Kjeldsen on Rheinberger via Epple April 28, 2009

Continuing on last week’s discussion about the sufficiency of current methodology, I’d like to take a look at Tinne Hoff Kjeldsen’s piece, “Egg-Forms and Measure-Bodies: Different Mathematical Practices in the Early History of the Modern Theory of Convexity,” from the latest Science in Context (free issue!), and particularly the function of her invocation of Hans-Jörg Rheinberger’s array of “epistemic things”.

For those not familiar with the modern theory of convexity, fear not.  I’m mainly interested in the topic because it is central to the mathematical theory of linear programming, which is an important part of the canon of operations research techniques, and Kjeldsen, a historian of mathematics, is the top expert on the subject.  She has a long line of papers explaining how the rather discontinuous history of convexity theory can be understood in terms of its development as parts of mathematicians’ varying projects—what she has previously referred to as different “tasks”.  Her work is extremely useful to people like me who need to figure out what any of this has to do with military doctrine-building and radical British scientists—you’d be surprised—and are reluctant to spend too much time on the nitty-gritty details on the history of things like convexity theory.

The history of mathematics is a nice place to address this issue, because this history is relatively coherent from antiquity to the present in comparison to other fields of study.  As a consequence, historians of mathematics have found it to be more legitimate to address transhistorical mathematical problems as addressed across large gaps of time.  In venues such as the Archive for History of Exact Sciences, history maintains a sort of unusual (more…)