As a contribution to mathematical practice (as opposed to mathematics itself), you might consider the emerging field of mathematical cognition (also known as cognitive science of mathematics), i.e. the study of mathematical ideas and their empirical grounding in human experiences, metaphors, generalizations, analogies and other cognitive mechanisms.

This subject has been explored informally and non-rigorously by mathematicians such as Saunders Mac Lane (see his Mathematics, Form and Function), but until recently it was not pursued by researchers trained in cognitive science. The best-known introduction is the book Where Mathematics Comes From by G. Lakoff and R. Nunez, but research has also been undertaken by Brian Rotman (Mathematics as sign: Writing, imagining, counting) and others.