Proof, Generality and the Prescription of Mathematical Action: A Nanohistorical Approach to Communication. (November 2015) - Chemla, Karine
Abstract: In this article I examine how mathematical procedures were written in ancient mathematical documents from China and elsewhere. Two key features are analyzed. Some of the texts for procedures require a 'circulation' (or movement) among the sentences that reveal competences that practitioners had to possess to use these texts in the contexts in which they worked. This feature of the text is correlated with the fact that the texts allow practitioners to derive different lists of actions for different cases. It thus discloses that generality was prized in this type of mathematical practice. The second feature noted is that some operations are prescribed using the reason why the operation should be carried out. This feature reveals how a text of procedure communicated not only actions, but also understanding of the actions. How the practitioner understood the operation to be executed requires examination. However, this feature undermines the widespread assumption that these texts were meant for practitioners who did not understand what they did and applied prescriptions blindly.