Techniques useful for people who are attempting to solve a difficult problem:
- RestYourMind
- TrustYourHunches
- Read and understand the instructions given for mental techniques outlined in ComputerAssistedProofFindingMethod, experiment with applying them to easier problems you want to solve. In particular, make sure to get enough mental rest and to avoid trying to force your mind to finish a task.
- Think about your mind and the way you think. GodelEscherBach? has some very interesting ideas on this subject.
- Think of your mind as a community, and strive to ensure that this community collaborates effectively. Timothy Gowers touched on this in his [experiment], where he described the "rules of engagement" that he uses within his mind; perhaps if you adopt his you might think as effectively as he does. The best general-purpose rule-set I know of is described in depth at Meatball:MeatballWiki. I imagine that here we will use these prototypes as a starting point to develop a set of rules appropriate for both this collaborative effort and for the minds of the people within it.
- BeLazy?, aiming to achieve your goal with as little apparent effort as possible.
- StriveForIntuitiveUnderstanding?, to allow your subconscious mind access to the problems you face.
- practice applying the IncompleteProofTechnique to problems which seem not quite beyond your ability to solve them.
- If you reach an impasse, find a way to frame the impasse as a problem to be solved, and use the IncompleteProofTechnique to attempt solving it.
- If a problem becomes too difficult, put it aside and work on something else. Two possibilities: you could discover a useful insight elsewhere, or it might just be too difficult for you to solve.