Ottawa, June 7 - 11, 2021
Among the women whose responses were consigned to the obscurity of a few vaguely qualitative remarks were Charlotte Angas Scott and Constance Herschel, fellow students at Girton College in Cambridge, who would both become resident lecturers there. Their responses and accompanying letters to Galton have been preserved and digitized by the University College London Digital Collections alongside all of Galton’s surviving correspondence on Mental Imagery.
This talk will situate the responses from Scott and Herschel on the imagery of geometry and numerals with respect to their mathematical training and popular perceptions (including Galton’s) of sex differences in imagery and abstract thought.
As a result, the analysis of applications has been persistently subjected to a counterproductive focus. In particular, the problem-solving character of applications has been concealed. Little attention has been paid to the fact that, in scientific enquiry, interrelated problems, rather than structured settings, present themselves first. Settings arise from after successful problem-solving techniques have been crystallised. Moreover, only after systematic work to bring problems under control has been carried out is it possible to consider certain facts as results of formal analysis, i.e. it is only after the construction of a problem-solving methodology by mathematical means that explanations arise as, possibly significant, byproducts.
My goal on this presentation is to refocus the study of applications around problem-solving and away from mirroring and explanation. I offer some reflections on what important phases of mathematised enquiry should be given prominence as a subject of closer analysis. In order to keep contact with mathematical practice, I develop my reflections in connection with the development of mathematical voting theory (especially Saari (1994)).
Baker, A. (2005) `Are there genuine mathematical explanations of physical phenomena?', Mind 114, pp.223–238.
Field, H. (1980) Science without numbers. Oxford: Clarendon Press.
Saari, D.G. (1994) Geometry of Voting. New York: Springer.