Jacopo da Firenze's Tractatus Algorismi and Early Italian Abbacus Culture

mathematics as soon as I started doing my own work in the ?eld – and, as it turned out, mostly on the history of pre-Modern mathematics. Along with other topics I maintained my interest in practitioners’ knowledge as it could be encountered in the sources – which, when we speak of pre-Modern mathematical practice, was often only possible through teaching material directed at future practitioners or otherwise re?ecting practitioners’ knowledge. Though for a long time I did not work directly on late medieval European vernacular mathematics, I collected material when I encountered it – in particular source editions. Much I found in Baldassare Boncompagni’s marvellous Bullettino, much I owe to Moritz Cantor and the circle around him. I also had the good luck to come in personal touch with Kurt Vogel and Gino Arrighi and to receive directly from them publications which even my excellent interlibrary service would have been unable to get hold of. Two accidents pushed me to capitalize on this material. First, in November 1996, at a meeting at the Mathematisches Forschungsinstitut Oberwolfach, Henk Bos asked me to improvise on 43 hours notice a presentation of what had happened in the historiography ofEuropean medievalmathematics duringthe lastforty years andto summarizethe picture which now emerged. I had no support at hand beyond my memory, my personal catalogue and my own writings from the last decade, catalogue and writings as present on my laptop.