What Are Heuristics (in Math)?

[SF49erfan]

Some math advice/tips guides say that having a knowledge of heuristics can assist with mathematical problem-solving.

I'm trying to get better at the subject over the summer before my first year of uni coming in the fall. I don't think, however, that I know what is meant when people use the term "heuristics." I'm wondering if someone wouldn't mind with a definition of this term and perhaps an example?

Greatly appreciate your help! TVM.

 

[HallsofIvy]

You are asking for the definition of a word. Is there a reason why you could not look it up yourself?

Checking Wikipedia gives:
Heuristic (Template:(IPAc-en); Greek: "Εὑρίσκω", "find" or "discover") refers to experience-based techniques for problem solving, learning, and discovery that give a solution which is not guaranteed to be optimal. Where the exhaustive search is impractical, heuristic methods are used to speed up the process of finding a satisfactory solution via mental shortcuts to ease the cognitive load of making a decision. Examples of this method include using a rule of thumb, an educated guess, an intuitive judgment, stereotyping, or common sense.

In more precise terms, heuristics are strategies using readily accessible, though loosely applicable, information to control problem solving in human beings and machines.

 

[Stephen Tashi]

and perhaps an example?

For example, figures with a given perimeter tend to have the most symmetrical shape that is allowed by other constraints. The plane figure with largest are for a given perimeter is a circle. The 4 sided polygon with largest area for a given perimeter is a square.

Another example, applying trigonometry to geometry problems tends to involve triangles, especially right triangles. So if you are tyring to figure out the length of a line segment in a diagram you should look for triangles. If you don' see any you should extend lines in the figure to make triangles and draw lines perpendicular to other lines to attempt to form right triangles.

 

[Ackbach]

Check out How to Solve It, by George Polya, and How to Solve It: Modern Heuristics, by Michalewicz and Fogel. Both are great on problem-solving and heuristics.