Article ID: CBB453451930

Euler and the Structure of Mathematics (2020)

unapi

When Euler began his mathematical career, analysis was not an autonomous and self-founding field of mathematics but only a method for solving geometrical problems. During Euler's activity, analysis emerged as a new field of mathematics whose methods differed from those of geometry. Moreover, Euler changed the architecture of this science and regarded analysis as lying at the heart of mathematics, while geometry and mechanics were considered as a sort of applied analysis. The new structure of mathematical sciences was successful, but this success soon showed the inadequacy of the Eulerian foundations of analysis. Sommario Quando Eulero iniziò la sua carriera scientifica, l'analisi non era un'autonoma disciplina matematica né aveva una sua propria fondazione, essendo considerata un metodo per risolvere problemi geometrici. Fu durante la vita di Eulero che essa emerse come una nuova disciplina matematica i cui metodi differivano da quelli della geometria. Essa fu vista come una teoria meramente discorsiva che operava solo con nozioni astratte e non usava rappresentazioni materiali. Partendo da questa concezione, Eulero innovò l'architettura delle scienze matematiche mettendo l'analisi al centro della matematica e concependo la geometria e la meccanica come campi di applicazione dell'analisi. La nuova strutturazione delle scienze matematiche fu un successo, ma proprio tale successo ben presto l'inadeguatezza dei fondamenti su cui Eulero aveva costruito la sua costruzione.

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Authors & Contributors
Knobloch, Eberhard
M. Rosa Massa-Esteve
Mellado-Romero, Antonio
Linero-Bas, Antonio
Herrero-Piñeyro, Pedro J.
Gómez-García, Francisco
Concepts
Mathematics
Mathematical analysis
Philosophy of mathematics
Infinitesimals
Calculus
Mathematics and its relationship to nature
Time Periods
18th century
17th century
19th century
20th century, early
20th century
Places
Switzerland
Sweden
Spain
France
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