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Crítica (México, D.F.)
versão impressa ISSN 0011-1503
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NIGRO PUENTE, Guillermo. Purity of Method and Theory Building: The Case of Kronecker and Dedekind in Algebraic Number Theory. Crítica (Méx., D.F.) [online]. 2023, vol.55, n.164, pp.57-91. Epub 03-Jun-2024. ISSN 0011-1503. https://doi.org/10.22201/iifs.18704905e.2023.1424.
The discussion of purity of method usually emphasizes the study of particular proofs of mathematical practice. A critique of this position questions the value of purity by claiming that “mathematical progress” depends essentially on the use of impure methods. This article shows that a more holistic perspective, focusing on how purity claims can operate in the construction of autonomous theories, allows us to identify a context where purity of method acquires value in mathematical practice. In particular, the relevance of such demands is shown in the case of Kronecker’s and Dedekind’s algebraic number theories.
Palavras-chave : autonomous theories; mathematical progress; holistic conception of the purity of the method; arithmetization; pure mathematics.