Though it's obviously important to put the hours in to understand your subject (the brain can only work with what it's given), a creative or insightful solution arises from those pseudo-random mental firings that are beyond our conscious control. The answer to a hard problem might be a mental path that your brain hasn't formed yet, making trying to think your way through to it a fruitless endeavor. At a certain point, it's important to step back, relax, and let your subconscious create more grist for the mill

I've got mixed opinions on this. On the one hand, I agree that thinking "harder" doesn't do anything directly useful, even if it maybe primes later useful thoughts. I even agree that creating anything genuinely new is heavily dependent on coincidence, in the sense that accidents can shorten a search in ways that intentional searching cannot.

However, on the other hand, it's also clear that failure to solve problems or get good ideas is very often a failure to consciously ask the right questions of your subconscious. A lot of times, the thing stopping people is that they simply haven't bothered to ask their brains for a solution in the first place... or that, having asked, they don't keep System 2 quiet enough to prevent verbal overshadowing of the search results coming back from System 1. (i.e., the real reason why brainstorming isn't supposed to include criticism.)