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Shaping Mathematics as a Tool: The Search for a Mathematical Model for Quasi-crystals

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Mathematics as a Tool

Part of the book series: Boston Studies in the Philosophy and History of Science ((BSPS,volume 327))

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Abstract

Although the use of mathematical models is ubiquitous in modern science, the involvement of mathematical modeling in the sciences is rarely seen as cases of interdisciplinary research. Often, mathematics is “applied” in the sciences, but mathematics also features in open-ended, truly interdisciplinary collaborations. The present paper addresses the role of mathematical models in the open-ended process of conceptualizing new phenomena. It does so by suggesting a notion of cultures of mathematization, stressing the potential role of the mathematical model as a boundary object around which negotiations of different desiderata can take place. This framework is then illustrated by a case study of the early efforts to produce a mathematical model for quasi-crystals in the first two decades after Dan Shechtman’s discovery of this new phenomenon in 1984.

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Notes

  1. 1.

    Shechtman’s discovery and the subsequent study of quasi-crystals is described and outlined in many publications, some of which are explicitly referred to in the following. The reader may also consult e.g. Brecque (1987/1988) and Steinhardt (2013).

  2. 2.

    Shechtman’s Nobel interview can be found online: http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2011/shechtman-interview.html

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Authors and Affiliations

  1. Section for History and Philosophy of Science, Department of Science Education, University of Copenhagen, Øster Voldgade 3, DK-1350, Copenhagen, Denmark

    Henrik Kragh Sørensen

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  1. Henrik Kragh Sørensen
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Correspondence to Henrik Kragh Sørensen .

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Editors and Affiliations

  1. Department of Philosophy, Bielefeld University, Bielefeld, Germany

    Johannes Lenhard

  2. Department of Philosophy, Bielefeld University, Bielefeld, Germany

    Martin Carrier

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Sørensen, H.K. (2017). Shaping Mathematics as a Tool: The Search for a Mathematical Model for Quasi-crystals. In: Lenhard, J., Carrier, M. (eds) Mathematics as a Tool. Boston Studies in the Philosophy and History of Science, vol 327. Springer, Cham. https://doi.org/10.1007/978-3-319-54469-4_5

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