Does mathematics look certain in the front,but fallible in the back?

摘要

In this paper we re-examine the implications of the differences between 'doing' and 'writing' science and mathematics, questioning whether the way that science and mathematics are presented in textbooks or research articles creates a misleading picture of these differences. We focus our discussion on mathematics, in particular on Reuben Hersh's formulation of the contrast in terms of Goffman's dramaturgical frontstage-backstage analogy and his claim that various myths about mathematics only fit with how mathematics is presented in the 'front', but not with how it is practised in the 'back'. By investigating examples of both the 'front' (graduate lectures in mathematical logic) and the 'back' (meetings between supervisor and doctoral students) we examine, first, whether the 'front' of mathematics presents a misleading picture of mathematics, and, second, whether the 'front' and 'back' of mathematics are so discrepant that mathematics really does look certain in the 'front', but fallible in the 'back'.