Pure Mathematics

Abstract

Mathematics falls roughly into two major divisions: pure mathematics and applied mathematics. The separation between these two subdivisions is inexact and mathematicians argue continually over the placement of the boundary that marks the end of one and the beginning of the other. The arguments are futile and one can imagine a sequence of pictures showing the transformation of the most applied of applied mathematicians on the left into the most pure of pure mathematicians on the right. At no place in between could you say, “Here is where the person becomes a pure mathematician,” just as in the familiar sequence of evolutionary pictures one cannot point to the exact moment at which the ape becomes human. But the difference between the ape and the human is clear and so is the difference between the extremes of applied and of pure mathematics. In the university, there is no hostility more bitter than that existing between the mathematician who is clearly on one side and the mathematician unequivocally on the other.