In the preface to the first edition of Courant-Hilbert's "Methoden der mathematischen Physik," R. Courant warned against a trend discernible in modern mathematics in which he saw a menace to the future development of mathematical analysis. He was referring to the tendency of many workers in this field to lose eight of the roots of mathematical analysis in physical and geometric intuition and to concentrate their efforts on the refinement and the extreme generalization of existing concepts. In the intervening years, this trend has become much more pronounced, and it has led to an increasing division of the workers in mathematical analysis into "pure" and "applied" mathematicians. One may deplore this development or welcome it—and many, notably among the "pure" variety, do welcome it—but it seems inevitable that fields like conformal mapping, whose methods are mathematical while their subject matter is derived from physical and geometric intuition, are bound to suffer in such a division.