Proclus on the Meaning of Mathesis

I have been drawing great inspiration for my work from Proclus' Commentary on the First Book of Euclid's Elements.  The text is far more than a commentary on Euclid, since it includes two prefatory essays on the philosophy of general mathematics and the philosophy of geometry.  This is really the origin of what we today call the philosophy of mathematics, and Proclus, in his usual systematic fashion, herein establishes mathematics within the metaphysical hierarchy established in his other Neoplatonic works such as the Elements of Theology, which was by no coincidence written after the style of Euclid's Elements.  The commentary portion includes lengthy discussions of the metaphysical aspects to Euclid's definitions.  Learning all of this really brings the Euclid text to life, as we begin to see mathematical objects as real beings.  Geometric investigation then becomes an exploration of this ontological universe; the theorems established in geometrical discourse such as was stimulated by the Elements becomes a map of this higher world.

Proclus

 
At the end of the first essay on general mathematics, Proclus has a whole paragraph on the meaning of mathesis as I intend it to be used here.  The greek word is μαθησις and is translated by Morrow as "learning".  I would prefer it have been left untranslated since there is really no English equivalent and Proclus gives a thorough definition of what it is.  Here is what he says:

This, then, is what learning (mathesis) is, recollection of the eternal ideas of the soul; and this is why the study that especially brings us the recollection of these ideas is called the science concerned with learning (mathematike).  Its name thus makes clear what sort of function this science performs.  It arouses our innate knowledge, awakens our intellect, purges our understanding, brings to light the concepts that belong essentially to us, takes away the forgetfulness and ignorance that we have from birth, set us free from the bonds of unreason; and all this by the favor of the god who is truly the patron of this science, who brings our intellectual endowments to light, fills everything with divine reason, moves our souls towards Nous, awakens us as it were from our heavy slumber, through our searching turns us back upon ourselves, through our birthpangs perfects us, and through the discovery of pure Nous leads us to the blessed life.  And so, dedicating this composition to him, we proceed to delineate the theory of the science of mathematics.

Pay particular attention to this last line: "dedicating this composition to him".  Proclus is saying that his Commentary was intended as a hymn to the god of mathematics.   This god is Hermes.  This is consistent with Proclus' theurgy and shows how he sees the study of geometry as a theurgical and soteriological endeavor.  But we have lost this completely from the mathematics of today, and my purpose with all of my blogs and Youtube channel is to bring this back to life.

Books mentioned in this post:

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."

First Post - Introduction and Purpose of This Blog

MATHESIS is inner knowledge of the self gained through mathematical knowledge.  The via mathesis is the system of training one follows to attain this knowledge.  It involves a variety of disciplines in addition to learning and studying mathematics and philosophy.  The purpose of this blog is to demonstrate how philosophical mathematics is used to develop higher consciousness and spiritual abilities.

This means that we must view mathematics very differently than how it is usually seen in the education system.  Mathematics is not to be learned to be of use in trade, industry, or business but rather mathematics is the instruction manual for a process of self-initiation into the deepest mysteries of life.  This process can only work if we allow the content of mathematics to work on our inner life, to transform our soul from within. 

How this process can be best described depends on our current understanding, and I will offer teachings from a variety of paradigms in the content you will find here.  At the most concrete level, the ideas will be grounded in the brain and the body, in actual neurology and brain anatomy, and the connection between memory and the brain.  From there we will gather together concepts related to subtle energies and etheric forces, combine these with laws of mental creation and mind power, and then we will see how this can spark the life of our deepest mystical philosophy, the attainment of mathesis.