Far from being frivolous, recreational mathematics cuts to the heart of being a mathematician and is deeply linked to development of graduate-level m… - William Rowan Hamilton

Confused is of course the best state a mathematician can be in; the struggle out of that state is the primary drive for progress.

Humane wis­dom understandeth some propositions so perfectly, and is as abso­lutely certain thereof, as Nature herself; and such are the pure Mathematical sciences, to wit, Geometry and Arithmetick: in which Divine Wisdom knows infinite more propositions, because it knows them all; but I believe that the knowledge of those few compre­hended by humane understanding, equalleth the divine, as to the certainty objectivè, for that it arriveth to comprehend the neces­sity thereof, than which there can be no greater certainty.

...[A]ll the measurements in the world do not balance one theorem by which the science of eternal truths is actually advanced.