Mathematics has a history of being a two-dimensional inscribing practice. We describe the potential evolution in doing, thinking, and learning mathematics with the emergence of a technological innovation that enables real-time 3D virtual and material interactions. Using the 3D drawing pen as a simple and recently available technology, we highlight how it helps re-think long-standing assumptions and dichotomies in mathematics education including, for example, the material distinction between diagram and manipulative, the semiotic distinction between icon and index, and the developmental progression of action-icon-symbol. We then speculate on the future possibilities of the shift in technological infrastructure that 3D pens and similar technology may give rise to
