This issue of the BSHM Bulletin carries two challenges to historians of mathematics and to all who use the history of mathematics, whether in the classroom, in popular lectures or television programmes, or elsewhere. One of the challenges comes from Annette Imhausen in her review of Eleanor Robson's Mathematics in ancient Iraq (p. 00). ‘Perhaps recent historians of mathematics have made too little effort’, she writes, ‘to explain the paradigm shift that their discipline has gone through’. In the last few years, historians of ancient mathematics have led the way in encouraging us to view the writings of earlier times not as primitive forerunners of modern mathematics but as manifestations of contemporary ways of thinking and of their own social and economic context. Reading an ancient text may be compared to seeing through a window, not to the future, but into the mind and culture of the person who wrote it. It sometimes seems harder to bring such contextual analysis to bear on more modern mathematics with its greater technical difficulties, but here too there have been significant new approaches, many of which position the history of mathematics more firmly within broader intellectual history. (The next issue of the Bulletin will explore one aspect of this: the interplay between mathematics and literature.)
The second challenge comes from Glen van Brummelen in his ‘musings on bringing the historiography of mathematics to the classroom’ (p. 1). How is the historian to convey to a non-specialist the subtleties of historical debate? How are we to move away from sterile questions of who was first or best and demonstrate instead that mathematics is dependent on time and place, an accumulation of individual insights and complex cultural transitions? How are we to put this across to teachers or television audiences who may be looking for a history of mathematics that is quickly and easily digestible? There is no single easy answer but the challenge matters. As Glen van Brummelen writes, ‘it is and always has been our responsibility to transform our insights into a format usable for the culture that supports our enterprise’.
Both Glen and Annette invite us to take the complexities of the history of mathematics seriously, not so that we drown it in a sea of footnotes, but so that doing or teaching the history of mathematics can become even for non-specialists a stimulating investigation into the richness and historical diversity of mathematical thought.