Recently, I have begun what I expect will be a broad-ranging and long-term program of research in mathematical cognition (watch this video or rea d this paper for a description of the approach). The work grows out of my long-standing interest in developmental transitions and in readiness to learn from new experiences as well as from the hope that a Parallel-Distributed Processing approach may shed light on some of the most awe-inspiring achievements of human thought --- the insights and structured reasoning systems that have been created by mathematicians. In this effort, we are combining experimental studies and computational modeling studies. The lab is seeking to recruit experimentally and/or computationally oriented students interested in contributing to this effort.