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Textual materiality and abstraction in mathematics.

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The material features of textual representations actively shape the creation of new mathematical concepts, challenging the notion that mathematics is purely abstract. This study examines historical mathematical texts to reveal this crucial link.

Keywords:
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Area of Science:

  • History of Mathematics
  • Philosophy of Mathematics
  • Science and Technology Studies

Background:

  • The historical development of mathematical concepts, particularly group theory, is often viewed through an increasingly abstract lens.
  • Existing scholarship frequently separates the material aspects of representations from conceptual development in mathematics.

Purpose of the Study:

  • To explore the role of textual representations in the creation of new mathematical objects.
  • To analyze how material features of representations influence conceptual change in mathematics.
  • To challenge the view that mathematical concepts are detached from material configurations.

Main Methods:

  • Analysis of historical mathematical texts by Joseph-Louis Lagrange and Évariste Galois.
  • Application of an analytical framework adapted from Bruno Latour's work on material and representational practices.
  • Examination of the interconnection between conceptual development and the materiality of representations.

Main Results:

  • Changes in the material aspects of textual representations play a crucial role in conceptual change.
  • The distinction between material and structural features of representations is not absolute in mathematical practice.
  • The materiality of inscriptions actively contributes to the conceptualization of mathematical objects.

Conclusions:

  • Mathematical concepts develop through an active interplay with their material representations, not in detachment from them.
  • The study problematizes the strict distinction between concrete inscriptions and abstract relations in understanding mathematical concept formation.
  • Materiality is integral to the evolution and abstraction of mathematical ideas.