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Beyond the methodology of mathematics research programmes

Corfield David

Philosophia Mathematica 6 (3):272-301 (1998)

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The importance of mathematical conceptualisation.David Corfield - 2001 - Studies in History and Philosophy of Science Part A 32 (3):507-533.details Mathematicians typically invoke a wide range of reasons as to why their research is valuable. These reveal considerable differences between their personal images of mathematics. One of the most interesting of these concerns the relative importance accorded to conceptual reformulation and development compared with that accorded to the achievement of concrete results. Here I explore the conceptualists' claim that the scales are tilted too much in favour of the latter. I do so by taking as a case study the debate (...) Download Export citation Bookmark 2 citations
Mathematical engineering and mathematical change.Jean-Pierre Marquis - 1999 - International Studies in the Philosophy of Science 13 (3):245 – 259.details In this paper, I introduce and examine the notion of “mathematical engineering” and its impact on mathematical change. Mathematical engineering is an important part of contemporary mathematics and it roughly consists of the “construction” and development of various machines, probes and instruments used in numerous mathematical fields. As an example of such constructions, I briefly present the basic steps and properties of homology theory. I then try to show that this aspect of contemporary mathematics has important consequences on our conception (...) Download Export citation Bookmark 1 citation

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