Heuristic is the art and science of discovery and invention. The word comes from the same Greek root as "Eureka": εὑρισκω, 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:
Grammatical note: The name of the topic is heuristic (not "heuristics"), a particular technique of directing your attention toward discovery is a heuristic, two or more of these are heuristics, and the adjective for "pertaining to how something is discovered" is heuristic.
For instance, people may tend to perceive more expensive beers as tasting better than inexpensive ones. This finding holds true even when prices and brands are switched; putting the high price on the normally relatively inexpensive brand is enough to lead experimental participants to perceive that beer as tasting better than the beer that is normally relatively expensive. One might call this "price implies quality" bias.
Much of the work of discovering heuristics in human decision makers was ignited by Amos Tversky and Daniel Kahneman, who shared an important influence on Behavioral finance. Critics led by Gerd Gigerenzer focus on how heuristics can be used to make principally accurate judgments rather than producing cognitive biases - heuristics that are "fast and frugal".
Lesser-known:
For instance, in the United States the Legal drinking age is 21, because it is argued that people need to be mature enough to make decisions involving the risks of Alcohol consumption. However, assuming people mature at different rates, the specific age of 21 would be too late for some and too early for others. In this case, the somewhat arbitrary deadline is used because it is impossible or impractical to tell whether one individual is mature enough that society can trust them with that kind of responsibility.
The same reasoning applies to patent law. Patents are justified on the grounds that inventors need to be protected in order to have incentive to invent (or else suffer the Tragedy of the commons if anyone could use their idea). So, it is argued that it is in the best interest of society to issue inventors a temporary government-granted Monopoly on their product so they can recoup their investment costs and make economic profit for a limited period of time. In the United States the length of this temporary monopoly is 20 years from the date the application for patent was filed, though the monopoly does not actually begin until the application has matured into a patent. However, like the drinking age problem above, the specific length of time would need to be different for every product in order to be efficient, but the 20-year number is used because it is difficult to tell what the number should be for any individual patent. More recently, some including Lawrence Lessig have argued that patents in different kinds of industries such as software patents should be protected for different lengths of time.
In Computer science, a heuristic is a technique designed to solve a problem that ignores whether the solution can be proven to be correct, but which usually produces a good solution or solves a simpler problem that contains or intersects with the solution of the more complex problem.
Heuristics are intended to gain computational performance or conceptual simplicity potentially at the cost of accuracy or precision.