The aim of the paper is to reconstruct the epistemological shifts in the development of algebraic thought during the period reaching from Lagrange to Noether. We believe that, first, it illustrates the usefulness of Wittgenstein’s concept of pictorial form (we prefer to call it form of language), because the evolution of algebra can most clearly be described as the development of form of language. Secondly, our analysis offers an example of the development of a concept (“to solve an algebraic equation”), thus bringing new material for the discussion of the nature of conceptual change. Finally, the development of algebra shows a resemblance with the evolution of subjectivity in western culture. The development of algebra can in this manner be seen in a broader evolutionary context.