No Problem Is Exhausted

2021 August 26

Even fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. Doing so, they miss an important and instructive phase of the work… A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted.

One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. We have a natural opportunity to investigate the connections of a problem when looking back at its solution.

— George Pólya, “How to Solve It“

Tags: mathematics