In this post we ramble on about Riemann surfaces, the uniformization theorem, universal covers, and two secret (or not-so-secret!) techniques that mathematicians use to study a given space. Our intent is to provide motivation for an upcoming mini-series on the automorphisms of the unit disc, upper half plane, complex plane, and Riemann sphere.

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.