Manufacturing a Mathematical Group: A Study in Heuristics

I examine the way a relevant conceptual novelty in mathematics, that is, the notion of group, has been constructed in order to show the kinds of heuristic reasoning that enabled its manufacturing. To this end, I examine salient aspects of the works of Lagrange, Cauchy, Galois and Cayley (Sect. 2). I...

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Bibliographic Details
Published inTopoi Vol. 39; no. 4; pp. 963 - 971
Main Author Ippoliti, Emiliano
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.09.2020
Springer Nature B.V
Subjects
Case studies
Education
Greek civilization
Heuristic
Hypotheses
Manufacturing
Mathematicians
Novels
Philosophy
Philosophy of Science
Philosophy of Technology
Discovery
Inference
Hypotheses
Logic
Inferential micro-structures
Heuristics
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Summary:I examine the way a relevant conceptual novelty in mathematics, that is, the notion of group, has been constructed in order to show the kinds of heuristic reasoning that enabled its manufacturing. To this end, I examine salient aspects of the works of Lagrange, Cauchy, Galois and Cayley (Sect. 2). In more detail, I examine the seminal idea resulting from Lagrange’s heuristics and how Cauchy, Galois and Cayley develop it. This analysis shows us how new mathematical entities are generated, and also how what counts as a solution to a problem is shaped and changed. Finally, I argue that this case study shows us that we have to study inferential micro-structures (Sect. 3), that is, the ways similarities and regularities are sought, in order to understand how theoretical novelty is constructed and heuristic reasoning is put forward.
ISSN:0167-7411
1572-8749
DOI:10.1007/s11245-018-9549-1