"No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite" David Hilbert
Mathematics and its methods often seems like an invisible, inaccessible, terra incognito domain, not unlike the summit of Mount Everest to many of us, who often come to agree with Wittengenstein's comment about her been a Poe-faced, stern mistress, whose continuous demands must be followed scrupulously by her suitor. Nevertheless, the love that she can eventually bestow on her lover can be immense and generous.
Personally, I find that Mathematics should be no more an act of the imagination as writing Music or reciting Poetry; true its language maybe different, but its ultimate intention like all acts of the imagination is to bring light into the darkness of the world. How it is possible to know and wonder at the heavenly orbits of the universe without understanding Conic Sections and their surfaces of revolution, to understand the great biological dance of life, in a butterfly's wing or in a heartbeat, without understanding the Fourier Series? Yet, on reflection we can still wonder without this knowledge too, and perhaps more innocently. However, I don't see why our understanding of the laws that inform our imagination while we observe such phenomena should automatically render them less beautiful to the mind.
Even at the human level is there anything in the world quite like the wonder at appreciating the beauty of form that we can observe in another human being, the curve and line of beauty that we seek out can be the profoundest meeting place between the three realms, of the sensuous, the abstract, and the spiritual. If we could take a snap-shot of such an experience, we would be able to derive these subtleties from a third person perspective- however- to be able to appreciate the three in one - would require powers of body, mind and spirit that we don't as yet acquire. The appreciation of form, in mathematics as in everyday life is as old as the abacus and perhaps more symbolic of our inherent need to understand such infinite states of beauty, states as infinite as the mathematics that inform them.