文档介绍：BULLETIN (New Series) OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 5, Number 2, September 1981
STUDIES IN THE HISTORY PLEX
FUNCTION THEORY II: INTERACTIONS AMONG
THE FRENCH SCHOOL, RIEMANN, AND WEIERSTRASS
BY E. NEUENSCHWANDER
Introduction. In most of the more recent books and monographs on the
history of mathematics, the chief founders of function theory, Cauchy,
Riemann and Weierstrass, are contrasted with each other. It is often claimed,
for instance, that their ideas and methods long remained without mutual
influence and were entirely unified only at the beginning of the twentieth
But if one consults earlier works standing somewhat closer to the
time period in question, one finds them less inclined to make such claims. For
example, in his Vorlesungen über die Entwicklung der Mathematik im 19.
Jahrhundert, Klein characterizes Riemann as follows: "After all, any rigid
one-sidedness pletely foreign to Riemann; he makes use of whatever he
comes upon and applies the most diverse methods, whenever he can thereby
advance and clarify his problem" [59, p. 254].2 One may thus inquire whether
the above-mentioned interactions among the three function theories did not
indeed begin much earlier, perhaps as far back as the time of Riemann
himself, of what intensity these were at that time, and whether one can still
detect specific influences on the basis of source materials from that time.
Since 1977 I have been occupied with particular aspects of these questions
(see the series of articles [80 - 85]). I have been able to show, among other
things, that Riemann knew and utilized the decisive works of the French
mathematicians even before his promotion (cf. [85]). In this article I propose
to set out the broad outlines of the interactions among the three theories and
briefly to cite the most important sources in each instance. For a more
detailed description of the mathematical developm