George Pólya (December 13, 1887 – September 7, 1985, in Hungarian Pólya György) was a Hungarian mathematician.

Pólya's four principles

First principle: Understand the problem

This seems so obvious that it is often not even mentioned, yet students are often stymied in their efforts to solve problems simply because they don't understand it fully, or even in part. Pólya taught teachers to ask students questions such as:

• Do you understand all the words used in stating the problem?


• What are you asked to find or show?


• Can you restate the problem in your own words?


• Can you think of a picture or a diagram that might help you understand the problem?


• Is there enough information to enable you to find a solution?


• Do you need to ask a question to get the answer?

Second principle: Devise a plan

Pólya mentions (1957) that there are many reasonable ways to solve problems. The skill at choosing an appropriate strategy is best learned by solving many problems. You will find choosing a strategy increasingly easy. A partial list of strategies is included:

• Guess and check


• Make an orderly list


• Eliminate possibilities


• Use symmetry


• Consider special cases


• Use direct reasoning


• Solve an equation

Also suggested:

• Look for a pattern


• Draw a picture


• Solve a simpler problem


• Use a model


• Work backward


• Use a formula


• Be creative


• Use your head/noggen

Third principle: Carry out the plan

This step is usually easier than devising the plan. In general (1957), all you need is care and patience, given that you have the necessary skills. Persist with the plan that you have chosen. If it continues not to work discard it and choose another. Don't be misled, this is how mathematics is done, even by professionals.

Fourth principle: Review/extend

Pólya mentions (1957) that much can be gained by taking the time to reflect and look back at what you have done, what worked and what didn't. Doing this will enable you to predict what strategy to use to solve future problems, if these relate to the original problem.