Mathematics as Sign: Writing, Imagining, Counting

Two features of mathematics stand out: its menagerie of seemingly eternal objects (numbers, spaces, patterns, functions, categories, morphisms, graphs, and so on), and the hieroglyphics of special notations, signs, symbols, and diagrams associated with them. The author challenges the widespread belief in the extra-human origins of these objects and the understanding of mathematics as either a purely mental activity about them or a formal game of manipulating symbols. Instead, he argues that mathematics is a vast and unique man-made imagination machine controlled by writing. Mathematics as Sign addresses both aspects mental and linguistic of this machine. The opening essay, Toward a Semiotics of Mathematics (long acknowledged as a seminal contribution to its field), sets out the author s underlying model. According to this model, doing mathematics constitutes a kind of waking dream or thought experiment in which a proxy of the self is propelled around imagined worlds that are conjured into intersubjective being through signs.