Doing the math: Calculating the role of evolution and enculturation in the origins of geometrical and mathematical reasoning

In this paper I review broadly embodied, phenomenological and evolutionary conceptions of the origin of mathematics. I relate these conceptions to Husserl's work on the origins of geometry, and recent research into the notion of extended expertise and the role of enculturation as they relate to mathematical reasoning. I suggest that the concept of ‘affordance space’ – the (abstract) range of possibilities provided by any change in body or environment – is a useful construct in working out the contributions of evolution and enculturation to mathematical reasoning.