Inquiry into the paths pursued by contemporary mathematical research leads naturally to the question of the extent to which the expansion of technology, which has been of such far-reaching significance for the natural sciences, has penetrated into the development of this most abstract of sciences, for mathematics has always been seen as closely parallel to the natural sciences. Certainly, mathematics cannot be designated a natural science in the strict sense, for its subject matter is taken not from natural objects but from abstract conceptual constructs, and it might therefore be more properly described as a humanistic discipline. Yet granting it membership in the natural sciences is nonetheless fully justified, for the conceptual world treated by the mathematician is precisely the one required by the natural scientist, and particularly the physicist, in order that he may gain a knowledge of nature. For this reason, mathematics has always developed hand in hand with the exact sciences and an exchange of problems and methods of solution has grown up through reciprocal inspiration.