I've been working on a problem for years. It's particularly vexatious, but some pieces fell into place think week and a solution is nearly in hand. It helps that I have a false deadline to toil under. Had, anyway; I digress.<p>I'm a daydreaming mathematician who works with very pragmatic physicists and engineers. I caught wind that the physicists have an unsolved problem, so rather than toil at my project, I spent the morning reading wikipedia in search of obnoxious questions for physicists, and split the afternoon between asking those questions and coding up my putative solution to the problem I'm supposed to solve. It fails.<p>Mulling over cryptic statements from physicists on the bus, a thought strikes in a flash. I get off the bus, talking to myself out loud, repeating the new inspiration until issues arise and solutions follow. I've been looking at it wrong.<p>When I arrive home, I understand that my new inspiration is the right approach, to a problem that isn't blocking my deadline. Another problem, just as hard and just as old, is. A solution strikes me in a flash, and I know I won't sleep that night, because it's still too big to fit the complete solution in my head.<p>There's a point where it's a bad idea to procrastinate with learning. But used judiciously, it distracts from the challenge -- the problem-solving processes are still running in the background but the foreground is engaged and full of wonder.