Poincaré and Hindemith cannot possibly be right. If they are spending their days actively thinking about other things, their brains are not unobtrusively solvi

Poincaré and Hindemith cannot possibly be right. If they are spending their days actively thinking about other things, their brains are not unobtrusively solving deep mathematical problems or composing complex pieces of music, perhaps over days or weeks, only to reveal the results in a sudden flash. No, the brain is reconfiguring itself during REM sleep to be more able to solve the sort of problem that you had been working on. It doesn't happen when you're thinking about other things, particularly. There's a ton of research relating REM sleep to improved skill at problem solving and Poincaré was certainly sleeping on the problems he was trying to solve.