Proverbs on Problems

A fitting conclusion for this chapter may be a few passages taken from a very interesting little book (now a classic) by G. Polya,¹ which any student of science, particularly researchers, should find instructive and interesting. Among hundreds of passages one can find worthy of using as proverbs, only twelve are given below in the four stages of research problems. (Note: these “proverbs” are taken from various sections of the book, and the words are not reproduced exactly.)

General

• It would be a mistake to think that solving problems is a purely intellectual affair. Determination and emotion play an important role.
• In order to solve a problem, it is not enough to recollect isolated facts. We must combine these facts, and their com­binations must be well adapted to the problem at hand.
• Do not forget that human superiority consists in going around an obstacle that cannot be overcome directly, in devising some suitable auxiliary problem when the original one appears insolvable.

At the Beginning

• Incomplete understanding of the problem, owing to lack of concentration, is perhaps the most widespread difficulty in solving problems.
• Visualize the problem as clearly and as vividly as you can. For the moment, do not concern yourself with details.
• Have you seen the problem in a slightly different form? Could you use it? Could you use its results? Could you use its method?

In Progress

• If you cannot solve the proposed problem, try to first solve some related problem.
• Consider your problem from various sides and seek con­tacts with your formerly acquired knowledge.
• Desiring to proceed from our initial conception to a more adequate, better-adapted conception, we try various stand­points and view the problem from different sides. We could hardly make any progress without variation of the problem.

At the End

• Did you use the whole hypothesis?
• Have you taken into account all essential notions involved in the problem?
• Looking back at the completed solution is an important and instructive phase of the work. He thinks not well that thinks not again.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.