The squaring of the circle occupies a privileged position within the depth-psychological corpus, functioning not as a mathematical curiosity but as what Jung explicitly names 'the archetype of wholeness.' Its trajectory runs from alchemical laboratory language—where it designated the magisterial achievement of the opus, the reconciliation of the angular (earthly, imperfect) with the circular (celestial, perfect)—into the symbolic vocabulary of individuation and the self. Jung's readings across Psychology and Alchemy, Aion, and The Archetypes and the Collective Unconscious establish the motif as a quaternary schema underlying visions of God, mandala formation, and the phenomenology of the self. The square names the fourfold material world; the circle names the infinite, the divine, the soul's native form. Their union thus enacts psychologically what the alchemists performed ritually: the reconciliation of spirit and matter, time and eternity, ego and self. Post-Jungian voices—Edinger, von Franz, Nichols, Place—extend this reading into therapeutic, cosmological, and iconographic contexts, while Peterson and Nichols trace it into modern symbolic systems. The term's power within this literature lies precisely in its paradoxical logic: it names what is geometrically impossible yet psychically necessary, the reconciliation of incommensurable opposites as the ground of wholeness.
The 'squaring of the circle' is one of the many archetypal motifs which form the basic patterns of our dreams and fantasies… it could even be called the archetype of wholeness.
Jung defines the squaring of the circle as the pre-eminent archetype of wholeness, the quaternary schema underlying all images of God and the self.
, The Archetypes and the Collective Unconscious, 1959thesis
Dorn says that the vessel 'should be made from a kind of squaring of the circle, so that the spirit and the soul of our material, separated from its body, may raise the body with them to the height of their own heaven.'
Jung cites Dorn to show that the alchemical vessel itself must embody the squaring of the circle, linking the geometric formula to the vertical integration of body, soul, and spirit.
, Aion: Researches into the Phenomenology of the Self, 1951thesis
The squaring of the circle, a favourite synonym for the magistery, has been accomplished. Anything angular is imperfect and has to be superseded by the perfect, here represented by the circle.
Jung reads an alchemical verse to demonstrate that the squaring of the circle names the completion of the opus—the supersession of imperfect angularity by the perfection of circular form.
, Mysterium Coniunctionis: An Inquiry into the Separation and Synthesis of Psychic Opposites in Alchemy, 1955thesis
We step back not quite three hundred years and find ourselves among scientists and natural philosophers who were seriously discussing the enigma of squaring the circle. This abstruse problem was itself a psychological projection of something much older and completely unconscious.
Jung argues that the historical obsession with squaring the circle was a projection of an unconscious archetype concerning the nature of God, the psyche, and wholeness.
, Psychology and Religion: West and East, 1958thesis
In alchemy, the miracle of self-realization, the harmonious union of earthly and heavenly truth, was called 'the squaring of the circle.' It stood for the idea that the impossible was, by God's grace, actualized.
Nichols identifies the squaring of the circle as the alchemical emblem of self-realization, the actualization by grace of the otherwise impossible union of earthly and heavenly reality.
, Jung and Tarot: An Archetypal Journey, 1980supporting
Squaring of the circle, taking the form of a circle in a square or vice versa.
Jung catalogues the squaring of the circle as a formal mandala motif—a circle in a square or square in a circle—within the typology of wholeness symbols.
, The Archetypes and the Collective Unconscious, 1959supporting
The hermaphrodite is holding a square and a compass, symbols for the squaring of the circle, yet another symbol of the transcending of duality in which the circle represents the celestial or spiritual world and the square represents the fourfold physical world.
Place reads the hermaphrodite's square and compass in alchemical iconography as emblems of the squaring of the circle, encoding the transcendence of the celestial-material duality.
, The Tarot: History, Symbolism, and Divination, 2005supporting
The circle and triangle is related to Jung's commentary on the alchemical idea of 'squaring the circle.'
Peterson links Bill Wilson's A.A. symbol of circle and triangle to Jung's alchemical commentary on the squaring of the circle as an emblem of psychological wholeness.
, The Shadow of a Figure of Light, 2024supporting
The alchemists were fond of picturing their opus as a circulatory process, as a circular distillation or as the uroboros, the snake biting its own tail… the lapis, as prima materia, stands at the beginning of the process as well as at the end.
Jung discusses the circulatory and recursive structure of the alchemical opus, providing the symbolic context within which the squaring of the circle functions as a culminating motif.
, Aion: Researches into the Phenomenology of the Self, 1951aside
Dismembering the victim corresponds to the idea of dividing the chaos into four elements or the baptismal water into four parts. The purpose of the operation is to create the beginnings of order in the massa confusa.
Jung traces the fourfold division of chaos in Zosimos's visions, establishing the quaternary ordering of matter that underlies the geometric symbolism of squaring the circle.
, Alchemical Studies, 1967aside