One of the things that mathematicians spend a lot of their time doing is trying to understand and learn new things. And while there are a lot of different methods for doing this, anecdotally two things that mathematicians do more than other people.
Gerhard Paseman already mentioned multiple viewpoints. Reading from multiple sources and try to approach things from multiple directions. (Often I feel, especially with students, that when they hit a wall with a text they're trying to learn from, they're not aware that certain aspects may be covered better elsewhere or that a different point of view really might make a difference.)
Even more important, though, is taking a step back and let things simmer, without actively thinking about them for more than a little at a time. There's a cycle of work and passive thinking that needs to take place. (Of course, this goes along with the famous story about Poincare's moment of inspiration while stepping on a bus.)