A mathematician can be totally isolated from any contact with nature and still go on about his business of constructing mathematical universes, which spring from his mind as pure creations of human intellect. Yet the most astounding result of modern natural science is the reiterated discovery (quite apart from this or that mathematical formulation of natural processes) that nature, too, is in its essence a fabric of mathematical relations. Put crudely, the mathematics that man projects out of his own consciousness somehow corresponds to a mathematical reality that is external to him, and which indeed his consciousness appears to reflect. How is this possible? It is possible, of course, because man himself is part of the same over-all reality, so that there is a fundamental affinity between the structures of his consciousness and the structures of the empirical world. Projection and reflection are movements within the same encompassing reality.
