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Article ID: CBB947622345

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

Goldstein, Catherine (Author)

Cahiers François Viète Center for Epistemology and History of Science and Technology (CFV)
Issue: III-1
Pages: 103-135

URI: https://journals.openedition.org/cahierscfv/954

DOI: 10.4000/cahierscfv.954

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Philosophy of mathematics Mathematics Algebra Number theory; number concept Classification 19th century Hermite, Charles Gauss, Carl Friedrich

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.

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