Masters, questions and challenges in the abacus schools (Q889614)

A peculiar Italian mathematical tradition between the Late Middle Ages and the Renaissance is the ``abacus mathematics'', where `abacus' was not the ancient computing tool constituted by a table with pebbles, but a set of techniques of the practical tradition embedded in Islamic mathematics, its computing methods with Indo-Arabic numbers and the beginning of a syntactic algebra. The paper shows some examples from this tradition drawn from some abacus masters of the 15th and 16th centuries, tracing the evolution from ancient arithmetic techniques (as the `false position') to more algebraic approaches.