``\dots das Wesen der reinen Mathematik verherrlichen''
type: Item
instance of: scholarly article
title: ``\dots das Wesen der reinen Mathematik verherrlichen''
zbMATH Open document ID: 0836.01009
DOI: 10.1007/PL00009906
author: Eberhard Knobloch
author: Helmut Pulte
author: Herbert Pieper
published in: Mathematische Semesterberichte
publication date: 1996-04-22T00:00:00Z
review text: Against the trends of his time, C. G. J. Jacobi (1804-1851) advocated an autonomous pure mathematics being independent from experiences and applications. Starting from this position he tried to explain progress in mathematics and its applicability for describing real world phenomena. The authors approach Jacobi's notion of mathematics and its tension with mathematical natural philosophy in three sections. In the first section Jacobi is presented as a typical representative of the neo-humanistic ideal of scientific knowledge in early 19th century Germany as it was already claimed by Alexander von Humboldt in 1797 who said that mathematics as a pure object of speculation not being applicable to the solution of practical problems will not loose anything from its dignity: everything is important which extends the limits of our knowledge. The differences between Jacobi's idealistic pure mathematics and French mathematics is illustrated by a comparison with Fourier's conception of mathematics as a pre-existing element of the universe. The authors maintain that both conceptions were opposed diametrically in theory, but were not consequently realized in practice. The authors explain the emergence and development of pure mathematics in Germany as a result of the new interest in foundations of mathematics which was a reaction to the 18th century emphasis of applied mathematics. They stress the influence of Kant's distinction between pure and empirical intuition which was used by G. S. Klügel for the distinction between pure and applied mathematics in his `Mathematisches Wörterbuch' (1808). The second section gives for the first time a German translation of Jacobi's inaugural lecture for entering the philosophical faculty of the University of Königsberg in Prussia on July 7, 1832. The lecture was published in its original Latin by \textit{W. von Dyck} [Sitzungsber., Bayer. Akad. Wiss., Math.-Naturwiss. Kl. 31, 203-208 (1901); reprinted in Math. Ann. 56, 252-256 (1903)]. In his…
reviewed by: Volker Peckhaus
Mathematics Subject Classification ID: 01A55
zbMATH DE Number: 817195
zbMATH Keywords: pure mathematics
zbMATH Keywords: natural philosophy
zbMATH Keywords: mathematical physics
Wikidata QID: Q64005250
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 817195