Book ID: CBB160173996

Theorie Des Fonctions Algebriques d'Une Variable (2019)

unapi

L'article Theorie des fonctions algebriques d'une variable publie en 1882 par les mathematiciens allemands Richard Dedekind et Heinrich Weber est fondateur de la geometrie algebrique moderne. Dedekind et Weber y reecrivent avec des outils algebrico-arithmetiques une large partie des concepts inventes pres de vingt ans auparavant par Bernhard Riemann pour l'etude des courbes algebriques. Pour cela, ils transferent a la theorie des fonctions de Riemann l'appareil conceptuel developpe par Dedekind en theorie des nombres et sa methodologie ensembliste et arithmetique, elargissant la feconde analogie entre geometrie et arithmetique. Nous en presentons la premiere traduction francaise. Accompagnee d'annotations et d'une preface, cette traduction donne aux lecteurs les clefs pour mieux comprendre cet article seminal, et sa place dans notre modernite mathematique, en le replacant dans son contexte mathematique mais egalement dans son contexte epistemologique. Cet ouvrage servira autant le philosophe desireux d'ancrer sa reflexion dans l'histoire des mathematiques que l'historien qui souhaiterait comprendre certaines racines epistemologiques de cet episode du developpement des mathematiques, que le mathematicien soucieux d'explorer l'histoire et la philosophie de sa discipline. The article Theory of algebraic functions of a variable published in 1882 by the German mathematicians Richard Dedekind and Heinrich Weber is the founder of modern algebraic geometry. Dedekind and Weber rewrite there with algebraic-arithmetic tools a large part of the concepts invented almost twenty years earlier by Bernhard Riemann for the study of algebraic curves. For this, they transfer to Riemann's theory of functions the conceptual apparatus developed by Dedekind in number theory and its set-theoretic and arithmetic methodology, broadening the fruitful analogy between geometry and arithmetic. We present the first French translation. Accompanied by annotations and a preface, this translation gives readers the keys to better understand this seminal article, and its place in our mathematical modernity, by placing it in its mathematical context but also in its epistemological context. This book will serve both the philosopher wishing to anchor his reflection in the history of mathematics and the historian who would like to understand certain epistemological roots of this episode in the development of mathematics, as well as the mathematician wishing to explore the history and philosophy of his discipline.

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Review François Lê (2021) Review of "Theorie Des Fonctions Algebriques d'Une Variable". Historia Mathematica (pp. 94-96). unapi

Citation URI
https://data.isiscb.org/isis/citation/CBB160173996/

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Authors & Contributors
Marchisotto, Elena Anne Corie
Smith, James T.
Vidal, J. Climent
Tur, J. Soliveres
Medvedev, F. A.
Gana, Francesco
Journals
Historia Mathematica
History and Philosophy of Logic
Archive for History of Exact Sciences
Berichte zur Wissenschaftsgeschichte
Studies in History and Philosophy of Science
British Society for the History of Mathematics Bulletin
Publishers
Princeton University Press
American Mathematical Society
Birkhäuser
Crítica
de Gruyter
Birkhäuser Basel
Concepts
Mathematics
Philosophy of mathematics
Set theory
Number theory; number concept
Algebra
Logic
People
Dedekind, Richard
Cantor, Georg Ferdinand Ludwig
Weber, Heinrich
Frege, Gottlob
Russell, Bertrand Arthur William
Kronecker, Leopold
Time Periods
19th century
20th century, early
18th century
20th century
Places
Russia
Ukraine
Germany
Italy
Institutions
University of Chicago
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