This article lays the foundations for a comprehensive formulation of Integral Mathematics. I introduce a number of definitions for an Integral Mathematics, including the perspective of Integral Mathematics in the context of a distinct discipline, Ken Wilber’s symbolic Integral Mathematics of primordial perspectives, and Integral Mathematics as a developmental line. I then focus on the perspective of Integral Mathematics as a distinct discipline and show that the “division” between the worlds of pure and applied mathematics is parallel to the distinction between the Left- and Right-Hand quadrants. I give a four-quadrant analysis for Integral Mathematics as a distinct discipline by applying the quadrants to Perfect Numbers from Recreational Number Theory. Finally, I give an example from Group Theory that illustrates how Integral Mathematics may be applied to explore shifts in levels of consciousness through meditation.