The Applicability of Mathematics

Current research in mathematics tends toward ever-more-varied abstraction. Yet the most far-reaching excursions into mathematical theory may lead to applications not only within mathematics itself but also in physics and the natural sciences in general. While it is true that much of the work published in mathematical journals consists of detailed and rather specialized investigations, one might think of them as “ patrols” sent into the unknown in all directions. Some of these turn out to encounter new areas of interest in the great game that the human mind plays with nature. Even though much of the activity in mathematical research may appear to be “ getting off on tangents,” the great sphere of knowledge is increasing at an important rate, and the applicability of mathematics to problems suggested by new discoveries seems to know no boundaries.