GOOD PROBLEMS ACCORDING TO HILBERT
1. Clear and easy to comprehend
ìA mathematical problem should be difficult, in order to entice us, yet not completely inaccessible lest it mocks at our efforts. It should provide a landmark on our way through the confusing maze and thus guide us towards hidden truth.î
Should lead to meaningful generalizations
Should be related to meaningful simpler problems
If we do not succeed in solving a mathematical problem , the reason is often do to our failure to recognize the more general standpoint from which the problem before us appears only as a single link in a chain of related problemsíí
``In dealing with mathematical problems, specialization plays, I believe, a still more important part then generalization. Perhaps in most cases where we seek in vain the answer to a question, the cause of the failure lies in the fact that problems simpler than the one in hand have been either not at all or incompletely solved.íí
2. Difficult yet not completely inaccessible
3. Should provide a strategic height towards a broader goal
| Previous slide | Next slide | Back to first slide | View graphic version |