Mathematical Cognition and the Arts

Abstract

This article revisits the study of mathematics in the arts, and vice versa, the arts in mathematics, with a view to connecting mathematical and artistic creativity to the same neural circuits-a proposition put forward for mathematics and language in a critical 2000 book by Lakoff and Nunez, Where Mathematics Comes From. This expanded perspective would open up suggestive avenues for connecting mathematics, language, and the arts as part of an imaginative blend that comes out in different forms but having the same underlying neural source. Whether or not this can be established empirically, it is plausible and highly interesting and, thus, needs to be explored seriously in order to see if equations to theorems are born of the same mental structures that produce music, poetry and drawing, as the philosopher Max Black [4] had anticipated before the advent of contemporary neuroscience in the early 1960s. The argument put forth here is that art can be studied through a mathematical lens, and that mathematics can be studied through an artistic lens, in order to glean what the common neural substratum is like. The approach is called hermeneutic, in line with critical approaches in the arts, from visual art to literature.