math-here] is all about but don't have time to take an entire course on it. What's more, the articles are accessible to both undergraduates and professional mathematicians alike, and are full of examples, context, and background. You'll also find historical entries on great mathematicians of the past as well as the history of math itself. There's even a chapter devoted to the influence of math in other disciplines such as music and art. And the end of the book contains a wonderfully written piece called "Advice to a Young Mathematician" in which five mathematicians (including Sir Michael Atiyah and Peter Sarnak) offer advice to those just entering the realm of mathematical research - a true gem.
All in all, The Princeton Companion to Mathematics does an excellent job of providing both a detailed yet bird's-eye view of the landscape of mathematics. I highly recommend it!