Aphorisms by George Polya, Part I
George Polya was born in Budapest, but left Europe for America in 1940. He became a professor of mathematics at Stanford University and remained at Stanford for the rest of his life. He worked on a wide variety of mathematical subjects but is best remembered for his classification of “wallpaper patterns,” the 17 symmetry groups found in any given plane. Polya’s description of these patterns fascinated the artist M.C. Escher, who based many of his works on these tessellations.
Polya is also remembered for his ideas about problem-solving and how it should be taught and carried out. In his book How To Solve it, Polya created a set of heuristic strategies for solving mathematical problems. He even cited a small collection of proverbs that he felt represented his approach.
“Solving problems is a fundamental human activity,” he wrote. “In fact, the greater part of our conscious thinking is concerned with problems … Some people are more and others less successful in attaining their ends and solving their problems. Such differences are noticed, discussed, and commented upon, and certain proverbs seem to have preserved the quintessence of such comments … It would be foolish to regard proverbs as an authoritative source of universally applicable wisdom but it wold be a pity to disregard the graphic description of heuristic procedures provided by proverbs.”
But Polya was more than anthologist; he was a talented aphorist himself. His problem-solving strategies are couched in concise, memorable sentences. First, some of Polya’s collected proverbs are appended below; tomorrow, some of his own aphorisms.
Being a collection of wise words on the subject of solving problems
Who understands ill, answers ill.
Think on the end before you begin.
A wise man begins in the end, a fool ends in the beginning.
Try all the keys in the bunch.
Do and undo, the day is long enough.
A wise man will make more opportunities than he finds.
If you will sail without danger you must never put to sea.
We soon believe what we desire.
Do it by degrees.
He thinks not well who thinks not again.