Resumo

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.