A plurality of algebras, 1200–1600: Algebraic Europe from Fibonacci to Clavius1

In memory of Jackie Stedall, friend and colleague As Jackie Stedall argued in her 2011 book, From Cardano's great art to Lagrange's reflections: filling a gap in the history of algebra, there was a ‘transition from the traditional algebra of equation-solving in the sixteenth and seventeenth centuries to the emergence of “modern” or “abstract” algebra in the mid nineteenth century’ (page vii). This paper traces the evolution from the thirteenth-century work of the Pisan mathematician, Leonardo Fibonacci, to the early seventeenth-century work of the German Jesuit Christoph Clavius of what came to be considered ‘traditional algebra’. It contends that rather than a single ‘traditional algebra’, in fact, a plurality of intimately related yet subtly different algebras emerged over the course of those four centuries in different yet interacting national settings.