Heuristic

[How to know how to do it.]
A heuristic is a replicable method or approach for directing one's attention in learning, discovery, or problem-solving. It is originally derived from the Greek "heurisko" (εὑρίσκω), which means "I find". (A form of the same verb is found in Archimedes' famous exclamation "eureka!" – "I have found [it]!") The term was introduced in the 4th century CE by Pappus of Alexandria.

The study of heuristics is sometimes called heuristic, but more often called heuristics. Heuristics, in this sense, is treated as a singular, like physics or mathematics.^[1]

The mathematician George Pólya popularized heuristics in the mid–20th century, in his book How to Solve It. He learned mathematical proofs as a student but he did not know, nor was he taught, the way mathematicians arrived at such proofs. How to Solve It is a collection of ideas about heuristics that he taught to maths students – ways of looking at problems and formulating solutions.

How to Solve It describes the following common and simple heuristics:

• 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).

Adjective: (e.g. "is it heuristic?") applies to research or intellectual pursuits. For example, a good theory or idea may be heuristic in that it attempts to find something out or stimulates further investigation. When critiquing theories in the sciences good theories tend to be heuristic....

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