The emergence of symbolic algebra as a shift in predominant models
The paper analyzes the emergence of symbolic algebra during the 15th and 16th centuries, as opposed to the earlier ``rhetorical algebra''. The author points out the necessity to consider mathematics in a proper historical context, and cites an example from Babylonian mathematics which corresponds to solving a quadratic equation, but which in fact should be interpreted geometrically. According to the author, there are six important stages in the development of the concept of equation: the expansion of arithmetical operators to polynomials, equating polynomial expressions, introduction of the second unknown, expansion of arithmetical operators to equations, introduction of letters for multiple unknowns, and systematic manipulation of linear equations to eliminate unknowns. The aim of the paper is to characterize algebraic problem solving as model-based reasoning and symbolic algebra as a shift from a geometrical to a symbolic mode of representation. The same historical period has also witnessed an increase of merchant activities and many authors who have published about bookkeeping also devoted themselves to algebra. In this context, it seems there is a parallel between symbolic algebra and money, which has the symbolic function of measuring wealth and the value of goods.
scientific article; zbMATH DE number 5790048