Lecture I

Now let us consider mathematical truths, the truths of geometry. A superficial observer would say: Oh yes, of course man gets his mathematics out of his head, or from somewhere or other (ideas on the subject are not very precise). But it is not so. Mathematics derives from an altogether different sphere. And if you study the human being, you will get to know the sphere from which mathematics comes. It is from the sense of movement and the sense of balance. It is from such depths that mathematical thought comes, depths to which we no longer penetrate with our ordinary soul-life. What enables us to develop mathematics lives at a deeper level than our ordinary soul-life. And thus we see that mathematics is really rooted in that part of us which is at the same time cosmic. In fact, we are only really subjective in what lies here (see diagram) from the sense of sight upwards. In respect of what lies down there we are like logs, as much so as the rest of the outer world. Hence we can never say that geometry, for instance, has anything of a subjective nature in it, for it originates from that in us wherein we ourselves are objective. It is concerned with the very same space which we measure when we walk, and which our movements communicate to us—the very same space which, when we have elicited it from ourselves in pictorial form, we then proceed to apply to what we see. Nor can there be any question of describing space as in any way subjective, for it does not come from the sphere whence the subjective arises.