Epistemological aspects of the history of modern algebra

The aim of the paper is to reconstruct the epistemological shifts in the de velopment of algebraic thought during the period reaching from Lagrange to Noether. We believe that, first, it illustrates the usefulness of Wittgenst ein's concept of pictorial form (we prefer to call it form of language), be cause the evolution of algebra can most clearly be described as the develop ment of form of language. Secondly, our analysis offers an example of the d evelopment of a concept ("to solve an algebraic equation"), thus bringing n ew material for the discussion of the nature of conceptual change. Finally, the development of algebra shows a resemblance with the evolution of subje ctivity in western culture. The development of algebra can in this manner b e seen in a broader evolutionary context.