I know about famous problems like the Riemann Hypothesis, Goldbach's Conjecture, the Poincaré Conjecture, and a few others. I assume only a very small number of highly experienced mathematicians actually work directly on these kinds of famous, centuries-old problems. So what does the majority of research mathematicians actually work on? What kinds of problems do they spend their time solving? What do those problems look like, and how do they choose them? Are they mostly creating new methods, extending existing theorems, or working on completely different kinds of questions?