Metaphors in Mathematics: Introduction and the Case of Algebraic Geometry

Abstract

Analogies play an essential role in Mathematics. George Lakoff and Rafael E. Nunez have shown in 'Where Mathematics Comes From' that our understanding of basic mathematics is deeply linked to our experience of the world. They claim that we understand mathematics throught Conceptual Metaphors between source domains (for example spatial relationships between objects) and target domains (abstract Mathematics). These metaphors are supposed to map certain basic schemata of thought, namely, cross-modal organizational structures. In fact the use of conceptual metaphor is a more general cognitive process, used not only in other sciences (as in physics [6], or Cell Biology and Ecology [7] ) but also in every aspect of our understanding of the world, for example in philosophy [8] and ethics [1]. In this paper, I deal with specific cases of metaphors in advanced and abstract mathematics linked to our conception of space. The goal is both to show that conceptual metaphor theory continues to apply with great success in these areas, and to try to understand the theory more deeply.

Keywords: metaphor theory, mathematics, cognitive science