I've had similar experiences to nostrademons. I often crack hard problems in the groggy netherworld just as I'm going to sleep or just as I'm waking up (or duri

I've had similar experiences to nostrademons. I often crack hard problems in the groggy netherworld just as I'm going to sleep or just as I'm waking up (or during an afternoon nap). Showers and long walks are also good for this purpose. I mainly dream about software these days, but I had similar experiences in college and grad school with physics. Freshman year I figured out the orbit in an inverse quartic potential during a nap (warning: you pass through the---bang!---center of force), and in grad school I unlocked the last remaining problem in my Ph.D. thesis during a one-hour random walk around campus. Incidentally, all this contributes to my conclusion that I'm not well-suited to a normal job. Even if I could get an employer to accept intellectually that they should pay me to take naps and go for long walks, I don't think they could ever really come to terms with it emotionally. Whereas the cofounder of my last startup probably never even noticed I occasionally napped and that I spent half my time walking around town; if he did, he certainly didn't care.