This paper describes the widespread public image of mathematics as cold, abstract and inhuman, and relates it to absolutist philosophies of mathematics. It is argued that this image is consistent with 'separated' values (Gilligan, 1982) which help to make mathematics a 'critical filter' denying access to many areas of study and to fulfilling professional occupations, especially for women in anglophone western countries. In contrast, an opposing humanised image of mathematics, consistent with 'connected' values, finds academic support in recent fallibilist philosophies of mathematics. It is argued that although these two philosophical positions have a major impact on the ethos of mathematics classrooms, there is no direct logical connection. It is concluded instead that the values realised in the classroom are probably the dominant factor in determining the learner's image and appreciation of mathematics (and hence, indirectly, that of society).
A widespread public image of mathematics is that it is difficult, cold, abstract, theoretical, ultra-rational, but important and largely masculine. It also has the image of being remote and inaccessible to all but a few super-intelligent beings with 'mathematical minds'. Many persons operating at high levels of competency in numeracy, graphicacy and computeracy in their professional life in the UK still say 'I'm no good at mathematics, I never could do it'. In contrast to the shame associated with illiteracy, innumeracy is almost a matter of pride amongst educated persons in western anglophone countries.
In fact, many such persons are not innumerate at all, and it is school or academic mathematics, not everyday mathematics, that they feel they cannot do. Numeracy, contextual mathematics, even ethnomathematics are perceived to be quite distinct from school/ academic mathematics, and the latter is understood to be 'real' mathematics. The popular image of mathematics sets it apart from daily concerns of the public, despite the many social applications of mathematics referred to daily in the mass media, from sports and weather to economic and social indicators. Thus the widespread public image of mathematics is largely a negative and remote one, alien to many persons' professional and personal concerns and their self-perceived abilities.
For many people the image of mathematics is associated with anxiety and failure. When Brigid Sewell was gathering data on adult numeracy for the Cockcroft Inquiry (1982), she asked a sample of adults on the street if they would answer some questions. Half of them refused to answer further questions when they understood it was about mathematics,