Excuse a copy-posting that is really designed as a jumping-off point for some other issues, such as "attention" and "problem-solving".
Heuristic is the art and science of discovery and invention. The word comes from the same Greek root as "eureka", which means "I find". A heuristic is a way of directing your attention fruitfully. The term was introduced by Pappus of Alexandria in the 4th century.
The mathematician George Polya popularized heuristic in the twentieth century in his book How to Solve It. He learned mathematical proofs as a student, but didn't know how mathematicians think of proofs, nor was this taught. "How to Solve It" is a collection of ideas about heuristic that he taught to math students: ways of looking at problems and casting about for solutions.
Some commonplace heuristics, all from How to Solve It:
- 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. This is the "inventor's paradox": a more ambitious plan may actually have more chances of success.