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Egg-Forms and Measure-Bodies: Different Mathematical Practices in the Early History of the Modern Theory of Convexity

Published online by Cambridge University Press:  01 March 2009

Tinne Hoff Kjeldsen
Tinne Hoff Kjeldsen*
Affiliation:
Roskilde University, Denmark
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Argument

Two simultaneous episodes in late nineteenth-century mathematical research, one by Karl Hermann Brunn (1862–1939) and another by Hermann Minkowski (1864–1909), have been described as the origin of the theory of convex bodies. This article aims to understand and explain (1) how and why the concept of such bodies emerged in these two trajectories of mathematical research; and (2) why Minkowski's – and not Brunn's – strand of thought led to the development of a theory of convexity. Concrete pieces of Brunn's and Minkowski's mathematical work in the two episodes will, from the perspective of the above questions, be presented and analyzed with the use of the methodological framework of epistemic objects, techniques, and configurations as adapted from Hans-Jörg Rheinberger's work on empirical sciences to the historiography of mathematics by Moritz Epple. Based on detailed descriptions and a comparison of the objects and techniques that Brunn and Minkowski studied and used in these pieces it will be concluded that Brunn and Minkowski worked in different epistemic configurations, and it will be argued that this had a significant influence on the mathematics they developed for those bodies, which can provide answers to the two research questions listed above.

Type
Research Article
Information
Science in Context , Volume 22 , Issue 1 , March 2009 , pp. 85 - 113
Copyright
Copyright © Cambridge University Press 2009

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