Integral Mathematics: An AQAL Approach

Elliot BenjaminArticle, Cognitive, Integrative Metatheory, Journal of Integral Theory & Practice, Mathematics Leave a Comment

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.

Integral Mathematics Perspectives

Mathematics is both an art form and a scientific discipline. When philosopher Ken Wilber writes about the differentiation of “The Big Three” (i.e., Art, Morals, and Science), mathematics is in the unique position of being both a subjective art form as well as an objective science. Mathematicians might recognize this as the division of the field into pure mathematics and applied mathematics. Author Jerry King, in The Art of Mathematics, stresses that these two disciplines of mathematics are as far apart as the mystical poet and the objective scientist. However, King also calls for the integration of pure mathematical thinking and pragmatic mathematical application. In other words, King is asking that the realms of art and science be integrated in a unified mathematics, quite analogous to the Integral model’s quest for integration in other disciplines of knowledge, including psychology, spirituality, medicine, law, politics, government, education, business, and so on. In this article, I would like to propose that we add mathematics to the growing list of emerging Integral disciplines.


About Elliot Benjamin

ELLIOT BENJAMIN, Ph.D., is a professional mathematician and mathematics professor with an avid interest in psychology, philosophy, and classical piano. He has a number of published papers in pure mathematics and has self-published books on recreational number theory, spirituality and cults, and art and mental illness. He lives in rural Maine, and his association with Integral Institute began in November 2003, when he met with Ken Wilber to discuss his interest in developing Integral Mathematics. He is also interested in applying his writings in the area of spirituality and cults to Integral Spirituality.