How do you foster creativity?

The following was on a bulletin board in the art class at the middle school where I taught.

Because I wanted my math class to be more like that art class - learners exploring the boundaries of their knowledge and skills - I posted a copy in my classroom.

Twenty years later, a copy is now thumbtacked to my office door. It reminds me that fostering creative problem solvers is one of my primary goals as a teacher of teachers. Some of the ideas may not be reasonable, but creativity sometimes requires a certain suspension of rationality.