The fifteenth-seventeenth century transformation of abbacus algebra: Perhaps – though not thought of by Edgar Zilsel and Joseph Needham – the best illustration of the `Zilsel-Needham thesis': Summer School on the History of Algebra, Institute for the History of the Natural Sciences, Chinese Academy of Science, 1–2 September 2011. Preprint

In 1942, Edgar Zilsel proposed that the sixteenth–seventeenth-century emergence
of Modern science was produced neither by the university tradition, nor by the
Humanist current of Renaissance culture, nor by craftsmen or other practitioners,
but through an interaction between all three groups in which all were
indispensable for the outcome. He only included mathematics via its relation
to the “quantitative spirit”. The present study tries to apply Zilsel’s perspective
to the emergence of the Modern algebra of Viète and Descartes (etc.), by tracing
the reception of algebra within the Latin-Universitarian tradition, the Italian
abbacus tradition, and Humanism, and the exchanges between them, from the
twelfth through the late sixteenth and early seventeenth century.