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CSS Colloquium - Henrik Kragh Sørensen: Cultures of mathematization: Tracing divergent views on explanations

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Mandag 16. september 2013,  kl. 10:15 - 12:00


1531-211 (Koll. D), Math Department

Cultures of mathematization: Tracing divergent views on explanations

Henrik Kragh Sørensen, Centre for Science Studies, Aarhus University

With the recent focus – institutionally, politically and philosophically – on interdisciplinary collaboration, the case of mathematization may offer a nuancing perspective. For centuries, mathematicians have applied their discipline to various sciences, and yet such mathematization is rarely described as interdisciplinary. The present paper aims to elucidate and discuss this point through looking at some recent cultures of mathematization, their epistemic division of labour, and the debates over what counts as good explanations in mathematization.

Although almost ubiquitous in modern science, the notion of mathematization is, itself, loaded with ambiguity. Mathematization shares commonalities with applied mathematics, yet it encompasses more than a body of knowledge: it is a process undertaken by disciplinary mathematicians and scientists sharing a collaborative culture. In the past, a variety of modelling and numerical perspectives were involved in mathematizing scientific problems and theories; and the process of mathematization was frequently opposed by existing disciplinary structures.

In a new project at Aarhus, we undertake philosophy-driven historical investigations of interdisciplinary collaborations involving mathematics in their temporally, geographically, and intellectually local cultures. These investigations are directed at the overlapping and interlocking concepts used or developed for the process of mathematization. In particular, the negotiations (tacit or explicit) of explanation and expertise bring forth new insights into the role of mathematics within collaborations within the sciences.  Thereby, we can address the co-existing disciplinary and interdisciplinary cultures in ways that also resemble the cultural co-existence also discussed in my contribution to the first Mathematical Cultures Conference (2012).

In my talk, I first present an outline of the current status of philosophical scholarship concerning interdisciplinary collaborations involving mathematics. I then sketch a preliminary overview and characterization of practices and cultures of mathematization drawing from a variety of collaborations with biology, geology, and physical chemistry during the past century. Focus will be on the cultural meeting between existing mathematical and scientific cultures and, in particular, on how the standards and goals of explanations were negotiated. This allows me to – provisionally – revisit the notion of interdisciplinary collaboration as it pertains to mathematics: When mathematics is involved, such collaborations are neither specifically new nor do they strictly follow the epistemic division of labour suggested by theoretical accounts of interdisciplinary expertise.