Differential Geometrical Performance and Poiesis

摘要

Mathematical Experience and Mathematical Performance Conventionally, we construe mathematics as knowledge, and the mathematical sign as representation of knowledge. In this essay I propose an alternative approach, pairing mathematical practice as performance with mathematical writing as technology of performance. This foregrounds mathematics as a poietic rather than a tautological practice, and to interpret this poietic practice I outline a materialist phenomenology. I argue that particular attention to differential geometers' practices of diagramming or sketching shapes, manipulating algebra, estimating analytic functions, or tracing kinetic processes offers us a chance to grasp how mathematical signs function outside speech yet in a thoroughly material way. What seems fruitful is to treat these practices not as recording or encoding mathematical entities, but as generating them. In other words, I treat mathematical writing not as a technology of representation but as a technology of embodied performance. Moreover, by looking at differential geometrical writing as a performance practice, I offer some examples of how finite gestures enact smooth ("infinitely dif-ferentiable"), "abstract," "objective," or infinite entities via finite traces. By recognizing that geometers exteriorize and materialize their imagination in common technologies of mathematical writing such as the backs of envelopes or chalk and chalkboard, we can avoid the problem of intersubjective communication. Shared and therefore objective mathematical entities are constituted in the interaction of geometers, their disciplinary logics, and technologies.