Arithmetization and Rigor as Beliefs in the Development of Mathematics

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Title: Arithmetization and Rigor as Beliefs in the Development of Mathematics
Authors: Segura, Lorena | Sepulcre, Juan Matias
Research Group/s: Sistémica, Cibernética y Optimización (SCO) | Curvas Alpha-Densas. Análisis y Geometría Local
Center, Department or Service: Universidad de Alicante. Departamento de Matemáticas
Keywords: Mathematics | Rigour | Arithmetization | Analysis | Function
Knowledge Area: Análisis Matemático
Issue Date: Mar-2016
Publisher: Springer Science+Business Media Dordrecht
Citation: Foundations of Science. 2016, 21(1): 207-214. doi:10.1007/s10699-015-9414-2
Abstract: With the arrival of the nineteenth century, a process of change guided the treatment of three basic elements in the development of mathematics: rigour, the arithmetization and the clarification of the concept of function, categorised as the most important tool in the development of the mathematical analysis. In this paper we will show how several prominent mathematicians contributed greatly to the development of these basic elements that allowed the solid underpinning of mathematics and the consideration of mathematics as an axiomatic way of thinking in which anyone can deduce valid conclusions from certain types of premises. This nineteenth century stage shares, possibly with the Heroic Age of Ancient Greece, the most revolutionary period in all history of mathematics.
Sponsor: The authors was partially supported by Vicerrectorado de Investigación, Desarrollo e Innovación de la Universidad de Alicante under Project GRE11-23.
URI: http://hdl.handle.net/10045/62691
ISSN: 1233-1821 (Print) | 1572-8471 (Online)
DOI: 10.1007/s10699-015-9414-2
Language: eng
Type: info:eu-repo/semantics/article
Rights: © Springer Science+Business Media Dordrecht 2015. The final publication is available at Springer via http://dx.doi.org/10.1007/s10699-015-9414-2
Peer Review: si
Publisher version: http://dx.doi.org/10.1007/s10699-015-9414-2
Appears in Collections:INV - CADAGL - Artículos de Revistas
INV - SCO - Artículos de Revistas

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