The definition of a good mathematical problem is the mathematics it generates rather than the problem itself. Andrew Wiles
A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. David Hilbert
As a single atom man is an enigma: as a whole he is a mathematical problem. As an individual he is a free agent, as a species the offspring of necessity. William Winwood Reade
This conviction of the solvability of every mathematical problem is a powerful incentive to the worker. We hear within us the perpetual call: There is the problem. Seek its solution. You can find it by pure reason, for in mathematics there is no ignorabimus. David Hilbert
A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a guide post on the mazy paths to hidden truths, and ultimately a reminder of our pleasure in the successful solution. David Hilbert