Four Principles
How to Solve It suggests the following steps when solving a mathematical problem:
- First, you have to understand the problem.
- After understanding, then make a plan.
- Carry out the plan.
- Look back on your work. How could it be better?
If this technique fails, Pólya advises: "If you can't solve a problem, then there is an easier problem you can solve: find it." Or: "If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?"
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Famous quotes containing the word principles:
“The mode of founding a college is, commonly, to get up a subscription of dollars and cents, and then, following blindly the principles of a division of labor to its extreme,—a principle which should never be followed but with circumspection,—to call in a contractor who makes this a subject of speculation,... and for these oversights successive generations have to pay.”
—Henry David Thoreau (1817–1862)
“Only conservatives believe that subversion is still being carried on in the arts and that society is being shaken by it.... Advanced art today is no longer a cause—it contains no moral imperative. There is no virtue in clinging to principles and standards, no vice in selling or in selling out.”
—Harold Rosenberg (1906–1978)