"Although the real theory might have been less useful than the complex in obtaining properties of special functions, its significance for the development of mathematics as a whole has been incomparably greater. It was in the real variable that the necessity for a rigorous theory of the number system of analysis was first recognized. ...the reconstruction of the real number system by Weierstrass in the 1860's and by Dedekind and Cantor in the 1870's led in the last three decades of the nineteenth century, to a profound reconsideration of the nature of all mathematical reasoning. This in turn initiated some of the most searching examinations of all deductive reasoning since the days or Aristotle. Thus the theory of the functions of a real variable since the 1870's has increasingly acquired more than merely a local interest: its problems, solved and unsolved, are significant in fields far distant from technical mathematics."