How do you solve hard problems if you can't make incremental progress?
leif: For hard (math) problems, which is where I find it hardest to make incremental progress, I usually just walk away, make myself some tea, or look for another problem.  Anything that stops me from consciously thinking about it allows my subconscious to sort through the information, and eventually, the answer will hopefully float to the top.  If that doesn't happen after long enough, when I do go back, I'll at least have gotten out of the circles I had been thinking myself into.