Mathematical Perspectives. Essays on Mathematics and its Historical Development

274 Pages·1981·17.719 MB·English

by  Joseph W. Dauben

Professor Dr. Kurt-Reinhard Biermann
Mathematical Perspectives
Essays on Mathematics and Its Historical Development
Edited by
JOSEPH W. DAUBEN
Department of History
Herbert H. Lehman College
City University of New York
Bronx, New York
and
The Graduate Center
City University of New York
New York, New York
Presented to Professor Dr. Kurt-Reinhard Biermann
on the Occasion of His 60th Birthday
,».(g)
ACADEMIC PRESS
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COPYRIGHT © 1981, BY ACADEMIC PRESS, INC.
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United Kingdom Edition published by
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Library of Congress Cataloging in Publication Data
Main entry under title:
Mathematical perspectives.
A collection of papers in honor of Kurt-R. Biermann.
English, French, or German.
Includes bibliographies and inoex.
1. Mathematics—History—Addresses, essays, lectures.
1. Dauben, Joseph Vvarren, Date. II. Biermann, Kurt-R.
QA21.M36 510'.9 80-1781
ISBN 0-12-204050-3
PRINTED IN THE UNITED STATES OF AMERICA
81 82 83 84 9 8 7 6 5 4 3 2 1
List of Contributors
Numbers in parentheses indicate the pages on which the authors' contributions begin.
Paul P. Bockstaele (1), Department of Mathematics, Katholieke Universiteit
Leuven, B-3030 Heverlee, Belgium
Pierre Dugac (13), Universite Pierre et Marie Curie, Paris, France
Wolfgang Eccarius (37), Amrastrasse 107, 59 Eisenach, Deutsche
Demokratische Republik
E. A. Fellmann (47), Arnold Böcklinstrasse 37, CH-4051 Basel, Switzerland
Menso Folkerts* (53), Universität Oldenburg, D-2900 Oldenburg,
Bundesrepublik Deutschland
/. Grattan-Guinness (95), Middlesex Polytechnic at Enfield, Middlesex EN3
4SF, England
A. P. Juschkewitsch (247), Institute of the History of Science and Technology,
Moscow K-12, USSR
*Present address: Institut für Geschichte der Naturwissenschaften der Universität München,
Deutsches Museum, D-8000 München 26, Bundesrepublik Deutschland.
ix
x List of Contributors
Eberhard Knobloch (139), Institut für Philosophie, Wissenschaftstheorie,
Wissenschafts- und Technikgeschichte, Technische Universität Berlin,
D-1000 Berlin 10, Bundesrepublik Deutschland
Uta C. Merzbach (167), The Smithsonian Institution,Washington, D.C. 20560
Olaf Neumann (179), Sektion Mathematik, Friedrich-Schiller-Universität,
DDR-69 Jena, Deutsche Demokratische Republik
Ivo Schneider (201), Institut für Geschichte der Naturwissenschaften der
Universität München, Deutsches Museum, D-8000 München 26,
Bundesrepublik Deutschland
Christoph J. Scriba (221), Institut für Geschichte der Naturwissenschaften,
Mathematik und Technik, Universität Hamburg, D-2000 Hamburg 13,
Bundesrepublik Deutschland
Kurt Vogel (237), Isoldenstrasse 14, D-8000 München 40, Bundesrepublik
Deutschland
Preface
The 13 essays in this collection were originally meant to comprise an issue of
the journal Historia Mathematica in honor of Professor Kurt-R. Biermann's 60th
birthday. In planning the volume, allowance was made for the possibility that ev­
eryone agreeing initially to contribute a paper might not manage to meet the final
deadline. This, however, did not prove to be the case, and when all contributions
were assembled, it appeared that the entire collection had the makings of a book.
In offering these essays as a supplement to Historia Mathematica, Academic
Press has acknowledged the original intention of the journal to honor Professor
Biermann, a member of its Editorial Board, for his many contributions to the his­
tory of mathematics. But it is also an indication of the growing interest in the sub­
ject that this collection of essays reflects a range of scholarship that is substantial
in its own right.
Professor Biermann's many contributions to the history of science are described
in the biographical essay which begins this volume. Moreover, the range of his
scholarly interests and the extent of his writing may be judged by the selected list
of his publications at the end of this book. The 13 articles which follow the bio­
graphical essay are a measure of the esteem in which he is held by his colleagues
XI
xii Preface
everywhere. Moreover, the editors of Historia Mathematica are pleased that these
authors could join forces in a supplement to the journal's usual quarterly appear­
ance. We dedicate this book to Professor Biermann, with great appreciation for
his scholarly contributions to the discipline and his professional contributions to
the promotion of the history of mathematics throughout the world. Among these
contributions are the strong support he has always given to Historia Mathematica,
and the service he continues to render as a member of the Executive Committee of
the International Commission on the History of Mathematics.
Kurt-Reinhard Biermann
Kurt-R. Biermann was born on December 5, 1919, in Bernburg. He left school
with the Abitur from the Lessing-Gymnasium in Berlin in 1938, and thereafter
continued his studies from 1940 until 1943 at the Technische Hochschule in
Charlottenburg and Stuttgart. Following the interruption of his education by the
Second World War, he began a series of correspondence courses in 1952 through
the Technische Hochschule in Dresden, which he continued until 1956. The fol­
lowing year he transferred to the Humboldt University in Berlin, German Demo­
cratic Republic, where he received his Ph.D. (Dr. rer. nat.) in 1964, summa cum
laude. In 1968 he was habilitated to teach the history of mathematics.
Biermann has been active at the Academy of Sciences of the German Demo­
cratic Republic since 1952; from 1956 until 1966 he served as Secretary of the
Euler Commission. As Secretary of the Commission, Biermann came in contact
with A. P. Yushkevich [born 1907; see Historia Mathematica 3, 259-278
(1976)], with whom Biermann has been amicably associated ever since. He has
also been a scientific member of the Alexander-von-Humboldt Research Institut
since 1958, and has served as its director since 1969.
Encouraged by Joseph E. Hofmann [1900-1973; see Historia Mathematica 2,
137-152 (1975)], Biermann began to study the manuscripts of G. W. Leibniz on
xiii
xiv Kurt-Reinhard Biermann
combinatorics and probability theory in 1954. Later he extended these studies to
include periods prior to and following the era of Leibniz. Similarly, his activities
in connection with the Humboldt Research Institute also occasioned a further ex­
tension of his scholarly interests, and he was led to combine his Humbolt studies
with his mathematical-historical concerns to investigate thoroughly the connec­
tions Humboldt had with German and French mathematicians. This resulted in a
large number of biographical articles on mathematicians who had corresponded
with Humboldt, who were encouraged and aided by him, or who had various other
contacts with him. Included in the list of such mathematicians are N. H. Abel, T.
Clausen, A. L. Crelle, C. G. J. Jacobi, F. Minding, J. Steiner, and F. Woepcke.
Above all, Biermann concerned himself intensively with P. G. Lejeune Dirichlet
and G. Eisenstein. Through the exploitation of previously unnoticed surviving
documents, he has done much to illuminate the essential details of the biographies
of the latter two mathematicians. Among Biermann's publications on these sub­
jects, mention is made here only of Dirichlet. Dokumente für sein Leben und
Wirken (Berlin: Akademie-Verlag, 1959) and the contribution to Eisenstein's
Mathematische Werke, 2 (New York: Chelsea Publishing Company, 1975),
919-929. As for the edition of Eisenstein's works, Biermann exercised considera­
ble influence upon the individual items to be included, as well as its general organ­
ization.
Biermann has also studied intensively the relations between Humboldt and C.
F. Gauss, whose life and work have been of special interest to him since 1959.
The publication of a great number of papers was followed in 1977 by his edition of
the correspondence between Humboldt and Gauss (Berlin: Akademie Verlag),
which appeared as Volume 4 in the series Beiträge zur Alexander-von-
Humboldt-Forschung, of which Biermann is the editor. Of special interest are a
number of articles in which Biermann has also deciphered and interpreted
encoded notes by Gauss.
Over the years, Biermann has broadened his research to include nearly all Ger­
man mathematicians who have worked in Berlin, especially Weierstrass, a subject
that provided yet another focus for Biermann's investigations [see, for example,
his article in the Journal für die reine und angewandte Mathematik, 223, 191-220
(1966)]. All of these detailed studies were incorporated into Biermann's major
study of mathematics and mathematicians at the University of Berlin, namely: Die
Mathematik und ihre Dozenten an der Berliner Universität. 1810-1920 (Berlin:
Akademie-Verlag, 1973). This work has met with great interest and has been uni­
versally acclaimed by critics the world over. For example, Ivor Grattan-Guinness
called it a "magnificent book, which will not only forever be authoritative for its
particular subject-matter but also stand as a model of institutional history within a
scientific discipline" [Annals of Science, 32, 404 (1975)]. Biermann went on to
publish a series of documents related to the history of the position of mathematics
and mathematicians in the Berlin Academy. For the first time, he drew upon a pre-
Kurt-Reinhard Biermann xv
viously untapped source for the history of mathematics: the scholarly recommen­
dations (Laudationes) that were officially considered in the election of new mem­
bers. They convey an impression of the appraisal of many well-known
mathematicians by competent contemporary specialists. Ever since Biermann's
first paper on this subject appeared (Vorschläge zur Wahl von Mathematikern in
die Berliner Akademie (Berlin: Akademie-Verlag, I960)), it has been an example
followed by other authors.
The selected bibliography of Biermann's publications listed at the end of this
volume includes eight monographs and 179 scientific papers (among them biogra­
phies for the Dictionary of Scientific Biography) which have appeared in 14 differ­
ent countries. The list does not include numerous short biographies, popular sci­
ence articles, or reviews. In all of his work, exactness and reliability have been
goals to which he has aspired. Hallmarks of his work include the mining of unpub­
lished archival sources and the critical use of the existing literature as well.
Biermann has succeeded in generalizing the experience he has gained, in particu­
lar with the dating of manuscripts, in order to make these results accessible to
other historians of science.
Biermann's contributions have been recognized in numerous ways; in 1966 he
was elected a corresponding member of the Academie internationale d'histoire
des sciences, and in 1971 he was made aMembre effectif of the Academy; since
1972 he has been a member of the Deutsche Akademie der Naturforscher
Leopoldina. Beginning in 1968, Biermann has assumed various functions for the
International Union of the History and Philosophy of Science/Division of the His­
tory of Science. From its inception in 1971, he has also served as an active mem­
ber of the Executive Committee of the International Commission on the History of
Mathematics of the IUHPS/DHS.
Since 1952 Biermann has been married to Dr. med. dent. Elisabeth Biermann-
Appuhn. They are the parents of two sons, Rainer and Jörg. Currently, Biermann
lives in Buch, a suburb of Berlin.
This supplement to Historia Mathematica is dedicated to Professor Dr. Kurt-R.
Biermann on the occasion of his 60th birthday, which was celebrated on Decem­
ber 5, 1979. It is with sincere best wishes for the future from the contributors to
this volume, and from Professor Biermann's many colleagues and friends in all
parts of the world, that this collection of papers is published as an expression of the
esteem in which he is held by historians and mathematicians everywhere.
JOSEPH W. DAUBEN