Search results for "discipline formation"

Branch Points of Algebraic Functions and the Beginnings of Modern Knot Theory

1995

Many of the key ideas which formed modern topology grew out of “normal research” in one of the mainstream fields of 19th-century mathematical thinking, the theory of complex algebraic functions. These ideas were eventually divorced from their original context. The present study discusses an example illustrating this process. During the years 1895-1905, the Austrian mathematician, Wilhelm Wirtinger, tried to generalize Felix Klein's view of algebraic functions to the case of several variables. An investigation of the monodromy behavior of such functions in the neighborhood of singular points led to the first computation of a knot group. Modern knot theory was then formed after a shift in mat…