Recent advances in physics render a reconsideration of the Place of Mathematics in the Interpretation of the Universe particularly timely. On the one hand, we have the introduction of non-euclidian geometry, which has given rise to much controversy informed or otherwise; on the other hand, we find mysterious forms of mathematics, invented to cope with the quantum difficulties, which so far have escaped metaphysical investigation or criticism. It would seem most desirable that these modes of interpreting reality should be examined (...) from the broader philosophical point of view. (shrink)