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.
Become a member today to access this Journal article and support the global emergence of Integral consciousness
Membership benefits include:
Receive full access to weekly conversations hosted by leading thinkers
Receive full access to the growing Journal of Integral Theory & Practice library
Stay connected by participating in Integral Life live events and discussions
Courses & Products
Get unlimited 20% discount off all products and courses from our friends and partners
Free Bonus Gifts
Download The Integral Vision eBook by Ken Wilber (worth $19 on Amazon) & The Ken Wilber Biography Series
Support of the movement
Support our mission of educating and spreading integral consciousness that is more critical than at any time in its history
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.