Heuristics are the strategies derived from previous experiences with similar problems. These strategies depend on using readily accessible, though loosely applicable, information to control problem solving in human beings, machines and abstract issues.[3][4]
The most fundamental heuristic is trial and error, which can be used in everything from matching nuts and bolts to finding the values of variables in algebra problems. In mathematics, some common heuristics involve the use of visual representations, additional assumptions, forward/backward reasoning and simplification.[5] Here are a few commonly used heuristics from George Pólya’s 1945 book, How to Solve It:[6]
If you are having difficulty understanding a problem, try drawing a picture. If you can't find a solution, try assuming that you have a solution and seeing what you can derive from that ("working backward"). If the problem is abstract, try examining a concrete example. Try solving a more general problem first (the "inventor's paradox": the more ambitious plan may have more chances of success).