Article ID: CBB947622345

« Découvrir des principes en classant » : la classification des formes quadratiques selon Charles Hermite (2016)


During the nineteenth century, the classification of algebraic forms plays a key role in the fields of algebra and number theory in particular. It often borrows its vocabulary (class, genus, types) from the natural sciences. Focussing on Carl Friedrich Gauss’s Disquisitiones arithmeticae and on the work of Charles Hermite, this article analyses two distinct classificatory practices. It shows how each of them transfers the characters of natural objets to forms and other associated mathematical concepts and how it deals with innovation, in particular the creation of new mathematical objects.

Citation URI

Similar Citations

Article Yap, Audrey; (2011)
Gauss' Quadratic Reciprocity Theorem and Mathematical Fruitfulness (/isis/citation/CBB001024184/)

Book Goldstein, Catherine; Schappacher, Norbert; Schwermer, Joachim; (2007)
The Shaping of Arithmetic after C. F. Gauss's Disquisitiones Arithmeticae (/isis/citation/CBB001035076/)

Article Bullynck, Maarten; (2010)
Factor Tables 1657--1817, with Notes on the Birth of Number Theory (/isis/citation/CBB001033636/)

Book Bussotti, Paolo; (2006)
From Fermat to Gauss: Indefinite Descent and Methods of Reduction in Number Theory (/isis/citation/CBB000772063/)

Article Jan R. Magnus; (2022)
Gauss on least-squares and maximum-likelihood estimation (/isis/citation/CBB054933541/)

Book Richard Dedekind; Heinrich Weber; (2019)
Theorie Des Fonctions Algebriques d'Une Variable (/isis/citation/CBB160173996/)

Article Boucard, Jenny; (2011)
Louis Poinsot et la théorie de l'ordre: un chaînon manquant entre Gauss et Galois? (/isis/citation/CBB001034693/)

Article Erika Luciano; Elena Scalambro; Lea Terracini; (2020)
Le lezioni di teoria dei numeri di Guido Fubini (1916-1917) (/isis/citation/CBB746462227/)

Article Lukas M. Verburgt; (2018)
Duncan F. Gregory and Robert Leslie Ellis: Second-Generation Reformers of British Mathematics (/isis/citation/CBB954232268/)

Book Gray, Jeremy; Parshall, Karen Hunger; (2007)
Episodes in the History of Modern Algebra (1800--1950) (/isis/citation/CBB000774194/)

Article Ferraro, Giovanni; Panza, Marco; (2012)
Lagrange's Theory of Analytical Functions and His Ideal of Purity of Method (/isis/citation/CBB001220403/)

Article Nastasi, Tina; (2008)
La storia del pensiero scientifico e il suo significato nell'opera di Federigo Enriques (/isis/citation/CBB001024085/)

Article Lambert, Kevin; (2013)
A Natural History of Mathematics: George Peacock and the Making of English Algebra (/isis/citation/CBB001320192/)

Thesis Lacey, Duane J.; (2007)
Euclid's Taxonomy of Irrationals (/isis/citation/CBB001560851/)

Article Grcar, Joseph F.; (2011)
How Ordinary Elimination Became Gaussian Elimination (/isis/citation/CBB001036217/)

Article Bartha, Paul; (2004)
Countable Additivity and the de Finetti Lottery (/isis/citation/CBB000410760/)

Authors & Contributors
Boucard, Jenny
Bullynck, Maarten
Bartha, Paul
Bussotti, Paolo
Gray, Jeremy
Parshall, Karen V. Hunger
Archive for History of Exact Sciences
Revue d'Histoire des Mathématiques
British Journal for the Philosophy of Science
Physis: Rivista Internazionale di Storia della Scienza
Studies in History and Philosophy of Science
Historia Mathematica
E. Rauner Verlag
American Mathematical Society
New School University
Librarie Philosophique J. Vrin
Number theory; number concept
Philosophy of mathematics
Gauss, Carl Friedrich
Gregory, Duncan Farquharson
Cauchy, Augustin Louis
Fermat, Pierre de
Kronecker, Leopold
Minkowski, Hermann
Time Periods
19th century
18th century
20th century, early
20th century
17th century
United States
Great Britain
University of Chicago

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment