Ruth felt that math was like sex—get all you can, but best not done in public. - William Rowan Hamilton

The progress of mathematics has been most erratic, and... intuition has played a predominant rôle in it. ...It was the function of intuition to create new forms; it was the acknowledged right of logic to accept or reject these new forms, in whose birth it had no part. ...the children had to live, so while waiting for logic to sanctify their existence, they throve and multiplied.

Mathematicians have constructed a very large number of different systems of geometry, Euclidean or non-Euclidean, of one, two, three, or any number of dimensions. All these systems are of complete and equal validity. They embody the results of mathematicians' observations of their reality, a reality far more intense and far more rigid than the dubious and elusive reality of physics. The old-fashioned geometry of Euclid, the entertaining seven-point geometry of Veblen, the space-times of Minkowski and Einstein, are all absolutely and equally real. ...There may be three dimensions in this room and five next door. As a professional mathematician, I have no idea; I can only ask some competent physicist to instruct me in the facts.
The function of a mathematician, then, is simply to observe the facts about his own intricate system of reality, that astonishingly beautiful complex of logical relations which forms the subject-matter of his science, as if he were an explorer looking at a distant range of mountains, and to record the results of his observations in a series of maps, each of which is a branch of pure mathematics. ...Among them there perhaps none quite so fascinating, with quite the astonishing contrasts of sharp outline and shade, as that which constitutes the theory of numbers.

It is impossible, and it has always been impossible, to grasp the meaning of what we nowadays call physics independently of its mathematical form.