Proclus on the Mathematical Imagination

Proclus' Commentary on the First Book of Euclid's Elements offers penetrating insight on the nature of mathematical being, showing how the Platonic Ideas of the mathematical concepts are received by the mind (nous) and projected onto the imagination, which serves as a mirror for the reflections of the soul.  Geometrical figures are therefore rightly understood as doorways into the Ideal World.  Contemplation of the relation between the figures and the Ideas can lead us into the Via Mathesis, that is, the spiritual path of self-knowledge gained through mathematical insight.

Proclus (410 - 485 CE)

The following text acts like a seed, that when planted in consciousness and grown through meditative techniques yields a plentiful harvest of seed-bearing fruit (emphasis mine):

"Therefore just as nature stands creatively above the visible figures, so the soul, exercising her capacity to know, projects on the imagination, as on a mirror, the ideas of the figures; and the imagination, receiving in pictorial form these impressions of the ideas within the soul, by their means affords the soul an opportunity to turn inward from the pictures and attend to herself.

"It is as if a man looking at himself in a mirror and marveling at the power of nature and at his own appearance should wish to look upon himself directly and possess such a power as would enable him to become at the same time the seer and the seen.

"In the same way, when the soul is looking outside herself at the imagination, seeing the figures depicted there and being struck by their beauty and orderedness, she is admiring her own ideas from which they are derived; and though she adores their beauty, she dismisses it as something reflected and seeks her own beauty.  She wants to penetrate within herself to see the circle and the triangle there, all things without parts and all in one another, to become one with what she sees and enfold their plurality, to behold the secret and ineffable figures in the inaccessible places and shrines of the gods, to uncover the unadorned divine beauty and see the circle more partless than any center, the triangle without extension, and every other object of knowledge that has regained unity."