"Let no one ignorant of geometry enter"

Plato’s Motto

The scho­liast on Aelius Aris­tides 125.14 (Din­dorf, Vol. 3) says the fol­low­ing:

ἐπεγέγραπτο ἔμπροσθεν τῆς διατριβῆς τοῦ Πλάτωνος ὅτι ἀγεωμέτρητος μηδεὶς εἰσίτω· ἀντὶ τοῦ ἄνισος καὶ ἄδικος. ἡ γὰρ γεωμετρία τὴν ἰσότητα καὶ τὴν δικαιοσύνην τηρεῖ.

‘In front of Plato’s school had been inscribed, “Let noone enter un-​​geometried” rather than “unequal” or “unjust,” for geom­e­try main­tains equal­ity and justness.’


At any rate, Pseudo-​​Galen (post 2 A.D.?) quotes the phrase at the begin­ning of ‘On the divi­sions of phi­los­o­phy,’ and makes geom­e­try a pre­lim­i­nary to the­ol­ogy:

ὁ μὲν οὖν Πλάτων εἰς φυσιολογικὸν καὶ θεολογικὸν αὐτὸ διαιρεῖ· τὸ γὰρ μαθηματικὸν οὐκ ἠβούλετο εἶναι μέρος τῆς φιλοσοφίας, ἀλλὰ προγύμνασμά τι ὥσπερ ἡ γραμματικὴ καὶ ἡ ῥητορική· ὅθεν καὶ πρὸ τοῦ ἀκροατηρίου τοῦ οἰκείου ἐπέγραψεν ‘ἀγεωμέτρητος μηδεὶς εἰσίτω’. τοῦτο δὲ ὁ Πλάτων ἐπέγραφεν, ἐπειδὴ εἰς τὰ πολλὰ θεολογεῖ καὶ περὶ θεολογίαν καταγίνεται· συμβάλλεται δὲ εἰς εἴδησιν τῆς θεολογίας τὸ μαθηματικόν, οὗτινός ἐστιν ἡ γεωμετρία.

‘Plato divided it (the­o­ret­i­cal phi­los­o­phy) into phys­i­ol­ogy and the­ol­ogy. In fact, he did not want math­e­mat­ics to be a part of phi­los­o­phy, but a sort of pro­gym­nasma like gram­mar and rhetoric. That’s why, before his pri­vate lecture-​​room, he inscribed “Let no one enter un-​​geometried.” He inscribed this since he dis­coursed on the­ol­ogy in all mat­ters and dwelt on the­ol­ogy, and included math­e­mat­ics, of which geom­e­try is a part, into theology’s forms of knowledge.’ See:Plato’s Motto Written by Dennis McHenry. December 10, 2005

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Polish Society of St. Thomas Aquinas-Plato's Academy

Candidates for philosophy to be properly prepared.

Plato introduction to the philosophy of mathematics has made, highlighting the non-the usual benefits of studying mathematics in the improvement mind. At the front of the AP, as the legend goes, was engraved the inscription: "There is no WStE-pu anyone who does not know geometry. " In the Republic (VII 528 a) Plato classification mathematical sciences conducted on the basis of views Pythagoreans, who shared in the mathematical sciences depending on what questions to give answer: "How much?" - arithmetic and music, "how much?" - geometry and mechanical chanika. Plato arranges in order of mathematical sciences: arithmetic, geometry (distinguished by the geometry of the flat - planimetry and spatial geometry -stereometry), astronomy, music, and considers that these sciences are related to the relation-my formal, uwidocznionymi eg decreasing their abstractness. http://www.ptta.pl/pef/pdf/a/akademiaplaton.pdf

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If the late character of our sources may incite us to doubt the autheticity of this tradition, there remains that, in its spirit, it is in no way out of character, as can be seen by reading or rereading what Plato says about the sciences fit for the formation of philosophers in book VII of the Republic, and especially about geometry at Republic, VII, 526c8-527c11. We should only keep in mind that, for Plato, geometry, as well as all other mathematical sciences, is not an end in itself, but only a prerequisite meant to test and develop the power of abstraction in the student, that is, his ability to go beyond the level of sensible experience which keeps us within the "visible" realm, that of the material world, all the way to the pure intelligible. And geometry, as can be seen through the experiment with the slave boy in the Meno (Meno, 80d1-86d2), can also make us discover the existence of truths (that of a theorem of geometry such as, in the case of the Meno, the one about doubling a square) that may be said to be "transcendant" in that they don't depend upon what we may think about them, but have to be accepted by any reasonable being, which should lead us into wondering whether such transcendant truths might not exist as well in other areas, such as ethics and matters relating to men's ultimate happiness, whether we may be able to "demonstrate" them or not.See: Frequently Asked Questions about Plato by Bernard SUZANNE

Most certainly that given perspective about the reality of geometry in the context  of the abstract,  it is buried deep within ourselves that our creativity leads us that much closer to the truth and points to a depth of our being. Have you not ever been there to know, that by such mapping schematically, any direction lies under the sociological underpinnings of our associations and our dealings with reality?

On any road to self discovery it was apparent to me that by observing levels of awareness that we usually don't take the time to observe, the more I looked, a abstract math of let's say Game Theory, was apparent. When being lead through a mathematical landscape, could we arrive at our everyday dealings in society?

Economically, it had to make sense that such algorithms could be written and many of us as observers of the information world are unaware of the constrains we have applied to our everyday reading of the economic world?